Giorgi Japaridze
Abstract
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is understood as its being a scheme of problems that always have algorithmic solutions. The earlier article “Propositional computability logic I” proved soundness and completeness for the (in a sense) minimal nontrivial fragment CL1 of computability logic. The present article extends that result to the significantly more expressive propositional system CL2. What makes CL2 more expressive than CL1 is the presence of two sorts of atoms in its language: elementary atoms, representing elementary computational problems (i.e. predicates), and general atoms, representing arbitrary computational problems. CL2 conservatively extends CL1, with the latter being nothing but the general-atom-free fragment of the former.
- Blass, A. 1992. A game semantics for linear logic. Ann. Pure Appl. Logic 56, 183--220.Google Scholar
Cross Ref
- Japaridze, G. 2003. Introduction to computability logic. Ann. Pure Appl. Logic 123, 1--99.Google ScholarCross Ref
- Japaridze, G. 2004a. Computability logic: A formal theory of interaction. Tech. Rep. arXiv:cs.LO/0404024, Villanova University. http://arxiv.org/abs/cs.LO/0404024.Google Scholar
- Japaridze, G. 2004b. Propositional computability logic I. ACM Trans. Comput. Logic (to appear). Google ScholarDigital Library
Index Terms
- Propositional computability logic II
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