10slides(1) - Chapter 10 Introduction to Intuitionistic Logic PART 1 INTRODUCTION The intuitionistic logic has developed as a result of certain

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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 pseudo-boolean algebras, called also Heyting algebras to memorize Heying first proof system. 3 An intuitionistic tautology is a formula that is true in all pseudo-boolean 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.

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10slides(1) - Chapter 10 Introduction to Intuitionistic Logic PART 1 INTRODUCTION The intuitionistic logic has developed as a result of certain

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