Towards a Practical Decision Procedure for Uniform Interpolants of EL-TBoxes - a Proof-Theoretic Approach

14 pages•Published: September 29, 2016

Abstract

We show how the problem of deciding the existence of uniform interpolants of TBoxes formulated in the Description Logic \EL can be divided into three subproblems based on a characterisation of the logical difference between \EL-TBoxes. We propose a proof-theoretic decision procedure for subsumer interpolants of general TBoxes formulated in the Description Logic \EL, solving one of these subproblems. A subsumer interpolant of a TBox depends on a signature and on a concept name. It is a TBox formulated using symbols from the signature only such that, both, it follows from the original TBox and it exactly entails the subsumers formulated in the signature that follow from the concept name \wrt~the original TBox. Our decision procedure first constructs a graph that exactly represents the part of original TBox that is describable using signature symbols only. Subsequently, it is checked whether a graph-representation of the original TBox can be simulated by the constructed graph, in which case a subsumer interpolant exists. We also evaluate our procedure by applying a prototype implementation on several biomedical ontologies.

Keyphrases: Description Logic EL, Gentzen-style proof calculus, Uniform Interpolation

In: Christoph Benzmüller, Geoff Sutcliffe and Raul Rojas (editors). GCAI 2016. 2nd Global Conference on Artificial Intelligence, vol 41, pages 147--160

Links:	https://easychair.org/publications/paper/bmx
	https://doi.org/10.29007/bsqm