Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 32 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Anomalous Monism | Quine | VI 100/101 Def Anomalous Monism/Quine: anomalous monism was baptized by Davidson, nowadays called "Token Materialism". Although there is no psychological substance, we have irreducible psychological ways of "sorting" physical states and events. Without "mental substance" there remain two problems of our mentalistic language: a syntactic and a semantic one. The syntactic distinguishing feature ((s) for propositional attitudes) was our content component, the constituent phrase "that p" - it was the phrase that thwarted extensionality: the substitutiveness of identity, the interchangeability of arbitrary terms and phrases of the same scope salva veritate. It thus obstructed classical predicate logic. >Propositional Attitudes/Quine. Solution today: spelling (preserves extensionality) and quoting de dicto. (>Semantic ascent: instead of talking about objects, talking about assertions.) VI 102 The remaining curiosity of psychological predicates de dicto (Quine pro) is then a purely semantic one: such predicates cannot be interlocked with self-sufficient concepts and causal laws. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Answers | AI Research | Norvig I 471 Answer/Answer sets/AI research/Norvig/Russell: Answer set programming can be seen as an extension of negation as failure or as a refinement of circumscription; >Negation. Norvig I 472 the underlying theory of stable model semantics was introduced by Gelfond and Lifschitz (1988)(1), and the leading answer set programming systems are DLV (Eiter et al., 1998)(2) and SMODELS (Niemel¨a et al., 2000)(3). The disk drive example comes from the SMODELS user manual (Syrj¨anen, 2000)(4). Lifschitz (2001(5)) discusses the use of answer set programming for planning. Brewka et al. (1997)(6) give a good overview of the various approaches to nonmonotonic logic. Clark (1978)(7) covers the negation-as-failure approach to logic programming and Clark completion. Van Emden and Kowalski (1976)(8) show that every Prolog program without negation has a unique minimal model. Recent years have seen renewed interest in applications of nonmonotonic logics to large-scale knowledge representation systems. >Knowledge Representation. 1. Gelfond, M. and Lifschitz, V. (1988). Compiling circumscriptive theories into logic programs. In Non- Monotonic Reasoning: 2nd International Workshop Proceedings, pp. 74–99. 2. Eiter, T., Leone, N., Mateis, C., Pfeifer, G., and Scarcello, F. (1998). The KR system dlv: Progress report, comparisons and benchmarks. In KR-98, pp. 406–417. 3. Niemela, I., Simons, P., and Syrj¨anen, T. (2000). Smodels: A system for answer set programming. In Proc. 8th International Workshop on Non-Monotonic Reasoning. 4. Syrjanen, T. (2000). Lparse 1.0 user’s manual.saturn.tcs.hut.fi/Software/smodels. 5. Lifschitz, V. (2001). Answer set programming and plan generation. AIJ, 138(1–2), 39–54. 6. Brewka, G., Dix, J., and Konolige, K. (1997). Nononotonic Reasoning: An Overview. CSLI Publications. 7. Clark, K. L. (1978). Negation as failure. In Gallaire, H. and Minker, J. (Eds.), Logic and Data Bases, pp. 293–322. Plenum. 8. Van Emden, M. H. and Kowalski, R. (1976). The semantics of predicate logic as a programming language. JACM, 23(4), 733–742. |
Norvig I Peter Norvig Stuart J. Russell Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010 |
| Answers | Russell | Norvig I 471 Answer/Answer sets/AI research/Norvig/Russell: Answer set programming can be seen as an extension of negation as failure or as a refinement of circumscription; Norvig I 472 the underlying theory of stable model semantics was introduced by Gelfond and Lifschitz (1988)(1), and the leading answer set programming systems are DLV (Eiter et al., 1998)(2) and SMODELS (Niemel¨a et al., 2000)(3). The disk drive example comes from the SMODELS user manual (Syrj¨anen, 2000)(4). Lifschitz (2001(5)) discusses the use of answer set programming for planning. Brewka et al. (1997)(6) give a good overview of the various approaches to nonmonotonic logic. Clark (1978)(7) covers the negation-as-failure approach to logic programming and Clark completion. Van Emden and Kowalski (1976)(8) show that every Prolog program without negation has a unique minimal model. Recent years have seen renewed interest in applications of nonmonotonic logics to large-scale knowledge representation systems. 1. Gelfond, M. and Lifschitz, V. (1988). Compiling circumscriptive theories into logic programs. In Non- Monotonic Reasoning: 2nd International Workshop Proceedings, pp. 74–99. 2. Eiter, T., Leone, N., Mateis, C., Pfeifer, G., and Scarcello, F. (1998). The KR system dlv: Progress report, comparisons and benchmarks. In KR-98, pp. 406–417. 3. Niemela, I., Simons, P., and Syrj¨anen, T. (2000). Smodels: A system for answer set programming. In Proc. 8th International Workshop on Non-Monotonic Reasoning. 4. Syrjanen, T. (2000). Lparse 1.0 user’s manual.saturn.tcs.hut.fi/Software/smodels. 5. Lifschitz, V. (2001). Answer set programming and plan generation. AIJ, 138(1–2), 39–54. 6. Brewka, G., Dix, J., and Konolige, K. (1997). Nononotonic Reasoning: An Overview. CSLI Publications. 7. Clark, K. L. (1978). Negation as failure. In Gallaire, H. and Minker, J. (Eds.), Logic and Data Bases, pp. 293–322. Plenum. 8. Van Emden, M. H. and Kowalski, R. (1976). The semantics of predicate logic as a programming language. JACM, 23(4), 733–742. |
Russell I B. Russell/A.N. Whitehead Principia Mathematica Frankfurt 1986 Russell II B. Russell The ABC of Relativity, London 1958, 1969 German Edition: Das ABC der Relativitätstheorie Frankfurt 1989 Russell IV B. Russell The Problems of Philosophy, Oxford 1912 German Edition: Probleme der Philosophie Frankfurt 1967 Russell VI B. Russell "The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202 German Edition: Die Philosophie des logischen Atomismus In Eigennamen, U. Wolf (Hg) Frankfurt 1993 Russell VII B. Russell On the Nature of Truth and Falsehood, in: B. Russell, The Problems of Philosophy, Oxford 1912 - Dt. "Wahrheit und Falschheit" In Wahrheitstheorien, G. Skirbekk (Hg) Frankfurt 1996 Norvig I Peter Norvig Stuart J. Russell Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010 |
| Axioms | Cresswell | Hughes I 120 Axiomatization/propositional calculus/Hughes/Cresswell: done in other way than with the propositional calculus. Instead of axioms we use axiom schemes and parallel theorem schemes, i.e. general principles which determine that any well-formed formula (wff) of a certain shape is a theorem. >Theorems, >Propositional calculus, >Predicate calculus, >Predicate logic, >Propositional logic, >Axiom systems. |
Cr I M. J. Cresswell Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988 Cr II M. J. Cresswell Structured Meanings Cambridge Mass. 1984 Hughes I G.E. Hughes Maxwell J. Cresswell Einführung in die Modallogik Berlin New York 1978 |
| Completeness | Lorenzen | Berka I187 Completeness/intuitionistic predicate calculus/Berka: the completeness with regard to the semantics of Kripke and Lorenzen has been proved several times, but always with classical means. Cf. >Kripke Semantics. An intuitionist completeness proof has not yet been found. On the contrary. Kreisel (1962)(2) proved that the intuitionist predicate calculus follows intuitionistically from the intuitionist Church thesis. >Church thesis, >Intuitionism, >Predicate calculus. 2. G. Kreisel. On Weak Completeness of Intuitionistic Predicate Logic. J.Symbolic Logic Volume 27, Issue 2 (1962), 139-158. |
