Modal deduction with applications in epistemic and temporal logics
Handbook of logic in artificial intelligence and logic programming (Vol. 4)
Modal tableaux with propagation rules and structural rules
Fundamenta Informaticae
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Single Step Tableaux for Modal Logics
Journal of Automated Reasoning
Using Resolution for Testing Modal Satisfiability and Building Models
Journal of Automated Reasoning
Rasiowa-Sikorski deduction systems in computer science applications
Theoretical Computer Science
MSPASS: Modal Reasoning by Translation and First-Order Resolution
TABLEAUX '00 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Superposition with Simplification as a Desision Procedure for the Monadic Class with Equality
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
A New Clausal Class Decidable by Hyperresolution
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
A Resolution Decision Procedure for Fluted Logic
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Encoding two-valued nonclassical logics in classical logic
Handbook of automated reasoning
Resolution decision procedures
Handbook of automated reasoning
Hyperresolution for guarded formulae
Journal of Symbolic Computation - Special issue: First order theorem proving
The design and implementation of VAMPIRE
AI Communications - CASC
AI Communications - CASC
The axiomatic translation principle for modal logic
ACM Transactions on Computational Logic (TOCL)
On the relation of resolution and tableaux proof systems for description logics
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Splitting without backtracking
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Using tableau to decide expressive description logics with role negation
ISWC'07/ASWC'07 Proceedings of the 6th international The semantic web and 2nd Asian conference on Asian semantic web conference
Second Order Quantifier Elimination: Foundations, Computational Aspects and Applications
Second Order Quantifier Elimination: Foundations, Computational Aspects and Applications
Blocking and other enhancements for bottom-up model generation methods
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Simulation and Synthesis of Deduction Calculi
Electronic Notes in Theoretical Computer Science (ENTCS)
Resolution with Order and Selection for Hybrid Logics
Journal of Automated Reasoning
Using tableau to decide description logics with full role negation and identity
ACM Transactions on Computational Logic (TOCL)
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This paper explores the use of resolution as a meta-framework for developing various, different deduction calculi. In this work the focus is on developing deduction calculi for modal dynamic logics. Dynamic modal logics are PDL-like extended modal logics which are closely related to description logics. We show how tableau systems, modal resolution systems and Rasiowa-Sikorski systems can be developed and studied by using standard principles and methods of first-order theorem proving. The approach is based on the translation of reasoning problems in modal logic to first-order clausal form and using a suitable refinement of resolution to construct and mimic derivations of the desired proof method. The inference rules of the calculus can then be read off from the clausal form. We show how this approach can be used to generate new proof calculi and prove soundness, completeness and decidability results. This slightly unusual approach allows us to gain new insights and results for familiar and less familiar logics, for different proof methods, and compare them not only theoretically but also empirically in a uniform framework.