MOLOG: A system that extends PROLOG with modal logic
New Generation Computing
Proc. of the 8th international conference on Automated deduction
Modal resolution in clausal form
Theoretical Computer Science
Strategies for modal resolution: results and problems
Journal of Automated Reasoning
Gentzen-type systems and resolution rules. Part I. Propositional logic
COLOG-88 Proceedings of the international conference on Computer logic
Logics and models of concurrent systems
Term rewriting and all that
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Why are modal logics so robustly decidable?
Current trends in theoretical computer science
Modal logic
Decidability by Resolution for Propositional Modal Logics
Journal of Automated Reasoning
Using Resolution for Testing Modal Satisfiability and Building Models
Journal of Automated Reasoning
Hilbert's epsilon-Terms in Automated Theorem Proving
TABLEAUX '99 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
A Road-Map on Complexity for Hybrid Logics
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Algorithms, Datastructures, and other Issues in Efficient Automated Deduction
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Proceedings of the 9th International Conference on Automated Deduction
System Description: Spass Version 1.0.0
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Vampire 1.1 (System Description)
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Deciding the guarded fragments by resolution
Journal of Symbolic Computation
Handbook of automated reasoning
Handbook of automated reasoning
A Superposition Decision Procedure for the Guarded Fragment with Equality
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Clausal resolution for normal modal logics
Journal of Algorithms
A Resolution-Based Decision Procedure for $\boldsymbol{\mathcal{SHOIQ}}$
Journal of Automated Reasoning
A new methodology for developing deduction methods
Annals of Mathematics and Artificial Intelligence
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We investigate labeled resolution calculi for hybrid logics with inference rules restricted via selection functions and orders. We start by providing a sound and refutationally complete calculus for the hybrid logic $\mathcal{H}(@,{\downarrow},\mathsf{A})$ , even under restrictions by selection functions and orders. Then, by imposing further restrictions in the original calculus, we develop a sound, complete and terminating calculus for the $\mathcal{H}(@)$ sublanguage. The proof scheme we use to show refutational completeness of these calculi is an adaptation of a standard completeness proof for saturation-based calculi for first-order logic that guarantees completeness even under redundancy elimination. In fact, one of the contributions of this article is to show that the general framework of saturation-based proving for first-order logic with equality can be naturally adapted to saturation-based calculi for other languages, in particular modal and hybrid logics.