|Decidability: a question, for example, whether a property applies to an object or not, is decidable if a result can be achieved within a finite time. For this decision process, an algorithm is chosen as a basis. See also halting problem, algorithms, procedures, decision theory.|
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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.
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.
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.
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.
Jaakko and Merrill B. Hintikka
The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989
J. Hintikka/M. B. Hintikka
Untersuchungen zu Wittgenstein Frankfurt 1996