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 FHL \ 2↓2, 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.

No abstract

No abstract

No abstract

Basic hybrid logic extends modal logic with the possibility of naming worlds by means of a distinguished class of atoms (called nominals) and the so-called satisfaction operator, that allows one to state that a given formula holds at the world named a, for some nominal a. Hence, in particular, hybrid formulae include "equality" assertions, stating that two nominals are distinct names for the same world. The treatment of such nominal equalities in proof systems for hybrid logics may induce many redundancies. This paper introduces an internalized tableau system for basic hybrid logic, significantly reducing such redundancies. The calculus enjoys a strong termination property: tableau construction terminates without relying on any specific rule application strategy, and no loopchecking is needed. The treatment of nominal equalities specific of the proposed calculus is briefly compared to other approaches. Its practical advantages are demonstrated by empirical results obtained by use of implemented systems. Finally, it is briefly shown how to extend the calculus to include the global and converse modalities.

XML documents and, more generally, semistructured data, can be seen as labelled graphs. In this paper we set a correspondence between such graphs and the models of a language of hybrid multimodal logic. This allows us to characterize a schema for semistructured data as a formula of hybrid multimodal logic, and instances of the schema (data graphs) as models of this formula. We also investigate how to express in such a logic integrity constraints on semistructured data, in particular some classes of constraints widely considered in the literature. The contribution of this work is twofold: 1) We generalize the notion of schema, by proposing a definition of schema were references are "well typed" (contrary to what happens with DTDs).2) We formalize semistructured data, schema for semistructured data and integrity constraints in a unique framework, namely hybrid multimodal logic.

No abstract

No abstract