Lorn I P. Lorenzen Constructive Philosophy Cambridge 1987 |
| Completeness | Quine | X 80 Completeness Theorem/deductive/Quantifier Logic/Quine: (B) A scheme fulfilled by each model is provable. Theorem (B) can be proven for many proof methods. If we imagine such a method, then (II) follows from (B). (II) If a scheme is fulfilled by every model, then e is true for all insertions of propositions. X 83 Proof Procedure/Evidence Method/Quine: some complete ones do not necessarily refer to schemata, but can also be applied directly to the sentences X 84 that emerge from the scheme by insertion. Such methods produce true sentences directly from other true sentences. Then we can leave aside schemata and validity and define logical truth as the proposition produced by these proof procedures. 1. VsQuine: this usually triggers a protest: the property "to be provable by a certain method of proof" is uninteresting in itself. It is only interesting because of the completeness theorem, which allows to equate provability with logical truth. 2. VsQuine: if one defines logical truth indirectly by reference to a suitable method of proof, one deprives the completeness theorem of its basis. It becomes empty. QuineVsVs: the danger does not exist at all: the principle of completeness in the formulation (B) does not depend on how we define logical truth, because it is not mentioned at all! Part of its meaning, however, is that it shows that we can define logical truth by merely describing the method of proof, without losing anything of what makes logical truth interesting in the first place. X 100 Fake Theory/quantities/classes/relation/Quine: is masked pure logic. Mathematics: begins when we accept the element relationship "ε" as a real predicate and accept classes as values of the quantified variables. Then we leave the realm of complete proof procedure. Logic: quantifier logic is complete. Mathematics: is incomplete. >Logical Truth/Quine. X 119 Intuitionism/Quine: gained buoyancy through Goedel's incompleteness evidence. XIII 157 Predicate Logic/completeness/Goedel/Quine: Goedel proved its completeness in 1930. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Decidability | Hintikka | I 7 Standard Semantics/Kripke Semantics/Hintikka: what differences are there? The ditch between them is much deeper than it first appears. Cocchiarella: Cocchiarella has shown, however, that even in the simplest quantifying case, of the monadic predicate logic, the standard logic is radically different from its Kripkean cousin. Decidability: monadic predicate logic is, as Kripke has shown, decidable. Kripke semantics: Kripke semantics is undecidable. Decidability: decidability implies axiomatizability. I 208 Decision Problem/predicate calculus/Hao Wang: thesis: the problem corresponds to the task of completely filling the Euclidean surface with square dominoes of different sizes. At least one stone of each size must be used. E.g. logical omniscience now comes in in the following way: At certain points I can truthfully say according to my perception: (5) I see that this Domino task is impossible to solve. In other cases, I cannot say that truthfully. >Logical omniscience. Problem/HintikkaVsBarwise/HintikkaVsSituation Semantics/Hintikka: according to Barwise/Perry, it should be true of any unsolvable Domino problem that I see the unsolvability immediately as soon as I see the forms of available stones because the unsolvability follows logically from the visual information. Solution/semantics of possible worlds/Hintikka: according to the urn model there is no problem. >Possible world semantics. I 209 Omniscience/symmetry/Hintikka: situational semantics: situational semantics needs the urn model to solve the second problem of logical omniscience. Semantics of possible worlds: on the other hand, it needs situational semantics itself to solve the first problem. >Situation semantics. |
Hintikka I Jaakko Hintikka Merrill B. Hintikka Investigating Wittgenstein German Edition: Untersuchungen zu Wittgenstein Frankfurt 1996 Hintikka II Jaakko Hintikka Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 |
| Decidability | Logic Texts | Hoyningen-Huene II 227 Decidability/undecidability/decision problem: propositional logic: is decidable and complete. Predicate logic: undecidable. There is no mechanical method by which for any predicate-logical formula, the decision can be brought about whether it is universally valid or not. >Validity, >Proof. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 |
| Descriptions | Logic Texts | Read III 127f Improper name/Quine: (= descriptions- only real names allow the substitution that can be found in the indistinguishability of identical. Improper names: lead to more complex form: E.g. "among the Roman orators there is a major one, and he denounced Catiline that". E.g. "Just one number counts the planets and it is more than seven"/Russell: here is only 7 a real name - hence these sentences may not be sentences in a conclusion of the principle of indistinguishability of the identical. >Leibniz principle, >Identity, >Indistinguishability, QuineVs:. problem : range: the marks must be eliminated, so that in the new wording no part corresponds with them. >Range, >Scope, >Narrow/wide. Strobach I 104 Indistinguishability/Strobach: requires Logic of the 2nd level: predicate logic 2nd level/PL2/Strobach: typical formula: Leibniz's Law: "x = y > (Fx ↔ Fy)". >Second order logic. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 Stro I N. Strobach Einführung in die Logik Darmstadt 2005 |
| Events | Meixner | I 167 f Event/Davidson/Meixner: from the true sentence "Hans laughed loudly" follows logically "Hans laughed" but not according to predicate logic. >Propositional Logic, >Predicate Logic. How can we receive a in conclusion predicate logic? Solution: We must assume that there are events as entities. ((s) for the quantification): "For at least one current event applies it is noisy and a laugh from Hans". (Ditto for the two part-state of affairs loudness and laughter). >"Adverbial analysis", >Quantification, >States of affairs. Event/ontology/Meixner: however, it is not even decided whether they are objects or functions. >Ontology, >Objects, >Function. Event/LewisVsDavidson: as properties they are functions. >Properties/Lewis, >Events/Lewis. DavidsonVsLewis: as individuals they are objects. >Events/Davidson. |
Mei I U. Meixner Einführung in die Ontologie Darmstadt 2004 |
