| Institute of Informatics>>> Acta Cybernetica>>> Past Issues>>> Volume 18, Number 1, 2007>>> |
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Intuitionistic computability logic
Abstract (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.
Keywords: computability logic, interactive computation, game semantics, linear logic, intuitionistic logic.
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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}
}