Implementation and Optimisation of a Tableau Algorithm for the Guarded Fragment
TABLEAUX '02 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
A Superposition Decision Procedure for the Guarded Fragment with Equality
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Guarded Fragments with Constants
Journal of Logic, Language and Information
Terminating Tableau Systems for Hybrid Logic with Difference and Converse
Journal of Logic, Language and Information
On the complexity of hybrid logics with binders
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Journal of Automated Reasoning
A proof procedure for hybrid logic with binders, transitivity and relation hierarchies
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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In this paper we provide the first (as far as we know) direct calculus deciding satisfiability of formulae in negation normal form in the fragment of hybrid logic with the satisfaction operator and the binder, where no occurrence of the - operator is in the scope of a binder. A preprocessing step, rewriting formulae into equisatisfiable ones, turns the calculus into a satisfiability decision procedure for the fragment HL(@, ↓) \-↓-, i.e. formulae in negation normal form where no occurrence of the binder is both in the scope of and contains in its scope a - operator. The calculus is based on tableaux, where nominal equalities are treated by means of substitution, and termination is achieved by means of a form of anywhere blocking with indirect blocking. Direct blocking is a relation between nodes in a tableau branch, holding whenever the respective labels (formulae) are equal up to (a proper form of) nominal renaming. Indirect blocking is based on a partial order on the nodes of a tableau branch, which arranges them into a tree-like structure.