The complementation problem for Bu¨chi automata with applications to temporal logic
Theoretical Computer Science
Temporal logic programming is complete and expressive
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Nonclausal deduction in first-order temporal logic
Journal of the ACM (JACM)
Temporal logic (vol. 1): mathematical foundations and computational aspects
Temporal logic (vol. 1): mathematical foundations and computational aspects
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
ACM Transactions on Computational Logic (TOCL)
A Decision Method for Temporal Logic Based on Resolution
Proceedings of the Fifth Conference on Foundations of Software Technology and Theoretical Computer Science
A New One-Pass Tableau Calculus for PLTL
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Temporal Logic with Fixed Points
Temporal Logic in Specification
Proceedings of the Conference on Logic of Programs
A Decision Method for Linear Temporal Logic
Proceedings of the 7th International Conference on Automated Deduction
A Simplified Clausal Resolution Procedure for Propositional Linear-Time Temporal Logic
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Search Strategies for Resolution in Temporal Logics
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
A method of automatic proof for the specification and verification of protocols
SIGCOMM '84 Proceedings of the ACM SIGCOMM symposium on Communications architectures and protocols: tutorials & symposium
Systematic Semantic Tableaux for PLTL
Electronic Notes in Theoretical Computer Science (ENTCS)
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
An Optimal On-the-Fly Tableau-Based Decision Procedure for PDL-Satisfiability
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
A resolution method for temporal logic
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
FM '09 Proceedings of the 2nd World Congress on Formal Methods
One-pass tableaux for computation tree logic
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Tableau Tool for Testing Satisfiability in LTL: Implementation and Experimental Analysis
Electronic Notes in Theoretical Computer Science (ENTCS)
An Introduction to Practical Formal Methods Using Temporal Logic
An Introduction to Practical Formal Methods Using Temporal Logic
A cut-free and invariant-free sequent calculus for PLTL
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Logical foundations for more expressive declarative temporal logic programming languages
ACM Transactions on Computational Logic (TOCL)
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Resolution is a well-known proof method for classical logics that is well suited for mechanization. The most fruitful approach in the literature on temporal logic, which was started with the seminal paper of M. Fisher, deals with Propositional Linear-time Temporal Logic (PLTL) and requires to generate invariants for performing resolution on eventualities. The methods and techniques developed in that approach have also been successfully adapted in order to obtain a clausal resolution method for Computation Tree Logic (CTL), but invariant handling seems to be a handicap for further extension to more general branching temporal logics. In this paper, we present a new approach to applying resolution to PLTL. The main novelty of our approach is that we do not generate invariants for performing resolution on eventualities. Hence, we say that the approach presented in this paper is invariant-free. Our method is based on the dual methods of tableaux and sequents for PLTL that we presented in a previous paper. Our resolution method involves translation into a clausal normal form that is a direct extension of classical CNF. We first show that any PLTL-formula can be transformed into this clausal normal form. Then, we present our temporal resolution method, called trs-resolution, that extends classical propositional resolution. Finally, we prove that trs-resolution is sound and complete. In fact, it finishes for any input formula deciding its satisfiability, hence it gives rise to a new decision procedure for PLTL.