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Intuitionistic computability logicAbstract (in LaTeX format)Computability logic (CL) is a systematic formal theory of computational tasks and resources, which, in a sense, can be seen as a semantics-based alternative to (the syntactically introduced) linear logic. With its expressive and flexible language, where formulas represent computational problems and ``truth'' is understood as algorithmic solvability, CL potentially offers a comprehensive logical basis for constructive applied theories and computing systems inherently requiring constructive and computationally meaningful underlying logics. Among the best known constructivistic logics is Heyting's intuitionistic calculus $\hint$, whose language can be seen as a special fragment of that of CL. The constructivistic philosophy of $\hint$, however, just like the resource philosophy of linear logic, has never really found an intuitively convincing and mathematically strict semantical justification. CL has good claims to provide such a justification and hence a materialization of Kolmogorov's known thesis ``$\hint$ = logic of problems''. The present paper contains a soundness proof for $\hint$ with respect to the CL semantics. Kewords: computability logic, interactive computation, game semantics, linear logic, intuitionistic logic. Full textAvailable electronic editions: PDF. Note that full text is available only for papers that are at least 10 years old. For more recent papers only the first page of the paper is provided. BibTeX entry@ARTICLE{Japaridze:2007:ActaCybernetica,author = {Giorgi Japaridze}, title = {Intuitionistic computability logic}, journal = {Acta Cybernetica}, year = {2007}, volume = {18}, number = {1}, pages = {77--113}, abstract = {Computability logic (CL) is a systematic formal theory of computational tasks and resources, which, in a sense, can be seen as a semantics-based alternative to (the syntactically introduced) linear logic. With its expressive and flexible language, where formulas represent computational problems and ``truth'' is understood as algorithmic solvability, CL potentially offers a comprehensive logical basis for constructive applied theories and computing systems inherently requiring constructive and computationally meaningful underlying logics. Among the best known constructivistic logics is Heyting's intuitionistic calculus $\hint$, whose language can be seen as a special fragment of that of CL. The constructivistic philosophy of $\hint$, however, just like the resource philosophy of linear logic, has never really found an intuitively convincing and mathematically strict semantical justification. CL has good claims to provide such a justification and hence a materialization of Kolmogorov's known thesis ``$\hint$ = logic of problems''. The present paper contains a soundness proof for $\hint$ with respect to the CL semantics.}, keywords = {computability logic, interactive computation, game semantics, linear logic, intuitionistic logic} }
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