Halpern, Y.J., and Kapron, B. Zero-one laws for modal logic. Annals of Pure and Applied Logic 69 (1994), 157-193. Home/Search Document Details and Download
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Adding the Everywhere Operator to Propositional Logic - Gries, Schneider (Correct)
....f g , with the conventional definition of evaluation) where every state is accessible from every other state. For example, the formula :2p for p a propositional variable is valid with respect this model, but it is not a theorem of S5. A number of sound an complete axiomatizations for C are known [13, 2, 1, 11, 9], dating from as early as 1973 see Gottlob survey [6] In Sec. 3, we give a new axiomatization for C, compare it with previous ones, and argue why we believe the new axiomatization is more suitable for actually writing formal proofs. The axiomatization presented in Sec. 3 uses an infinite ....
....(j= C C 1 ) and : and (j= C Cn ) implies hMonotonicity of and , Theorem (9) n Gamma 1 times)i ( C C 1 ) and : and ( C Cn ) C C 1 : Cn C ff ut Comparison with earlier complete axiomatizations As mentioned in Sec. 1, a number of complete axiomatizations of C have been given [13, 2, 1, 11, 9]. All of them are similar in nature to the following one, which we take from [9] Begin with Schematic S5 (see Table 2) Instead of adding inference rule Textual Substitution, add as axioms all formulas of the form 3ffi for ffi a satisfiable propositional formula (i.e. a propositional formula that ....
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Halpern, Y.J., and Kapron, B. Zero-one laws for modal logic. Annals of Pure and Applied Logic 69 (1994), 157-193.
Adding the Everywhere Operator to Propositional Logic - Gries, Schneider (Correct)
....propositional formula (i.e. a propositional formula that evaluates to t in at least one world of the S5c model) Lemma (7) now holds trivially, and we can prove completeness with respect to S5c validity in the same way that we proved completeness of 10 S5c. This general approach is mentioned in [6]. This axiomatization appeared unsatisfactory to us because it refers to the semantic concept of satisfiability. However, in private communications with us, both Rob Goldblatt and Joe Halpern explained how this semantic concept can be eliminated, leading to a complete (syntactic) axiomatization. ....
Halpern, Y.J., and Kapron, B. Zero-one laws for modal logic. Annals of Pure and Applied Logic 69 (1994), 157-193.
The Modal Logic of the Countable Random Frame - Goranko, Kapron Self-citation (Kapron) (Correct)
.... the in nitary logic over bounded number of variables L 1; proved in [Kolaitis and Vardi 92] for some pre x de ned fragments of monadic second order logic in [Kolaitis and Vardi 90] who also established strong relations between decidability and 0 1 laws of such fragments; for modal logic in [Halpern and Kapron 94] The Modal Logic of the Countable Random Frame 3 In general, however, the 0 1 law turns out to be rather a rare phenomenon than a rule. It can be easily seen that the presence of a single constant in the language is fatal for it; still, it was proved in [Lynch 85] that every sentence in a ....
....well behaved, being closed under nitary rules of inference, such as modus ponens: if A and A B are true in almost every nite model, then so is B. In modal logic there are two basic notions of validity: in models and in frames. Respectively, there are two concepts of almost sure validity. Halpern and Kapron 94] prove the 0 1 law for both of them. The result for almost sure model validity (called in [Halpern and Kapron 94] structure validity ) follows easily from Fagin s theorem, as model validity can be expressed in rst order logic by means of van Benthem s standard translation (see [van Benthem ....
[Article contains additional citation context not shown here]
J. Halpern and B. Kapron, Zero-one laws for modal logic, Ann. Pure and Appl. Logic, 69, 1994, pp. 157-193.
The Modal Logic of the Countable Random Frame - Goranko, Kapron (2000) Self-citation (Kapron) (Correct)
.... the in nitary logic over bounded number of variables L 1; proved in [Kolaitis and Vardi 90] for some pre x de ned fragments of monadic second order logic in [Kolaitis and Vardi 90] who also established strong relations between decidability and 0 1 laws of such fragments; for modal logic in [Halpern and Kapron 94] However, in general, the 0 1 law turns out to be rather a rare phenomenon than a rule. It can be easily seen that the presence of a single constant in the language is fatal for it; however, it was proved in [Lynch 85] that every sentence in a rst order languages with only unary functions does ....
....well behaved, being closed under nitary rules of inference, such as modus ponens: if A and A B are true in almost every nite model, then so is B. In modal logic there are two basic notions of validity: in models and in frames. espectively, there are two concepts of almost sure validity. Halpern and Kapron 94] prove he 0 1 law for both of them. The result for almost sure model validity (called in [Halpern and Kapron 94] structure validity ) follows easily from Fagin s theorem, as model validity can be expressed in rst order logic by means of van Benthem s standard translation (see [van Benthem 85] ....
[Article contains additional citation context not shown here]
J. Halpern and B. Kapron, Zero-one laws for modal logic, Ann. Pure and Appl. Logic, 69, 1994, 157- 193.
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