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
Hybrid Logics and Ontology Languages
Electronic Notes in Theoretical Computer Science (ENTCS)
Terminating Tableau Systems for Hybrid Logic with Difference and Converse
Journal of Logic, Language and Information
A tableaux based decision procedure for a broad class of hybrid formulae with binders
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
On the complexity of hybrid logics with binders
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
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 FHL (full hybrid logic with the binder, including the global and converse modalities), where no occurrence of a universal operator is in the scope of a binder. By means of a satisfiability preserving translation of formulae, the calculus can be turned into a satisfiability decision procedure for the fragment $\textsf{FHL}\setminus\Box \mathord\downarrow\Box$ , 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 universal operator. The calculus is based on tableaux 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.