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Second-Order Description Logics: Semantics, Motivation, and a Calculus

Eight years ago, Tim Berners-Lee, James Hendler and Ora Lassila published their seminal paper [6] describing the evolution of the current web from a human-processable environment to a machine-processable one. The basic idea was to annotate web resources and give them a machine-processable meaning; the Semantic Web was born. Many efforts have been placed in the last years by the Semantic Web community in the attempt to standardize both the language for representing the content of web resources and the production of annotations/metadata. On the one hand, such efforts successfully led to the affirmation of standard languages for machine-processable representation of web pages content, like the recent W3C recommendation OWL2. On the other hand, it produced the Linked Data initiative: a set of best practices for publishing and connecting data on the Web. These two initiatives are tightly connected. In fact, data published following the Linked Data best practices are interpreted thanks to the ontological layer developed using OWL2. Despite a large effort in annotating and representing the semantic content of a resource (in a semi-automatic way) we see the lack of reasoning engines able to fully exploit such representation power. During the last years highly optimized reasoning engines have been developed for classical deductive reasoning tasks such as subsumption/classification, consistency checking and instance retrieval. At the same time, non-standard reasoning tasks have been proposed in the Description Logics literature as an answer to new issues related to knowledge-based domains especially in retrieval scenarios, ontology design and maintenance and automated negotiation. The most relevant reasoning tasks we may cite are: explanation [18], interpolation [23], concept abduction and concept contraction [10], concept unification [3], concept difference [25], concept similarity [8], concept rewriting [2], negotiation [22], least common subsumer [5], most specific concept [1] and knowledge base completion [4]. For each of the above mentioned tasks a specific algorithmic approach has been proposed and very often only for a particular (sometimes simple) Description Logic. Although the need for such reasoning tasks has been widely recognized, there is not yet a unified view—at least from an algorithmic perspective. Indeed, some of the above mentioned tasks share some properties from a computational point of view and sometimes are very related to each other. Moreover, most of the problems in the cited reasoning tasks are of the form: “Find one or more concept(s) C such that {sentence involving C }” and we are really interested in exhibiting such a concept, not just proving its exProc. 23rd Int. Workshop on Description Logics (DL2010), CEUR-WS 573, Waterloo, Canada, 2010.