CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
On the relation of resolution and tableaux proof systems for description logics
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Automated theorem proving by resolution in non-classical logics
Annals of Mathematics and Artificial Intelligence
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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 t1 驴 t2 is obtained by using a hyperresolution calculus.