The complexity of Gentzen systems for propositional logic

Canonical Propositional Gentzen-Type Systems

Canoni al Propositional Gentzen-Type Systems

Proof Complexity of Intuitionistic Propositional Logic

We explore the proof complexity of intuitionistic propositional logic (IPL). The problem of determining whether or not an intuitionistic formula is valid is PSPACE-Complete via a reduction from QBF . In view of this reduction (due to Statman), it is natural to compare the proof-theoretic strength of a standard axiomatic system for IPL with a similar proof system for classical quantified Boolean...

Proof Complexity of Propositional Default Logic

Default logic is one of the most popular and successful formalisms for non-monotonic reasoning. In 2002, Bonatti and Olivetti introduced several sequent calculi for credulous and skeptical reasoning in propositional default logic. In this paper we examine these calculi from a proof-complexity perspective. In particular, we show that the calculus for credulous reasoning obeys almost the same bou...

Complexity of Propositional Independence and Inclusion Logic

We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence and inclusion logic and their extensions by the classical negation.