| Freedom | Quine | XIII 67 Freedom/Quine: XIII 68 Limitation/Quine: is freedom of the 2nd level: is freedom from decisions. Limitation/Quine: the dialectics of freedom and limitation can be seen in an example of logic: there is a technique of predicate logic to prove the invalidity of a formula (e.g. in methods of logic 3rd and 4th edition) by systematically replacing its variables in a certain way. XIII 69 These used expressions must come from a certain class. But this is not mandatory, they can also come from outside the class. The restriction is nevertheless welcome to us, because it makes our work easier. We do not have to look any further when we have the result for the restricted case. >Classes/Quine. Freedom: this shows that restriction can mean freedom. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Inference | AI Research | Norvig I 471 Reasoning/inference/artificial intelligence/AI research/Norvig/Russell: The three main formalisms for dealing with nonmonotonic inference—circumscription (McCarthy, 1980)(1), default logic (Reiter, 1980(2)), and modal nonmonotonic logic (McDermott and Doyle, 1980)(3) - were all introduced in one special issue of the AI Journal. Delgrande and Schaub (2003)(4) discuss the merits of the variants, given 25 years of hindsight. Answer set programming can be seen as an extension of negation as failure or as a refinement of circumscription; Norvig I 472 the underlying theory of stable model semantics was introduced by Gelfond and Lifschitz (1988)(5), and the leading answer set programming systems are DLV (Eiter et al., 1998)(6) and SMODELS (Niemel¨a et al., 2000)(7). The disk drive example comes from the SMODELS user manual (Syrjanen, 2000)(8). Lifschitz (2001)(9) discusses the use of answer set programming for planning. Brewka et al. (1997)(10) give a good overview of the various approaches to nonmonotonic logic. Clark (1978)(11) covers the negation-as-failure approach to logic programming and Clark completion. Van Emden and Kowalski (1976)(12) show that every Prolog program without negation has a unique minimal model. Recent years have seen renewed interest in applications of nonmonotonic logics to large-scale knowledge representation systems. The BENINQ systems for handling insurance-benefit inquiries was perhaps the first commercially successful application of a nonmonotonic inheritance system (Morgenstern, 1998)(13). Lifschitz (2001)(9) discusses the application of answer set programming to planning. Norvig I 473 Spatial reasoning: The earliest serious attempt to capture commonsense reasoning about space appears in the work of Ernest Davis (1986(14), 1990(15)). The region connection calculus of Cohn et al. (1997)(16) supports a form of qualitative spatial reasoning and has led to new kinds of geographical information systems; see also (Davis, 2006)(17). As with qualitative physics, an agent can go a long way, so to speak, without resorting to a full metric representation. Psychological reasoning: Psychological reasoning involves the development of a working psychology for artificial agents to use in reasoning about themselves and other agents. This is often based on so-called folk psychology, the theory that humans in general are believed to use in reasoning about themselves and other humans. ((s) Cf. >Folk psychology/Philosophical theories). When AI researchers provide their artificial agents with psychological theories for reasoning about other agents, the theories are frequently based on the researchers’ description of the logical agents’ own design. Psychological reasoning is currently most useful within the context of natural language understanding, where divining the speaker’s intentions is of paramount importance. Minker (2001)(18) collects papers by leading researchers in knowledge representation, summarizing 40 years of work in the field. The proceedings of the international conferences on Principles of Knowledge Representation and Reasoning provide the most up-to-date sources for work in this area. 1. McCarthy, J. (1980). Circumscription: A form of non-monotonic reasoning. AIJ, 13(1–2), 27–39. 2. Reiter, R. (1980). A logic for default reasoning. AIJ, 13(1–2), 81–132. 3. McDermott, D. and Doyle, J. (1980). Nonmonotonic logic: i. AIJ, 13(1–2), 41–72. 4. Delgrande, J. and Schaub, T. (2003). On the relation between Reiter’s default logic and its (major) variants. In Seventh European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, pp. 452–463. 5. Gelfond, M. and Lifschitz, V. (1988). Compiling circumscriptive theories into logic programs. In Non- Monotonic Reasoning: 2nd International Workshop Proceedings, pp. 74–99. 6. Eiter, T., Leone, N., Mateis, C., Pfeifer, G., and Scarcello, F. (1998). The KR system dlv: Progress report, comparisons and benchmarks. In KR-98, pp. 406–417. 7. Niemela, I., Simons, P., and Syrjanen, T. (2000). Smodels: A system for answer set programming. In Proc. 8th International Workshop on Non-Monotonic Reasoning. 8. Syrjanen, T. (2000). Lparse 1.0 user’s manual.saturn.tcs.hut.fi/Software/smodels. 9. Lifschitz, V. (2001). Answer set programming and plan generation. AIJ, 138(1–2), 39–54. 10. Brewka, G., Dix, J., and Konolige, K. (1997). Nononotonic Reasoning: An Overview. CSLI Publications. 11. Clark, K. L. (1978). Negation as failure. In Gallaire, H. and Minker, J. (Eds.), Logic and Data Bases, pp. 293–322. Plenum. 12. Van Emden, M. H. and Kowalski, R. (1976). The semantics of predicate logic as a programming language. JACM, 23(4), 733–742. 13. Morgenstern, L. (1998). Inheritance comes of age: Applying nonmonotonic techniques to problems in industry. AIJ, 103, 237–271 14. Davis, E. (1986). Representing and Acquiring Geographic Knowledge. Pitman and Morgan Kaufmann. 15. Davis, E. (1990). Representations of Commonsense Knowledge. Morgan Kaufmann 16. Cohn, A. G., Bennett, B., Gooday, J. M., and Gotts, N. (1997). RCC: A calculus for region based qualitative spatial reasoning. GeoInformatica, 1, 275–316. 17. Davis, E. (2006). The expressivity of quantifying over regions. J. Logic and Computation, 16, 891– 916. 18. Minker, J. (2001). Logic-Based Artificial Intelligence. Kluwer Norvig I 570 Inference/temporal models/AI research/Norvig/Russell: (…) the basic inference tasks that must be solved: a) Filtering: This is the task of computing the belief state—the posterior distribution over the most recent state - given all evidence to date. Filtering is also called state estimation. >Belief states/Norvig. b) Prediction: This is the task of computing the posterior distribution over the future state, given all evidence to date. That is, we wish to compute P(Xt+k | e1:t) for some k > 0. Norvig I 571 c) Smoothing: This is the task of computing the posterior distribution over a past state, given all evidence up to the present. That is, we wish to compute P(Xk | e1:t) for some k such that 0 ≤ k < t. d) Most likely explanation: Given a sequence of observations, we might wish to find the sequence of states that is most likely to have generated those observations. That is, we wish to compute argmaxx1:t P(x1:t | e1:t). In addition to these inference tasks (…): Learning: The transition and sensor models, if not yet known, can be learned from observations. Just as with static >Bayesian networks, dynamic Bayes net learning can be done as a by-product of inference. Inference provides an estimate of what transitions actually occurred and of what states generated the sensor readings, and these estimates can be used to update the models. >Change/AI research, >Uncertainty/AI research. Norvig I 605 Ad a) The particle filtering algorithm (…) has a particularly interesting history. The first sampling algorithms for particle filtering (also called sequential Monte Carlo methods) were developed in the control theory community by Handschin and Mayne (1969)(1), and the resampling idea that is the core of particle filtering appeared in a Russian control journal (Zaritskii et al., 