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arXiv: 0902.0899

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Comparative concept similarity over Minspaces: Axiomatisation and Tableaux Calculus

Régis Alenda (  Corresponding author ) 1, Nicola Olivetti 1, Camilla Schwind 2

(2009-02-02)

We study the logic of comparative concept similarity $\CSL$ introduced by Sheremet, Tishkovsky, Wolter and Zakharyaschev to capture a form of qualitative similarity comparison. In this logic we can formulate assertions of the form " objects A are more similar to B than to C". The semantics of this logic is defined by structures equipped by distance functions evaluating the similarity degree of objects. We consider here the particular case of the semantics induced by \emph{minspaces}, the latter being distance spaces where the minimum of a set of distances always exists. It turns out that the semantics over arbitrary minspaces can be equivalently specified in terms of preferential structures, typical of conditional logics. We first give a direct axiomatisation of this logic over Minspaces. We next define a decision procedure in the form of a tableaux calculus. Both the calculus and the axiomatisation take advantage of the reformulation of the semantics in terms of preferential structures.

1:	Laboratoire des Sciences de l'Information et des Systèmes (LSIS)
	CNRS : UMR6168 – Arts et Métiers ParisTech – Université Paul Cézanne - Aix-Marseille III – Université de la Méditerranée - Aix-Marseille II – Université de Provence - Aix-Marseille I – Université Sud Toulon Var
2:	Laboratoire d'informatique Fondamentale de Marseille (LIF)
	CNRS : UMR6166 – Université de la Méditerranée - Aix-Marseille II – Université de Provence - Aix-Marseille I

Subject

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Computer Science/Artificial Intelligence

Keyword(s): Tableaux proving – Comparative similarity Logic

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From: Camilla Schwind <>

Submitted on: Thursday, 5 February 2009 12:53:53

Updated on: Thursday, 5 February 2009 13:55:53