The intuitionistic fragment of computability logic at the propositional level

Details The intuitionistic fragment of computability logic at the propositional level The intuitionistic fragment of computability logic at the propositional level

2006-02-05

arxiv.org/abs/cs/0602011v2

Annals of Pure and Applied Logic 147 (2007), pp. 187-227

Computer Science

Logic in Computer Science

Scientific paper

10.1016/j.apal.2007.05.001

This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games between a machine and its environment. Intuitionistic implication is understood as algorithmic reduction in the weakest possible -- and hence most natural -- sense, disjunction and conjunction as deterministic-choice combinations of problems (disjunction = machine's choice, conjunction = environment's choice), and "absurd" as a computational problem of universal strength. See http://www.cis.upenn.edu/~giorgi/cl.html for a comprehensive online source on computability logic.

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