A formally verified abstract account of Gödel's incompleteness theorems

We present an abstract development of Gödel’s incompleteness theorems, performed with the help of the Isabelle/HOL theorem prover. We analyze sufficient conditions for the theorems’ applicability to a partially specified logic. In addition to the usual benefits of generality, our abstract perspective enables a comparison between alternative approaches from the literature. These include Rosser’s variation of the first theorem, Jeroslow’s variation of the second theorem, and the S ́wierczkowski–Paulson semantics-based approach. As part of our framework’s validation, we upgrade Paulson’s Isabelle proof to produce a mech- anization of the second theorem that does not assume soundness in the standard model, and in fact does not rely on any notion of model or semantic interpretation

Recovering and exploiting structural knowledge from CNF formulas

International audienc

QUBE: A system for deciding quantified boolean formulas satisfiability

Deciding the satisfiability of a Quantified Boolean Formula (QBF) is an important research issue in Artificial Intelligence. Many reasoning tasks involving planning [1], abduction, reasoning about knowledge, non monotonic reasoning [2], can be directly mapped into the problem of deciding the satisfiability of a QBF. In this paper we present quBE, a system for deciding QBFs satisfiability. We start our presentation is Section 2 with some terminology and definitions necessary for the rest of the paper. In Section 3 we present a high level description of QuBE's basic algorithm. QuBE's available options are described in Section 4. We end our presentation is Section 5 with some experimental results showing QuBE effectiveness in comparison with other systems. QuBE, and more information about QuBE are available at www.mrg.dist.unige.it/star/qub

A branching heuristics for quantified renamable Horn formulas

Abstract. Many solvers have been designed for QBFs, the validity problem for Quantified Boolean Formulas for the past few years. In this paper, we describe a new branching heuristics whose purpose is to promote renamable Horn formulas. This heuristics is based on Hébrard’s algorithm for the recognition of such formulas. We present some experimental results obtained by our qbf solver Qbfl with the new branching heuristics and show how its performances are improved.