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Conference Paper

On uniform word problems involving bridging operators on distributive lattices


Sofronie-Stokkermans,  Viorica
Automation of Logic, MPI for Informatics, Max Planck Society;
Programming Logics, MPI for Informatics, Max Planck Society;

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Sofronie-Stokkermans, V. (2002). On uniform word problems involving bridging operators on distributive lattices. In Automated Reasoning with Analytic and Related Methods: International Conference, TABLEAUX 2002 (pp. 235-250). Berlin, Germany: Springer.

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In this paper we analyze some fragments of the universal theory of distributive lattices with many sorted bridging operators. Our interest in such algebras is motivated by the fact that, in description logics, numerical features are often expressed by using maps that associate numerical values to sets (more generally, to lattice elements). We first establish a link between satisfiability of universal sentences with respect to algebraic models and satisfiability with respect to certain classes of relational structures. We use these results for giving a method for translation to clause form of universal sentences, and provide some decidability results based on the use of resolution or hyperresolution. Links between hyperresolution and tableau methods are also discussed, and a tableau procedure for checking satisfiability of formulae of type $t_1 \leq t_2$ is obtained by using a hyperresolution calculus.