Correctness and worst-case optimality of Pratt-style decision procedures for modal and hybrid logics

Authors:
Mark Kaminski;Thomas Schneider;Gert Smolka
Affiliations:
Saarland University, Germany;University of Bremen, Germany;Saarland University, Germany
Venue:
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Year:
2011

Citing 20
Cited 3

Decision procedures and expressiveness in the temporal logic of branching time

Journal of Computer and System Sciences
Automata-Theoretic techniques for modal logics of programs

Journal of Computer and System Sciences
An automata theoretic decision procedure for the propositional mu-calculus

Information and Computation
Attributive concept descriptions with complements

Artificial Intelligence
Logics of programs

Handbook of theoretical computer science (vol. B)
An essay in combinatory dynamic logic

Information and Computation
EXPTIME tableaux for ALC

Artificial Intelligence
Combining deduction and model checking into Tableaux and algorithms for converse-PDL

Information and Computation
Modal logic

Modal logic
Dynamic Logic

Dynamic Logic
Tableau Algorithms for Description Logics

TABLEAUX '00 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
RACER System Description

IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Propositional modal logic of programs

STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Optimizing Terminological Reasoning for Expressive Description Logics

Journal of Automated Reasoning
Models of program logics

SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
EXPTIME Tableaux with Global Caching for Description Logics with Transitive Roles, Inverse Roles and Role Hierarchies

TABLEAUX '07 Proceedings of the 16th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
An Optimal On-the-Fly Tableau-Based Decision Procedure for PDL-Satisfiability

CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Clausal graph tableaux for hybrid logic with eventualities and difference

LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Optimal and cut-free tableaux for propositional dynamic logic with converse

IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Terminating tableaux for hybrid logic with eventualities

IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning

Constructive formalization of hybrid logic with eventualities

CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Constructive completeness for modal logic with transitive closure

CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
A Goal-Directed Decision Procedure for Hybrid PDL

Journal of Automated Reasoning

Quantified Score

Hi-index	0.00

Visualization

Abstract

We extend Pratt's worst-case optimal decision procedure for PDL to a richer logic with nominals, difference modalities, and inverse actions. We prove correctness and worst-case optimality. Our correctness proof is based on syntactic models called demos. The main theorem states that a formula is satisfiable if and only if it is contained in a demo. From this theorem the correctness of the decision procedure is easily obtained. Our development is modular and we extend it stepwise from modal logic with eventualities to the full logic.