A set-based reasoner for the description logic \shdlssx (Extended Version)

We present a \ke-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic \dlssx (\shdlssx, for short). Our application solves the main TBox and ABox reasoning problems for \shdlssx. In particular, it solves the consistency problem for \shdlssx-knowledge bases represented in set-theoretic terms, and a generalization of the \emph{Conjunctive Query Answering} problem in which conjunctive queries with variables of three sorts are admitted. The reasoner, which extends and optimizes a previous prototype for the consistency checking of \shdlssx-knowledge bases (see \cite{cilc17}), is implemented in \textsf{C++}. It supports \shdlssx-knowledge bases serialized in the OWL/XML format, and it admits also rules expressed in SWRL (Semantic Web Rule Language).Comment: arXiv admin note: text overlap with arXiv:1804.11222, arXiv:1707.07545, arXiv:1702.0309

Deduction by combining semantic tableaux and integer programming

. In this paper we propose to extend the current capabilities of automated reasoning systems by making use of techniques from integer programming. We describe the architecture of an automated reasoning system based on a Herbrand procedure (enumeration of formula instances) on clauses. The input are arbitrary sentences of first-order logic. The translation into clauses is done incrementally and is controlled by a semantic tableau procedure using unification. This amounts to an incremental polynomial CNF transformation which at the same time encodes part of the tableau structure and, therefore, tableau-specific refinements that reduce the search space. Checking propositional unsatisfiability of the resulting sequence of clauses can either be done with a symbolic inference system such as the Davis-Putnam procedure or it can be done using integer programming. If the latter is used a number of advantages become apparent. Introduction In this paper we propose to extend the current capabilit..

The CIFF Proof Procedure for Abductive Logic Programming with Constraints: Theory, Implementation and Experiments

We present the CIFF proof procedure for abductive logic programming with constraints, and we prove its correctness. CIFF is an extension of the IFF proof procedure for abductive logic programming, relaxing the original restrictions over variable quantification (allowedness conditions) and incorporating a constraint solver to deal with numerical constraints as in constraint logic programming. Finally, we describe the CIFF system, comparing it with state of the art abductive systems and answer set solvers and showing how to use it to program some applications. (To appear in Theory and Practice of Logic Programming - TPLP)