# Automatic Strengthening of Graph-Structured Knowledge Bases

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## Abstract

We consider the problem of identifying inherited content in knowledge representation structures called *concept graphs (CGraphs)*. A CGraph is a visual representation of a concept; in the following, CGraphs and concepts are used synonymously. A CGraph is a node- and edge-labeled directed graph. Labeled (binary) edges represent relations between nodes, which are considered instances of the concepts in their node labels. CGraphs are arranged in a taxonomy (is-a hierarchy). The taxonomy is a directed acyclic graph, as multiple inheritance is allowed. A taxonomy and set of CGraphs is called a graph-structured knowledge base (GSKB).

A CGraph can inherit content from other CGraphs – intuitively, if *C* and *D* are CGraphs, then *C* may contain content inherited from *D*, i.e. labeled nodes and edges “from *D*” can appear in *C*, if *D* is a direct or indirect superconcept of *C*, or if *C* contains a node being labeled with either *D* or some subclass of *D*. In both cases, *C* is said to refer to *D*.

This paper contains three contributions. First, we describe and formalize the problem from a logical point of view and give a first-order semantics for CGraphs. We show that the identification of inherited content in CGraphs depends on some form of hypothetical reasoning and is thus not a purely deductive inference task, as it requires unsound reasoning. Hence, this inference is different from the standard subsumption checking problem, as known from description logics (DLs) [1]. We show that the *provenance problem* (from where does a logical atom in a CGraph get inherited?) strongly depends on the solution to the *co-reference problem* (which existentials in the first-order axiomatization of concepts as formulas denote identical domain individuals?) We demonstrate that the desired inferences can be obtained from a so-called *strengthened GSKB*, which is an augmented variant of the input GSKB. We present an algorithm which augments and strengthens an input GSKB, using model-theoretic notions. Secondly, we are addressing the problem from a graph-theoretic point of view, as this perspective is closer to the actual implementation. We show that we can identify inherited content by computing so-called *concept coverings,* which induce inherited content from superconcepts by means of *graph morphisms.* We argue that the algorithm solves a challenging (NP-hard) problem. Thirdly, we apply the algorithm to the large-scale biological knowledge base from the AURA project [2], and present a preliminary evaluation of its performance.

## Keywords

Prefer Model Equality Atom Concept Graph Concept Atom Relation Atom## Preview

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