Return to search

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 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.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:553496
Date January 2012
CreatorsTrybus, Adam
ContributorsPratt-Hartmann, Ian
PublisherUniversity of Manchester
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttps://www.research.manchester.ac.uk/portal/en/theses/an-axiom-system-for-a-spatial-logic-with-convexity(cd19b55f-b4e5-4782-90f2-d3c0ad79891b).html

Page generated in 0.0016 seconds