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An Axiom System for a Spatial Logic with Convexity

Trybus, Adam

[Thesis]. Manchester, UK: The University of Manchester; 2012.

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Abstract

A spatial logic is any formal language with geometric interpretation. Research on region-based spatial logics, where variables are set to range over certain subsets of geometric space, have been investigated recently within the qualitative spatial reasoning paradigm in AI. We axiomatised the theory of (ROQ(R^2), conv, ≤) , where ROQ(R^2) is the set of regular open rational polygons of the real plane; conv is the convexity property and ≤ is the inclusion relation. We proved soundness and completeness theorems. We also proved several expressiveness results. Additionally, we provide a historical and philosophical overview of the topic and present contemporary results relating to affine spatial logics.

Bibliographic metadata

Type of resource:
Content type:
Form of thesis:
Type of submission:
Degree type:
Doctor of Philosophy
Degree programme:
PhD Computer Science
Publication date:
Location:
Manchester, UK
Total pages:
147
Abstract:
A spatial logic is any formal language with geometric interpretation. Research on region-based spatial logics, where variables are set to range over certain subsets of geometric space, have been investigated recently within the qualitative spatial reasoning paradigm in AI. We axiomatised the theory of (ROQ(R^2), conv, ≤) , where ROQ(R^2) is the set of regular open rational polygons of the real plane; conv is the convexity property and ≤ is the inclusion relation. We proved soundness and completeness theorems. We also proved several expressiveness results. Additionally, we provide a historical and philosophical overview of the topic and present contemporary results relating to affine spatial logics.
Thesis main supervisor(s):
Thesis advisor(s):
Language:
en

Institutional metadata

University researcher(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:154840
Created by:
Trybus, Adam
Created:
30th January, 2012, 22:23:37
Last modified by:
Trybus, Adam
Last modified:
1st June, 2012, 13:01:56

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