Concepts as Modalities in Description Logics

Abstract

Motivated by the colloquial language term of a “glass gummy bear”, an additional type of concept composition for description logics is suggested. This composition type is then axiomatically formalized and called concept generalization. Consistency of the formalization is checked. By proving axiom K and Go ̈del rule, it is shown that this logic is in fact a multi-modal logic. Concepts could be both modal operators and predicate symbols. A Kripke semantics is presented (the adequacy is future work). In this semantics, the TBox axioms hold for any view, assertions in the ABox hold for the natural view (a selected world in the Kripke structure) only. The relationship to other formalisms is outlined. Further examples are discussed at the end.

Leibniz on Reasoning about Impossible Concepts

“…To make it more readable, a binary operator was used instead of : This means, a "veggie burger" is translated into veggie burger. See [3] for a closer look on the still tentative logic applied to the "veggie burger" knowledge base.…”

“…For example, a "possible car" 3 car could be a car-like vehicle that we only see from distance and therefore cannot exactly identify. 3 It could also be a bus, for example. The modal operator "necessary" 2 has no equivalent as a generalization concept.…”