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- W2891016125 abstract "In 1936, Stanislaw Jaśkowski gave a construction of an interesting sequence of what he called matrices, which we would today call finite Heyting Algebras. He then gave a very brief sketch of a proof that if a propositional formula holds in each of these algebras then it is provable in intuitionistic propositional logic (IPL). The sketch just describes a certain normal form for propositional formulas and gives a very terse outline of an inductive argument showing that an unprovable formula in the normal form can be refuted in one of the algebras. Unfortunately, it is far from clear how to recover a complete proof from this sketch. In the early 1950s, Gene F. Rose gave a detailed proof of Jaśkowski's result, still using the notion of matrix rather than Heyting algebra, based on a normal form that is more restrictive than the one that Jaśkowski proposed. However, Rose's paper refers to his thesis for additional details, particularly concerning the normal form. This note gives a proof of Jaśkowski's result using modern terminology and a normal form more like Jaśkowski's. We also prove a semantic property of the normal form enabling us to give an alternative proof of completeness of IPL for the Heyting algebra semantics. We outline a decision procedure for IPL based on our proofs and illustrate it in action on some simple examples." @default.
- W2891016125 created "2018-09-27" @default.
- W2891016125 creator A5007731933 @default.
- W2891016125 date "2018-09-02" @default.
- W2891016125 modified "2023-09-27" @default.
- W2891016125 title "On the Jaśkowski Models for Intuitionistic Propositional Logic" @default.
- W2891016125 hasPublicationYear "2018" @default.
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