1975)(2). It was later reinvented in statistics as sequential importance sampling resampling, or SIR (Rubin, 1988(3); Liu and Chen, 1998(4)), in control theory as particle filtering (Gordon et al., 1993(5); Gordon, 1994(6)), in AI as survival of the fittest (Kanazawa et al., 1995)(7), and in computer vision as condensation (Isard and Blake, 1996)(8). The paper by Kanazawa et al. (1995)(7) includes an improvement called evidence reversal whereby the state at time t+1 is sampled conditional on both the state at time t and the evidence at time t+1. This allows the evidence to influence sample generation directly and was proved by Doucet (1997)(9) and Liu and Chen (1998)(4) to reduce the approximation error. Particle filtering has been applied in many areas, including tracking complex motion patterns in video (Isard and Blake, 1996)(8), predicting the stock market (de Freitas et al., 2000)(10), and diagnosing faults on planetary rovers (Verma et al., 2004)(11). A variant called the Rao-Blackwellized particle filter or RBPF (Doucet et al., 2000(12); Murphy and Russell, 2001)(13) applies particle filtering to a subset of state variables and, for each particle, performs exact inference on the remaining variables conditioned on the value sequence in the particle. In some cases RBPF works well with thousands of state variables. >Utility/AI research, >Utility theory/Norvig, >Rationality/AI research, >Certainty ffect/Kahneman/Tversky, >Ambiguity/Kahneman/Tversky. 1. Handschin, J. E. and Mayne, D. Q. (1969). Monte Carlo techniques to estimate the conditional expectation in multi-stage nonlinear filtering. Int. J. Control, 9(5), 547–559. 2. Zaritskii, V. S., Svetnik, V. B., and Shimelevich, L. I. (1975). Monte-Carlo technique in problems of optimal information processing. Automation and Remote Control, 36, 2015–22. 3. Rubin, D. (1988). Using the SIR algorithm to simulate posterior distributions. In Bernardo, J. M., de Groot,M. H., Lindley, D. V., and Smith, A. F. M. (Eds.), Bayesian Statistics 3, pp. 395–402. Oxford University Press. 4. Liu, J. S. and Chen, R. (1998). Sequential Monte Carlo methods for dynamic systems. JASA, 93, 1022–1031. 5. Gordon, N., Salmond, D. J., and Smith, A. F. M. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings F (Radar and Signal Processing), 140(2), 107–113. 6. Gordon, N. (1994). Bayesian methods for tracking. Ph.D. thesis, Imperial College. 7. Kanazawa, K., Koller, D., and Russell, S. J. (1995). Stochastic simulation algorithms for dynamic probabilistic networks. In UAI-95, pp. 346–351. 8. Isard, M. and Blake, A. (1996). Contour tracking by stochastic propagation of conditional density. In ECCV, pp. 343–356. 9. Doucet, A. (1997). Monte Carlo methods for Bayesian estimation of hidden Markov models: Application to radiation signals. Ph.D. thesis, Université de Paris-Sud. 10. de Freitas, J. F. G., Niranjan, M., and Gee, A. H. (2000). Sequential Monte Carlo methods to train neural network models. Neural Computation, 12(4), 933–953. 11. Verma, V., Gordon, G., Simmons, R., and Thrun, S. (2004). Particle filters for rover fault diagnosis. IEEE Robotics and Automation Magazine, June. 12. Doucet, A., de Freitas, N., Murphy, K., and Russell, S. J. (2000). Rao-blackwellised particle filtering for dynamic bayesian networks. In UAI-00. 13. Murphy, K. and Russell, S. J. (2001). Rao-blackwellised particle filtering for dynamic Bayesian networks. In Doucet, A., de Freitas, N., and Gordon, N. J. (Eds.), Sequential Monte Carlo Methods in Practice. Springer-Verlag. |
Norvig I Peter Norvig Stuart J. Russell Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010 |
| Lambda Calculus | Lambda Calculus, philosophy: The lambda calculus provides a way to avoid problems related to paradoxes, since, unlike the quantification of predicate logic, it does not make any existence assumptions. Where the quantification (Ex)(Fx) is translated colloquially as "There is an x with the property F" (in short "Something is F"), the translation of the corresponding form in the Lambda calculus is "An x, so that...". See also 2nd order logic. |
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| Logic | Logic Texts | Hoyningen-Huene II 148f Relation of logic to reality: A: No one can read this book in three days. B: A hard-working student can read this book in three days. Whether there are hard-working students is something that cannot be captured with the statement logic. The inconsistency of the example can only be detected with the predicate logic. Other inconsistencies cannot be captured by the means of logic at all: A: Hans is a giant. - B: Hans is a dwarf. --- Read III 62f Difference compact/non-compact: classical logic is a logic of the 1st level. A categorical set of axioms for arithmetic must be a second-level logic. (Quantifiers also for properties). >Second order logic. Logic first order/second order are not to be distinguished syntactically, but semantically! E.g. Napoleon has all properties of an emperor: are not syntactically to be distinguished, whether logic 1st or 2nd level. III 70ff VsClassical Logic: This reduction, of course, fails. For "nothing is round and square" is necessarily true, but its non-logical components cannot be interpreted in any way that makes this statement false. Allowing variable areas of definition for classical representation was a catastrophe. The modality has returned. We can make a substitution, but we cannot really change the range. >Range, >Modality. If an object is round, it follows that it is not square. But this conclusion is not valid thanks to the form, but thanks to the content. III 79 It was a mistake to express the truth-preservation criterion as "it is impossible that the premisses are true and the conclusion false". Because it is not so obvious that there is a need to conclude from A to B. Provided he is cowardly, it follows that he is either cowardly or - what one wants. But simply from the fact that he is cowardly does not follow that if he is not cowardly - what one wants. >EFQ/ex falso quodlibet. III 151 Logic 1st order: individuals, 2nd order: variables for predicates, distribution of the predicates by quantifiers. 1st level allows restricted vocabulary of the 2nd level: existence and universal quantifier! >Existential quantification, >Universal quantification, >Existence predicate, >Existence. III 161 Free logic: no existence assumptions - no conclusion from the absence of the truth value to falsehood - global evaluation. >Truth value, >Truth value gaps, >Truth value agglomeration, >Valuation. --- Menne I 26 Justification of Logic/Menne: the so-called logical principles of identity, of consistency, and the excluded middle are not sufficient to derive the logic. In addition, ten theorems and rules of the propositional logic are needed, just to derive the syllogistic exactly. These axioms do not represent obvious ontological principles. Kant: transcendental justification of logic. It must be valid a priori. >Logic/Kant. Menne I 28 The justification from the language: oversees that there is no explicit logic at all if the language itself already contained logic. Precisely because language does not always proceed logically, the logic is needed for the standardization of language. Menne: there must be a recursive procedure for justification. >Justification, >Recursion. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 Me I A. Menne Folgerichtig Denken Darmstadt 1997 |
