The Computational Complexity of Propositional Cirquent Calculus

The Computational Complexity of Propositional Cirquent Calculus

Introduced in 2006 by Japaridze, cirquent calculus is a refinement of sequent calculus. The advent of cirquent calculus arose from the need for a deductive system with a more explicit ability to reason about resources. In particular, cirquent calculus has been instrumental in axiomatizing various fundamental fragments of Computability Logic, a formal theory of (interactive) computability. The s...

Cirquent calculus deepened

Cirquent calculus is a new proof-theoretic and semantic framework, whose main distinguishing feature is being based on circuit-style structures (called cirquents), as opposed to the more traditional approaches that deal with tree-like objects such as formulas, sequents or hypersequents. Among its advantages are greater efficiency, flexibility and expressiveness. This paper presents a detailed e...

A Computational Structure for the Propositional Calculus

Despite the long history and descriptive simplicity of the propositional calculus, practical aspects of its implementation on the computer remain an active area of study. We propose a representation of the propositional calculus which is straightforward, yet compact and sufficiently flexible to circumvent the combinatorial difficulties posed by many problems. The methodology does not involve te...

The Computational Complexity of Propositional STRIPS Planning

I present several computational complexity results for propositional STRIPS planning, i.e., STRIPS planning restricted to ground formulas. Diierent planning problems can be deened by restricting the type of formulas, placing limits on the number of pre-and postconditions, by restricting negation in pre-and postconditions, and by requiring optimal plans. For these types of restrictions, I show w...

Computational complexity of propositional dynamic logics