A Propositional Cirquent Calculus for Computability Logic

Abstract Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization $$\text{ CL18 }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:mtext>CL18</mml:mtext> <mml:mspace/> </mml:mrow> </mml:math> of the basic propositional fragment of computability logic —the game-semantically conceived logic of computational resources and tasks. The nonlogical atoms of this fragment represent arbitrary so called static games, and the connectives of its logical vocabulary are negation and the parallel and choice versions of conjunction and disjunction. The main technical result of the article is a proof of the soundness and completeness of $$\text{ CL18 }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:mtext>CL18</mml:mtext> <mml:mspace/> </mml:mrow> </mml:math> with respect to the semantics of computability logic.