| Modal Logic | Stalnaker | I 144 Quantified Modal Logic/Stalnaker: quantified modal logic arises not simply from the joining of modal predicate logic and extensional quantifier theory. >Quantifier theory, >Quantifiers, >Quantification. Problem: the increase in expressiveness allows Leibniz’s Law and the existential generalization appear doubtful. >Existential generalization. Problems: first, there is a problem in the status of sentences and second there is a problem in the relation between domains of individuals. >Domains, >Sentences. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Models | Stalnaker | I 146 Model/Stalnaker: a model is a pair consisting of an object domain D and a valuation function V. >Valuation function, >Domains. I 149 Model: For our modal predicate logic is then a quadruple ‹W,R,D,v›. D is the range function of W on the sets of individuals. For w ε W, Dw is the range of the world w. Valuation function: the valuation function attributes intensions to descriptive expressions. Intension: the intension here is a function of possible worlds on extensions. >Intensions, >Extensions. Necessity operator: The semantic rule of the necessity operator remains unchanged. >Operators. I 150 The rules for predicate logic are generalizations of the extensional rules. We only add an index for the worlds. E.g. rule for Universal quantification/universal quantifier/Stalnaker: IF Φ has the form ∀F, then is νs w (Φ) = 1 gdw. νs w(F) = D w. otherwise = 0. >Quantification, >Universal quantification. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Non-Existence | Non-existence, philosophy: non-existence is not simply expressible for the classical predicate logic which attributes properties through quantification in the form of (Ex)(Fx) "There is at least one x, with the property F" (in short "There is at least one F"), since existence is not a property. The form "There is at least one x that does not exist" is contradictory. See also existence predicate, "There is", existence, unicorn example, pegasus example, round square, proof of God's existence. |
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| Pegasus Example | Pegasus example: are cases that refer to non-existent objects in everyday language. The problem here is the predicate logical analysis of the corresponding statements. Here the form (Ex) (Fx) (There is an object described by property F) would be needed. However, existence and non-existence would be simultaneously attributed to the object in question. "There is an object that does not exist" is contradictory. On the other hand, the statement "There is a flying horse" is simply wrong. See also existence, existence predicate, non-existence, there is, unicorn example. |
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| Propositional Logic | Propositional Logic: analyzes the relationship of whole statements, e.g. A v B, where A and B stand for complete sentences. - Difference: predicate logic: this is fine-grained and represents the attribution of predicates. |
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| Propositional Logic | Wessel | I 35 Propositional Logic can be built in three different ways: 1) semantic (truth-functional), >Truth functions, >Semantics. 2) as a system of natural deduction, >Natural deduction, >G. Gentzen. 3) as axiomatic structure. >Axioms, >Axiom systems. Cf. >Predicate logic, >Logic. |
Wessel I H. Wessel Logik Berlin 1999 |
| Quantification | Quantification: is a function within the predicate logic, in which a property is attributed to an object yet to be determined. A) Existence quantification e.g. (Ex) (Fx): "At least one object x is F". It is assumed that the object denoted by x exists. B) Universal quantification (notation (x) ...) "For all x applies ...". Both forms of quantification can be negated, covering most of the everyday cases. In addition, a subject domain must be chosen, within which the statements that result from the insertion of objects are meaningful. See also existence, non-existence, existence assumption, existence predicate, universal quantification, existence quantification, domains, opacity, intensional objects. |
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| Quantifiers | Quantifiers: in the predicate logic, quantifiers are the symbol combinations (Ex) and (x) for the set of objects to which one or more properties are attributed to. A) Existence quantification (Ex)(Fx) ("At least one x"). B) Universal quantification (x)(Fx) ("Everything is F"). For other objects e.g. y, z,… are chosen. E.g. (x) (Ey) (Fx > Gy). See also quantification, generalized quantifiers. |
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| Reasoning | AI Research | Norvig I 471 Reasoning/inference/artificial intelligence/AI research/Norvig/Russell: The three main formalisms for dealing with nonmonotonic inference—circumscription (McCarthy, 1980)(1), default logic (Reiter, 1980(2)), and modal nonmonotonic logic (McDermott and Doyle, 1980)(3) - were all introduced in one special issue of the AI Journal. Delgrande and Schaub (2003)(4) discuss the merits of the variants, given 25 years of hindsight. Answer set programming can be seen as an extension of negation as failure or as a refinement of circumscription; Norvig I 472 the underlying theory of stable model semantics was introduced by Gelfond and Lifschitz (1988)(5), and the leading answer set programming systems are DLV (Eiter et al., 1998)(6) and SMODELS (Niemel¨a et al., 2000)(7). The disk drive example comes from the SMODELS user manual (Syrjanen, 2000)(8). Lifschitz (2001)(9) discusses the use of answer set programming for planning. Brewka et al. (1997)(10) give a good overview of the various approaches to nonmonotonic logic. Clark (1978)(11) covers the negation-as-failure approach to logic programming and Clark completion. Van Emden and Kowalski (1976)(12) show that every Prolog program without negation has a unique minimal model. Recent years have seen renewed interest in applications of nonmonotonic logics to large-scale knowledge representation systems. The BENINQ systems for handling insurance-benefit inquiries was perhaps the first commercially successful application of a nonmonotonic inheritance system (Morgenstern, 1998)(13). Lifschitz (2001)(9) discusses the application of answer set programming to planning. Norvig I 473 Spatial reasoning: The earliest serious attempt to capture commonsense reasoning about space appears in the work of Ernest Davis (1986(14), 1990(15)). The region connection calculus of Cohn et al. (1997)(16) supports a form of qualitative spatial reasoning and has led to new kinds of geographical information systems; see also (Davis, 2006)(17). As with qualitative physics, an agent can go a long way, so to speak, without resorting to a full metric representation. Psychological reasoning: Psychological reasoning involves the development of a working psychology for artificial agents to use in reasoning about themselves and other agents. This is often based on so-called folk psychology, the theory that humans in general are believed to use in reasoning about themselves and other humans. ((s) Cf. >Folk psychology/Philosophical theories). When AI researchers provide their artificial agents with psychological theories for reasoning about other agents, the theories are frequently based on the researchers’ description of the logical agents’ own design. Psychological reasoning is currently most useful within the context of natural language understanding, where divining the speaker’s intentions is of paramount importance. Minker (2001)(18) collects papers by leading researchers in knowledge representation, summarizing 40 years of work in the field. The proceedings of the international conferences on Principles of Knowledge Representation and Reasoning provide the most up-to-date sources for work in this area. 1. McCarthy, J. (1980). Circumscription: A form of non-monotonic reasoning. AIJ, 13(1–2), 27–39. 