An Axiom System for a Spatial Logic with Convexity
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Adam Trybus, PhD
brianervinmamaril@gmail.com
The University of Manchester
Trybus' Works
An Axiom System for a Spatial Logic with Convexity
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... Read More
ETD Test 20
ETD Test 20
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.
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