A Short Introduction to Intuitionistic Logic
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 Assume automated deduction Chapter classical logic Coherence Theorem completeness proof component connective Consider the following correspond to redexes Craig interpolant cut rule cut-free deductive term DEFINITION derivable in NJp Derivable Rules Disjunctive translation double negation easy to prove example finite following deduction Frame Conditions hence as required implies implies induction hypothesis induction step Inference rules Interpolation Theorem Introduction to Intuitionistic Intuitionistic Predicate Logic intuitionistic propositional logic Kripke model Lambda Calculus LEMMA monotonicity multisets n-ary natural deduction negative formula Negative Translation normal form NUMBER THEORY obtained one-premise Partial Orders pointed frame premise principal formula Program Interpretation Proof-Search in Predicate Proof.Part propositional variable proved by ADC pruned quantifiers reduction sequence rules are derivable satisfying saturated set second sequent sequent is derivable Short Introduction subformulas System LJ Takashi Ono tautology Term Assignment THEOREM 8.2 topological completeness transfer rule transitive closure truth underivable uniquely correspond valid