81 research outputs found
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
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