The Davis-Putnam-Logemann-Loveland procedure (DPLL) was introduced in the early

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This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur

We provide a resolution-based proof procedure for modal, description and hybrid logic that improves on previous proposals in important ways. It avoids translations into large undecidable logics, and works directly on modal, description or hybrid logic formulas instead. In addition, by using the hybrid machinery it avoids the complexities of earlier propositional resolution-based methods for modal logic. It combines ideas from the method of pre xes used in tableaux, and resolution ideas in such a way that some of the heuristics and optimizations devised in either eld are applicable.

Abstract. We describe a system for the automated certification of safety properties of NASA software. The system uses Hoare-style program verification technology to generate proof obligations which are then processed by an automated first-order theorem prover (ATP). For full automation, however, the obligations must be aggressively preprocessed and simplified. We describe the unique requirements this places on the ATP and demonstrate how the individual simplification stages, which are implemented by rewriting, influence the ability of the ATP to solve the proof tasks. Experiments on more than 25,000 tasks were carried out using Vampire, Spass, and e-setheo. 1

We describe a system for the automated certification of safety properties of NASA software. The system uses Hoare-style program verification technology to generate proof obligations which are then processed by an automated first-order theorem prover (ATP). We discuss the unique requirements this application places on the ATPs, focusing on automation, proof checking, and usability. For full automation, however, the obligations must be aggressively preprocessed and simplified, and we demonstrate how the individual simplification stages, which are implemented by rewriting, influence the ability of the ATPs to solve the proof tasks. Our results are based on 13 certification experiments that lead to more than 25,000 proof tasks which have each been attempted by Vampire, Spass, e-setheo, and Otter. The proofs found by Otter have been proof-checked by IVY. 1

We aim to demonstrate that automated deduction techniques, in particular those following the model computation paradigm, are very well suited for database schema/query reasoning. Specifically, we present an approach to compute completed paths for database or XPath queries. The database schema and a query are transformed to disjunctive logic programs with default negation, using a description logic as an intermediate language. Our underlying deduction system, KRHyper, then detects if a query is satisfiable or not. In case of a satisfiable query, all completed paths -- those that fulfill all given constraints -- are returned as part of the computed models.

This paper views modal logics as languages that are especially tailored for describing relational structures. After pointing out the connections between modal logics and other elds, it describes a natural extension to traditional modal languages: hybrid logics.

We describe a combination of the NORA/HAMMR software component retrieval tool and the ILF system which provides the necessary infrastructure to apply different first-order theorem provers to the emerging proof problems. This framework allows the cooperation of independent deductive subsystems in two different modes. Our results show that both modes -- competition between problem variants or provers and proper cooperation following the TECHS approach -- improve the success rate considerably.