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About this paper
Giorgi Japaridze
A Survey of Computability Logic presents a game-semantic framework that treats logical formulas as interactive computational problems rather than merely truth-valued statements. It unifies classical logic, constructive computation, resource-sensitive reasoning, and complexity-bounded computation, while reviewing sound and complete systems for several restricted fragments and constructive methods for extracting algorithms from proofs.
Key insights
- Classical logic emerges as the zero-interaction fragment of Computability Logic, while ordinary function computation appears as a restricted form of interaction.
- Choice and blind operators distinguish constructive knowledge of an answer from the mere truth or existence of an answer; recurrence operators distinguish different modes of resource reuse.
- Uniform validity requires one interpretation-independent strategy, making it suitable for general-purpose problem solving, and proof systems can provide executable strategies rather than only semantic guarantees.
Summary by alphaXiv.
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