Comparative concept similarity over Minspaces: Axiomatisation and Tableaux Calculus

TL;DR

This paper develops an axiomatisation and tableaux calculus for the logic of comparative concept similarity over minspaces, providing a formal framework and decision procedure for qualitative similarity comparisons.

Contribution

It introduces a novel axiomatisation and tableaux calculus for CSL over minspaces, linking semantics to preferential structures and enabling decision procedures.

Findings

Semantic equivalence with preferential structures

Axiomatisation of CSL over Minspaces

Decision procedure via tableaux calculus

Abstract

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.