Abstract

( † = corresponding author) We address two problems in underspecified graph-structured knowledge bases (GSKBs): the co-reference and the provenance problem. Both prob-lems are important for a variety of reasons. The for-mer asks “Which existentially quantified variables in different but related axioms of a GSKB possibly denote identical domain individuals?”, and the lat-ter “From which axioms in a GSKB is a piece of knowledge getting derived? ” To decide the former, we need to be able to prove equality between dif-ferent variables – a GSKB in which this is possible is called a strenghtened GSKB, and an underspec-ified GSKB otherwise. The latter occur naturally in many knowledge acquisition contexts, and are also easier to author. We hence present an algo-rithm which rewrites an underspecified GSKB into a strengthened GSKB, by virtue of Skolemization and addition of equality atoms such that the co-reference information can be drawn from it. This enlarges the logical theory (the deductive closure) of the GSKB and strengthens its inferential power, hence affecting the provenance information. Our algorithm is model-theoretic in nature and exploits a novel class of desirable, preferred models, which capture the desired co-references. The algorithm is a logical reconstruction of an implemented algo-rithm that we successfully applied to a large-scale biological knowledge base, in which it identified more that 22,000 equality atoms. 1