2. Reiter, R. (1980). A logic for default reasoning. AIJ, 13(1–2), 81–132. 3. McDermott, D. and Doyle, J. (1980). Nonmonotonic logic: i. AIJ, 13(1–2), 41–72. 4. Delgrande, J. and Schaub, T. (2003). On the relation between Reiter’s default logic and its (major) variants. In Seventh European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, pp. 452–463. 5. Gelfond, M. and Lifschitz, V. (1988). Compiling circumscriptive theories into logic programs. In Non- Monotonic Reasoning: 2nd International Workshop Proceedings, pp. 74–99. 6. Eiter, T., Leone, N., Mateis, C., Pfeifer, G., and Scarcello, F. (1998). The KR system dlv: Progress report, comparisons and benchmarks. In KR-98, pp. 406–417. 7. Niemela, I., Simons, P., and Syrjanen, T. (2000). Smodels: A system for answer set programming. In Proc. 8th International Workshop on Non-Monotonic Reasoning. 8. Syrjanen, T. (2000). Lparse 1.0 user’s manual.saturn.tcs.hut.fi/Software/smodels. 9. Lifschitz, V. (2001). Answer set programming and plan generation. AIJ, 138(1–2), 39–54. 10. Brewka, G., Dix, J., and Konolige, K. (1997). Nononotonic Reasoning: An Overview. CSLI Publications. 11. Clark, K. L. (1978). Negation as failure. In Gallaire, H. and Minker, J. (Eds.), Logic and Data Bases, pp. 293–322. Plenum. 12. Van Emden, M. H. and Kowalski, R. (1976). The semantics of predicate logic as a programming language. JACM, 23(4), 733–742. 13. Morgenstern, L. (1998). Inheritance comes of age: Applying nonmonotonic techniques to problems in industry. AIJ, 103, 237–271 14. Davis, E. (1986). Representing and Acquiring Geographic Knowledge. Pitman and Morgan Kaufmann. 15. Davis, E. (1990). Representations of Commonsense Knowledge. Morgan Kaufmann 16. Cohn, A. G., Bennett, B., Gooday, J. M., and Gotts, N. (1997). RCC: A calculus for region based qualitative spatial reasoning. GeoInformatica, 1, 275–316. 17. Davis, E. (2006). The expressivity of quantifying over regions. J. Logic and Computation, 16, 891– 916. 18. Minker, J. (2001). Logic-Based Artificial Intelligence. Kluwer |
Norvig I Peter Norvig Stuart J. Russell Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010 |
| Redundancy Theory | Quine | VII (i) 164 Redundancy Theory/Quine: it is doubtful whether the connection of "Fa" with "Fa is true" is analytic. XIII 214 Redundancy Theory/QuineVsRedundancy Theory/truth/Quine: the truth has been said to disappear, because the truth of the sentence is simply the sentence. ("Disapearance theory of truth") This is wrong: the quotation marks must not be taken lightly. We can only say that the adjective "true" is dispensable if it is applied to sentences that explicitly lie before us. Truth-predicate/true/generalization/Quine: is necessary to say that all sentences of a certain form are wrong. Or For example, a sentence that is not literal (not literally passed down) is true or false. Or E.g. that the slander paragraphs cannot be applied to true sentences or E.g. that you will tell the truth, the whole truth and nothing but the truth. N.B.: if you translate such sentences into the predicate logic, the subject of the truth- predicate is not a quotation, but a variable. These are the cases where the truth-predicate is not superfluous. Disquotation/truth/definition/Quine: the disquotational approach may still be useful when it comes to defining truth. Truth-Definition/truth/Quine: it identifies all discernible truths that the truth of the sentence is communicated by the sentence itself. But that is not a strict definition; it does not show us who could eliminate the adjective "true" XIII 215 from all contexts in which it can occur grammatically. It only shows us where we can eliminate it in contexts with quotations. Paradox/Quine: we have seen above (see liar paradox) that definability can contain a self-contradiction. It is remarkable how easily definable we found truth in the present context. How easy it can be and at the same time possibly fatal. Solution/Tarski: Separation object language/meta language. Recursion/Tarski/Quine: shows how the truth-term is first applied to atomic sentences and then to compositions of any complexity. Problem: Tarski could not yet define truth because of the variables. Sentences with variables can be true in some cases and false in others. (Open Sentences). Only closed sentences (where all variables are bound by quantifiers) can be true or false. Fulfillment/Recursion/Tarski/Quine: what Tarski recursively defines is fulfillment of a sentence by an object; is not truth. These objects are then the possible values of the free variables. After that, truth trivially results as a waste product. Def Truth/Fulfillment/Tarski: a closed sentence is true if it is fulfilled by the sequence of length 0, so to speak. Liar Paradox/Tarski/Quine: Tarski's construction is masterly and coherent, but why doesn't it ultimately solve the paradox? This is shown by the translation into symbolic logic when the sentence is formulated in object language (see paradoxes above, last section). Paradox/logical form/liar/Quine: the word "true" has the context "x is true" in the explicit reconstruction where "x" is the subject of quantifiers. Problem: the recursive definition of truth and fulfillment does not show how to "fulfill x". XIII 216 or "x is true" is eliminated. Solution: this only works if "x is true" or "fulfilled" is predicated by an explicitly given open or closed sentence. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Referential Quantification | Referential Quantification: is an expression for the form of quantification normally used in predicate logic ("There is at least one object x with the property ..." or "For all objects x applies...."). Here, something is said about objects, with their existence being presupposed. On the other hand, substitutional quantification is about linguistic expressions ("There is a true sentence that ..."). The decisive difference between the two types of quantification is that, in the case of the possible replacement of a linguistic expression by another expression, a so-called substitution class must be assumed which cannot exist in the case of objects since the everyday subject domain is not classified into classes is. E.g. you can replace a table by some box, but not the word table by an available word. See also substitutional quantification, quantification, substitution, inference, implication, stronger/weaker. |
