Japaridze, Giorgi - From formulas to cirquents in computability logic

lmcs:1121 - Logical Methods in Computer Science, April 21, 2011, Volume 7, Issue 2 - https://doi.org/10.2168/LMCS-7(2:1)2011
From formulas to cirquents in computability logic

Authors: Japaridze, Giorgi

Computability logic (CoL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Its expressions represent interactive computational tasks seen as games played by a machine against the environment, and "truth" is understood as existence of an algorithmic winning strategy. With logical operators standing for operations on games, the formalism of CoL is open-ended, and has already undergone series of extensions. This article extends the expressive power of CoL in a qualitatively new way, generalizing formulas (to which the earlier languages of CoL were limited) to circuit-style structures termed cirquents. The latter, unlike formulas, are able to account for subgame/subtask sharing between different parts of the overall game/task. Among the many advantages offered by this ability is that it allows us to capture, refine and generalize the well known independence-friendly logic which, after the present leap forward, naturally becomes a conservative fragment of CoL, just as classical logic had been known to be a conservative fragment of the formula-based version of CoL. Technically, this paper is self-contained, and can be read without any prior familiarity with CoL.

Volume: Volume 7, Issue 2
Published on: April 21, 2011
Submitted on: July 12, 2010
Keywords: Computer Science - Logic in Computer Science,Computer Science - Artificial Intelligence,Computer Science - Computational Complexity,Mathematics - Logic,F.1.1, F.1.2, F.1.3


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