An Axiom System for a Spatial Logic with Convexity

Authors:
Adam Trybus
Affiliations:
University of Manchester, United Kingdom, email: trybusa@cs.man.ac.uk
Venue:
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Year:
2010

Citing 2
Cited 0

Constraint Networks of Topological Relations and Convexity

Constraints
First-order qualitative spatial representation languages with convexity

Spatial Cognition and Computation

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Abstract

This paper presents a part of work in progress on axiomatizing a spatial logic with convexity and inclusion predicates (hereinafter called convexity logic), with some intended interpretation over the real plane. More formally, let Lconv,≤ be a language of first order logic and two non-logical primitives: conv (interpreted as a property of a set of being convex) and ≤ (interpreted as the set inclusion relation). We let variables range over regular open rational polygons in the real plane (denoted ROQ(R2)). We call the tuple M = ---where primitives are defined as indicated above ---a standard model. We propose an axiomatization of the theory of M and prove soundness and completeness for this axiomatization.