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| Scope | Logic Texts | Read III 127f Improper names/Quine: (= descriptions). Only real names allow the substitution, which finds itself in the indistinguishability of the identical. >Name, >Description, >Rigidity, >Substitution. Improper names: they lead to more complex forms: e.g. "There is one greatest among the Roman orators, and he accused Catilina". - e.g. "Exactly one number counts the planets and it is bigger than seven." Russell: here, only 7 is a real name. Therefore, these sentences cannot be upper and lower sentence in a conclusion of the principle of the indistinguishability of the identical. >Indistinguishability, >Leibniz principle, >Identity. QuineVs: Problem: Scope: the descriptions must be eliminated in such a way that no new constituent will correspond to them in the new formulation. --- Strobach I 104 Indistinguishability/Strobach: requires Logic of the 2nd level: predicate logic 2nd level/PL2/Strobach: typical formula: Leibniz's Law: "x = y > (Fx ↔ Fy)". >Second order logic. --- Read III 133/134 Scope/Descriptions/Possible World/Read: Narrow scope: the description refers to different objects in different possible worlds - wide scope: the same object in different possible worlds - real names: always large scope. >Rigidity, >Descriptions, >Singular Terms, >Proper names. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 Stro I N. Strobach Einführung in die Logik Darmstadt 2005 |
| Second Order Logic, HOL | 2nd order Logic: Predicate logic of the 2nd order goes beyond predicate logic of the 1st level allowing quantification over properties and relations, and not just objects. Thus comparisons of the powerfulness of sets become possible. Problems which are expressed in everyday terms with terms such as "greater", "between", etc., and e.g. the specification of all the properties of an object require predicate logic of the 2nd order. Since the 2nd level logic is not complete (because there are, for example, an infinite number of properties of properties), one often tries to get on with the logic of the 1st order. |
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| Strength of Theories | Hintikka | II 7 Standard Semantics/Kripke Semantics/Hintikka: what differences are there? The ditch between standard semantics and Kripke semantics is much deeper than it first appears. Cocchiarella: Cocchiarella has shown, however, that even in the simplest quantifying case of the monadic predicate logic, the standard logic is radically different from its Kripke cousin. Decidability: monadic predicate logic is, as Kripke has shown, decidable. Kripke semantics: Kripke semantics is undecidable. Decisibility: Decisibility implies axiomatizability. Stronger/weaker/Hintikka: as soon as we go beyond monadic predicate logic, we have a logic of considerable strength, complexity, and unruliness. Quantified standard modal logic of the 1. level/Hintikka: the quantified standard modal logic of the 1. level is in a sense more powerful than the 2. level logic (with standard semantics). The latter is, of course, already very strong, so that some of the most difficult unresolved logical and quantum-theoretical problems can be expressed in terms of logical truth (or fulfillment) in logical formulas of the second level. Def equally strong/stronger/weaker/Hintikka: (here): the terms "stronger" and "weaker" are used to show an equally difficult decision-making problem. Decision problem: the standard logic of the 2. level can be reduced to that for quantified standard modal logic of the 1. level. Reduction: this reduction is weaker than translatability. II 9 Quantified standard modal logic of the 1. level/Hintikka: this logic is very strong, comparable in strength with the 2. level logic. It follows that it is not axiomatizable (HintikkaVsKripke). The stronger a logic is, the less manageable it is. II 28 Branching Quantifiers/stronger/weaker/Hintikka: E.g. branching here: 1. Branch: there is an x and b knows... 2. Branch: b knows there is an x ... Quantification with branched quantifiers is extremely strong, almost as strong as 2. level logic. Therefore, it cannot be completely axiomatized (quantified epistemic logic with unlimited independence). II 29 Variant: variants are simpler cases where the independence refers to ignorance, combined with a move with a single, non-negated operator {b} K. Here, an explicit treatment is possible. II 118 Seeing/stronger/weaker/logical form/Hintikka: a) stronger: recognizing, recognizing as, seeing as. b) weaker: to look at, to keep a glance on, etc. Weaker/logical form/seeing/knowing/Hintikka: e.g. (Perspective, "Ex") (15) (Ex) ((x = b) & (Ey) John sees that (x = y)). (16) (Ex)(x = b & (Ey) John remembers that x = y)) (17) (Ex)(x = b & (Ey) KJohn (x = y)) Acquaintance/N.B.: in (17) b can be John's acquaintance even if John does not know b as b! ((S) because of y). II 123 Everyday Language/ambiguity/Hintikka: the following expression is ambiguous: (32) I see d Stronger: (33) (Ex) I see that (d = x) That says the same as (31) if the information is visual or weaker: (34) (Ex) (d = x & (Ey) I see that (x = y)) This is the most natural translation of (32). Weaker: for the truth of (34) it is enough that my eyes simply rest on the object d. I do not need to recognize it as d. |
Hintikka I Jaakko Hintikka Merrill B. Hintikka Investigating Wittgenstein German Edition: Untersuchungen zu Wittgenstein Frankfurt 1996 Hintikka II Jaakko Hintikka Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 |
| Substitution | Logic Texts | Read III 127f Improper name/Quine: (= descriptions) - Only real names allow the substitution, which finds itself in the indistinguishability of the identical. Improper names: lead to a more complex form: for example, "there is one greatest orator among the Roman orators, and he accused Catilina." - e.g. "Exactly one number counts the planets and it is bigger than seven." Russell: here only 7 is a real name. >Description. Hence, these sentences cannot be upper and lower sentence in a conclusion of the principle of the indistinguishability of the identical. QuineVs: Problem: Scope: the descriptions must be eliminated in such a way that in the new formulation no component corresponds to them. --- Strobach I 104 Indistinguishability/Strobach: requires Logic of the 2nd level: predicate logic 2nd level/PL2/Strobach: typical formula: Leibniz's Law: "x = y > (Fx ↔ Fy)". >Second order logic. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 Stro I N. Strobach Einführung in die Logik Darmstadt 2005 |
| Syllogisms | Logic Texts | Hoyningen-Huene II 187 Syllogisms/predicate calculus/Hoyningen-Huene: e.g. All A are B. - all B are C So: Some C are A. - This is valid in the syllogistic because the premise "All A are B" is to be understood that its truth presupposes the existence of at least one A. In predicate logic, however, it is not valid because no existence is guaranteed by the premise. >Propositional logic, >Predicate calculus. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 |
