Automated theorem proving by resolution in non-classical logics

Abstract

This paper is an overview of a variety of results, all centered around a common theme, namely embedding of non-classical logics into first order logic and resolution theorem proving. We present several classes of non-classical logics, many of which are of great practical relevance in knowledge representation, which can be translated into tractable and relatively simple fragments of classical logic. In this context, we show that refinements of resolution can often be used successfully for automated theorem proving, and in many interesting cases yield optimal decision procedures

Interpolation in local theory extensions

“…The combination of Chem, AChem and BioChem is inconsistent (we wrongly added to Γ 1 the constraint reaction ⊆ oxydation instead of oxydation ⊆ reaction). This can be proved as follows: By results in [14] (p.156 and p.166) the combination of Chem, AChem and BioChem is inconsistent if and only if…”

Interpolation in Local Theory Extensions

“…This can be proved as follows: By results in [14] (p.156 and p.166) the combination of Chem, AChem and BioChem is inconsistent if and only if…”

Locality and Applications to Subsumption Testing in EL and Some of its Extensions

“…In [20] we studied the link between TBox subsumption in E L and uniform word problems in the corresponding classes of semilattices with monotone functions. We now show that these results naturally extend to the description logic E L + .…”

“…In [20] we proved that the algebraic counterpart of the description logic E L -namely the class of semilattices with monotone operators -has a local axiomatization -S L ∪ Mon(Σ ) -i.e. an axiomatization with the property that for every set G of ground clauses…”