Japaridze, Giorgi - On the system CL12 of computability logic

lmcs:1577 - Logical Methods in Computer Science, July 28, 2015, Volume 11, Issue 3
On the system CL12 of computability logic

Authors: Japaridze, Giorgi

Computability logic (see http://www.csc.villanova.edu/~japaridz/CL/) is a long-term project for redeveloping logic on the basis of a constructive game semantics, with games seen as abstract models of interactive computational problems. Among the fragments of this logic successfully axiomatized so far is CL12 --- a conservative extension of classical first-order logic, whose language augments that of classical logic with the so called choice sorts of quantifiers and connectives. This system has already found fruitful applications as a logical basis for constructive and complexity-oriented versions of Peano arithmetic, such as arithmetics for polynomial time computability, polynomial space computability, and beyond. The present paper introduces a third, indispensable complexity measure for interactive computations termed amplitude complexity, and establishes the adequacy of CL12 with respect to A-amplitude, S-space and T-time computability under certain minimal conditions on the triples (A,S,T) of function classes. This result very substantially broadens the potential application areas of CL12. The paper is self-contained, and targets readers with no prior familiarity with the subject.

Source : oai:arXiv.org:1203.0103
DOI : 10.2168/LMCS-11(3:1)2015
Volume: Volume 11, Issue 3
Published on: July 28, 2015
Submitted on: March 2, 2012
Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic


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