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Title: An axiom system for a spatial logic with convexity
Author: Trybus, Adam
ISNI:       0000 0004 2720 138X
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2012
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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.
Supervisor: Pratt-Hartmann, Ian Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: logic ; mathematical logic ; spatial logic ; convexity ; axiomatization