Proof complexity of propositional default logic

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...

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...

Propositional Proof Complexity

Propositional Proof Complexity and Rewriting

In this work we want to find a new framework for propositional proofs (and in particular for resolution proofs) utilizing rewriting techniques. We interpret the well-known propositional proof system resolution using string rewriting systems (semi-Thue system [70], [71]) Σn and Σn corresponding to tree-like proofs and sequence-like proofs, respectively. We prove that the system Σn is complete an...

Propositional Proof Complexity An Introduction

1 Preface and Acknowledgements This article is an abridged and revised version of a 1996 McGill University technical report [14]. The technical report was based on lectures delivered by the author at a workshop in Holetown, Barbados and on the authors prepared overhead transparencies. The audience at this workshop wrote scribe notes which then formed the technical report [14]. The material sele...