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Unformatted text preview: Chapter 10: Introduction to Intuitionistic Logic PART 1: INTRODUCTION The intuitionistic logic has developed as a result of certain philosophical views on the foundation of mathematics, known as in tuitionism . Intuitionism was originated by L. E. J. Brouwer in 1908. The first Hilbert proof system (Hilber style formalization) of the intuitionistic logic is due to A. Heyting (1930). 1 We present here a Hilbert style proof system developed by Rasiowa in 1959 that is equiv alent to the Heyting’s original formaliza tion. We discuss the relationship between intuition istic and classical logic. We also present the original version of Gentzen work (1935). Gentzen was the first who formulated a first syntactically decidable formalization for clas sical and intuitionistic logic and proved its equivalence with the Heyting’s original Hilbert style formalization (famous Gentzen’s Haupt satz). 2 We present first, as it has happened histor ically, the intutionistic proof systems called also formalizations of the intuitionistic logic. The semantics for the intuitionistic logic will be presented in a seperate chapter. Intuitionistic semantics was fist defined by Tarski in 1937, and Tarski and Stone in 1938 in terms of pseudoboolean algebras, called also Heyting algebras to memorize Heying first proof system. 3 An intuitionistic tautology is a formula that is true in all pseudoboolean algebras....
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This note was uploaded on 02/12/2011 for the course CSE 541 taught by Professor Bachmair,l during the Spring '08 term at SUNY Stony Brook.
 Spring '08
 Bachmair,L
 Computer Science

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