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On Some Meta-Theoretic Topological Features of the Region Connection Calculus
Journal article   Peer reviewed

On Some Meta-Theoretic Topological Features of the Region Connection Calculus

Nathaniel Gan
Logic and logical philosophy, Vol.32(4), pp.639-669
01/12/2023

Abstract

Arts & Humanities Logic Philosophy Science & Technology Science & Technology - Other Topics
This paper examines several intended topological features of the Region Connection Calculus (RCC) and argues that they are either underdetermined by the formal theory or given by the complement axiom. Conditions are identified under which the axioms of RCC are satisfied in topological models under various set restrictions. The results generalise previous results in the literature to non-strict topological models and across possible interpretations of connection. It is shown that the intended interpretation of connection and the alignment of self-connection with topological connection are underdetermined by the axioms of RCC, which suggests that additional axioms are necessary to secure these features. It is also argued that the complement axiom gives RCC models much of their topological structure. In particular, the incompatibility of RCC with interiors is argued to be given by the complement axiom.
url
https://doi.org/10.12775/LLP.2023.002View
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