The University of Edinburgh -
Division of Informatics
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Research Paper #593

Title:Functional Lattices for Taxonomical Reasoning
Authors:Levy,J; Agusti,J; Mana,F
Date: 1992
Presented:Submitted to the Thrid International Conference on Principles of Knowledge Representation and REasoning, KR'92.
Abstract:Taken in the abstract, taxonomies, a key subject of knowledge representation languages, are partial order relations and a good way to deal with them is to embed them inside a complete distributive lattice. If we take the semantics as a guide for the design of these languages, nothing suggests the separation made in the syntax of most of them between objects (singletons) and concepts (the rest of sets). On the contrary, it seems natural to define functions and relations operating on all elements of the lattice and not only on objects as frequently happens in KRI. The language TERMCOR presented here is based on three main ideas. Firstly, no distinction is made between concepts (types) and objects (values): we have only one kind of expression to represent both. Secondly, concepts and functions are viewed without distinction as elements of the same reflexive lattice. Reflexivity allows the definition of two powerful recursive operators which we have used to handle with terminological cycles, but losing the decidability property: Thirdly, conceptual taxonomies are represented by sets of conditional subsumptions on which a complete subsumption algorithm operates. As stated below, similar ideas have appeared separatedly in different frameworks; putting these ideas together in TERMCOR we believe to address simply and directly the basic expressivity needs of taxonomic KRL. We have translated some constructs of TF directly to TERMCOR to show this expressivity. Other expressions have no direct translation and we must use the expressivity of our language in other ways as our example shows.

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