Using Resolution for Testing Modal Satisfiability and Building Models

Authors:
Ullrich Hustadt;Renate A. Schmidt
Affiliations:
Centre for Agent Research and Development, Department of Computing and Mathematics, Manchester Metropolitan University, Chester Street, Manchester M1 5GD, UK. e-mail: u.hustadt@doc.mmu.ac. ...;Centre for Agent Research and Development, Department of Computing and Mathematics, Manchester Metropolitan University, Chester Street, Manchester M1 5GD, UK. e-mail: r.a.schmidt@doc.mmu.a ...
Venue:
Journal of Automated Reasoning
Year:
2002

Citing 15
Cited 16

A Structure-preserving Clause Form Translation

Journal of Symbolic Computation
Reasoning in description logics

Principles of knowledge representation
Resolution Strategies as Decision Procedures

Journal of the ACM (JACM)
Resolution Methods for the Decision Problem

Resolution Methods for the Decision Problem
Automated Deduction Techniques for Classification in Description Logic Systems

Journal of Automated Reasoning
Decidability by Resolution for Propositional Modal Logics

Journal of Automated Reasoning
Saturation-Based Theorem Proving (Abstract)

ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
An Automata-Theoretic Approach to Constraint LTL

FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
FaCT and DLP

TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Simplification: A General Constraint Propagation Technique for Propositional and Modal Tableaux

TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Strongly Analytic Tableaux for Normal Modal Logics

CADE-12 Proceedings of the 12th International Conference on Automated Deduction
The Search Efficiency of Theorem Proving Strategies

CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Building Decision Procedures for Modal Logics from Propositional Decision Procedure - The Case Study of Modal K

CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
A Resolution Decision Procedure for the Guarded Fragment

CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
On evaluating decision procedures for modal logic

IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1

Combinations of Modal Logics

Artificial Intelligence Review
Computational Space Efficiency and Minimal Model Generation for Guarded Formulae

LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
Verification within the KARO Agent Theory

FAABS '00 Proceedings of the First International Workshop on Formal Approaches to Agent-Based Systems-Revised Papers
Extracting models from clause sets saturated under semantic refinements of the resolution rule

Information and Computation
Constructing decision procedures in equational clausal logic

Fundamenta Informaticae
The CADE-18 ATP System Competition

Journal of Automated Reasoning
Representing and Building Models for Decidable Subclasses of Equational Clausal Logic

Journal of Automated Reasoning
The state of CASC

AI Communications
The axiomatic translation principle for modal logic

ACM Transactions on Computational Logic (TOCL)
Decision Procedures for Expressive Description Logics with Intersection, Composition, Converse of Roles and Role Identity

IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
A new methodology for developing deduction methods

Annals of Mathematics and Artificial Intelligence
Resolution with Order and Selection for Hybrid Logics

Journal of Automated Reasoning
A Tableau Calculus for Minimal Modal Model Generation

Electronic Notes in Theoretical Computer Science (ENTCS)
Framework for an automated comparison of description logic reasoners

ISWC'06 Proceedings of the 5th international conference on The Semantic Web
Reasoning support for expressive ontology languages using a theorem prover

FoIKS'06 Proceedings of the 4th international conference on Foundations of Information and Knowledge Systems
Constructing Decision Procedures in Equational Clausal Logic

Fundamenta Informaticae

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a translation-based resolution decision procedure for the multimodal logic iK(m)(∩,∪,⌣) defined over families of relations closed under intersection, union, and converse. The relations may satisfy certain additional frame properties. Different from previous resolution decision procedures that are based on ordering refinements, our procedure is based on a selection refinement, the derivations of which correspond to derivations of tableaux or sequent proof systems. This procedure has the advantage that it can be used both as a satisfiability checker and as a model builder. We show that tableaux and sequent-style proof systems can be polynomially simulated with our procedure. Furthermore, the finite model property follows for a number of extended modal logics.