A Short Introduction to Intuitionistic LogicSpringer Science & Business Media, 20.12.2005 - 131 Seiten Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order logic. One device for making this book short was inventing new proofs of several theorems. The presentation is based on natural deduction. The topics include programming interpretation of intuitionistic logic by simply typed lambda-calculus (Curry-Howard isomorphism), negative translation of classical into intuitionistic logic, normalization of natural deductions, applications to category theory, Kripke models, algebraic and topological semantics, proof-search methods, interpolation theorem. The text developed from materal for several courses taught at Stanford University in 1992-1999. |
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abbreviation antecedent rule automated deduction Chapter 11 classical logic Coherence Theorem complete sequent completeness proof component Consider the following correspond to redexes Craig interpolant cut elimination deductive term DEFINITION derivability of sequents derivable as follows derivable in NJp Disjunctive translation double negation easy to prove EXAMPLE finite following deduction hence as required implies implies induction hypothesis induction step Inference rules introduction rule Introduction to Intuitionistic INTUITIONISTIC LOGIC Grigori intuitionistic propositional logic Kripke model largest R-closed subset LEMMA monotonicity n-ary natural deduction negative formula negative translation non-invertible rule normal form NUMBER THEORY obtained partial order Permutative conversions principal formula Program Interpretation proof-search Proof.Exactly Proof.Part Propositional System LJpm propositional variable proved by ADC pruned quantifiers reduction sequence rule is derivable satisfying saturated set second sequent sequent is derivable Short Introduction simpler sequent subformulas system NJp tautology Term Assignment Theorem 7.1 topological completeness underivable uniquely correspond valid