| Validity | Logic Texts | Salmon I 41 Validity/W.Salmon: affects arguments (= groups of statements), not individual statements. Menne I 25 Menne: We become aware of laws through experience, but that does not mean that their validity is based on experience. Hoyningen-Huene II 100 Propositional logic: Validity of conclusions of propositional logic: conditions: 1. The validity of the conclusion depends on the multiple occurrence of certain (partial) statements. II 101 2. The validity is dependent on certain junction points occurring in it. 3. The validity is independent of the sense of the (partial) statements. II 102 Def Truth transfer/Hoyningen-Huene: positive: the truth of the premises guarantees the truth of the conclusion. 4. The validity of the conclusion requires truth transfer, i.e. that a true premise conjunction never occurs together with a false conclusion. >Truth transfer, Predicate logic: II 229 Adequacy conditions 1. The validity of the conclusion depends on the multiple occurrence of predicates (which refer to the same range of individuals) and possibly the logical constants (from the same range of individuals). II 230 2. The validity depends on the quantifiers and possibly the connectives that occur. 3. The validity is independent of the sense. 4. Validity requires truth transfer. >Connective, >Sense, >Quantifier, >Logical constant. Read III 71 Validity/Read: Problems: VsClassical logic: Classical logic does not succeed in including as valid those inferences whose correctness is based on the connections between non-logical expressions. If an object is round, then it follows that it is not square. But this conclusion is not valid thanks to its form, but thanks to its content. Logical Universe: Problem: one can find inferences whose invalidity can only be seen by looking at a larger universal range of definitions. ((s) See also Problems with the introduction of new connectives: >tonk.) |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Sal I Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 German Edition: Logik Stuttgart 1983 Sal II W. Salmon The Foundations Of Scientific Inference 1967 SalN I N. Salmon Content, Cognition, and Communication: Philosophical Papers II 2007 Me I A. Menne Folgerichtig Denken Darmstadt 1997 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 |
| Words | Gärdenfors | I 21 Words/Gärdenfors: express our terms. --- I 115 Words/Gärdenfors: why are there any at all? If we answer from a linguistic point of view, we are immediately involved in syntactic considerations. For example, we then try to find "arguments" of verbs. Problem: already the distinction transitive/intransitive is unclear. Also the assumption that verbs are used "predicatively" comes from the philosophy and the predicate logic and is an artificial construction. (GärdenforsVsPhilosophy, GärdenforsVsLogic). Syntax/Gärdenfors: the semantic theory in this book should be free of syntax, i.e. the semantic concepts should not depend on grammatical categories. I do not mean that syntax does not contribute to meaning, only lexical semantics should be operated independently of syntax. --- I 231 Words/Gärdenfors: are not simply meaning units - they occur in classes. > Word classes/Gärdenfors. |
Gä I P. Gärdenfors The Geometry of Meaning Cambridge 2014 |
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| Resnik, M. | Lewis Vs Resnik, M. | Schwarz I 82 Plural quantifier/Quantification/Lewis/Schwarz: is common in everyday language. Predicate logic: here it has to be replaced by singular constructions: Example "the numbers" may then stand for the class of all numbers, example "are few" expresses a property(!) of this class. Plural/Michael Resnik: (1988)(1) is the correct interpretation of everyday language plurals. LewisVsResnik: (Inwagen dito): on the one hand "the classes" is unproblematic, but on the other hand there is not the class of all classes, so you can't translate it that way. Question: in the above one-to-one correspondence, isn't it hidden and quantified via classes? 1. Michael D. Resnik [1988]: “Second-Order Logic Still Wild”. Journal of Philosophy, 85: 75–87 |
Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 Schw I W. Schwarz David Lewis Bielefeld 2005 |
| Russell, B. | Hilbert Vs Russell, B. | Klaus von Heusinger, Eselssätze und ihre Pferdefüsse Uni Konstanz Fachgruppe Sprachwissenschaft Arbeitspapier 64; 1994 Heusinger I 1 Epsilon/Heusinger: brings a new representation of certain and undefined NP: these are interpreted like pronouns as context-dependent terms, which are represented by a modified epsilon operator. This is interpreted as a selection function. VsRussell/VsIota Operator: this operator is less flexible because it is subject to the uniqueness condition. Context Dependency: is also dynamic in that the context reflects the advancing state of information. I 30 EO/Hilbert/Bernays/Heusinger: term building operator that makes the term x Fx from a formula F and a variable x. It can be understood as a generalized iota operator to which neither the condition of uniqueness nor the condition of existence applies. Iota Operator/HilbertVsRussell: has no contextual definition for Hilbert, but an explicit definition. I.e. ix Fx may be introduced if the condition of uniqueness and existence expressed in (48i) is derivable for the formula F. Problem: this is impractical because you do not always see if the formula meets the conditions. Eta Operator/Solution/Hilbert: may be introduced as in (48ii) if there is at least one element that makes F true. Its content is interpreted as a selection function. Uniqueness Condition: has therefore been replaced by the selection principle. Problem: also this condition of existence cannot be seen in the formula. Solution/Hilbert: Epsilon Operator/EO: is defined according to (48iii) even if F is empty, so that an epsilon term is always well defined. I 38 Determination/VsRussell/Heusinger: this means that determination is not attributed to uniqueness (>Iota operator) but to the more general concept of salinity (according to Lewis). Generality/(s): whether salience (which is itself context-dependent) is more general than uniqueness is questionable). Determination/Heusinger: is either a) a global property, such as it applies to unique and functional concepts (deictic use), or b) local: determined by the context. (anaphoric use) Both have a dynamic element. Rucker I 263 HilbertVsRussell: improved shortly after the publishing of Principia Mathematica(1) the techniques to elaborate with their help his idea of the "formal system". Mathematics/Logics/Hilbert: idea to understand all relations like x = y, x = 0, and z = x + y as special predicates in predicate logic: G(x,y), N(x), and S(x,y,z). Then the axioms of mathematics can be regarded as formulae of predicate logic and the proof process becomes the simple application of the rules of logic to the axioms. I 264 this allows mechanical solution methods. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
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The author or concept searched is found in the following theses of the more related field of specialization.
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Reference |
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| Barcan-Formula | Stalnaker, R. | I 145 Modal Propositional Logic/mAL/AL/extensional predicate logic/extPL/PL/Stalnaker: I want to investigate here 1. a weaker version of the converse of the barcan formula 2. the principle of necessity, not of identity but of diversity. Thesis: although both are validated by a very general semantic theory, they are independent principles that can no longer be derived by combining extensional predicate logic (PL) and modal propositional logic (AL). |
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