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.