Decidability of General Extensional Mereology

Studia Logica 101 (3):619-636 (2013)
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Abstract

The signature of the formal language of mereology contains only one binary predicate P which stands for the relation “being a part of”. Traditionally, P must be a partial ordering, that is, ${\forall{x}Pxx, \forall{x}\forall{y}((Pxy\land Pyx)\to x=y)}$ and ${\forall{x}\forall{y}\forall{z}((Pxy\land Pyz)\to Pxz))}$ are three basic mereological axioms. The best-known mereological theory is “general extensional mereology”, which is axiomatized by the three basic axioms plus the following axiom and axiom schema: (Strong Supplementation) ${\forall{x}\forall{y}(\neg Pyx\to \exists z(Pzy\land \neg Ozx))}$ , where Oxy means ${\exists z(Pzx\land Pzy)}$ , and (Fusion) ${\exists x\alpha \to \exists z\forall y(Oyz\leftrightarrow \exists x(\alpha \land Oyx))}$ , for any formula α where z and y do not occur free. In this paper, I will show that general extensional mereology is decidable, and will also point out that the decidability of the first-order approximation of the theory of complete Boolean algebras can be shown in the same way

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Hsing-Chien Tsai
National Chung Cheng University

Citations of this work

Mereology.Achille C. Varzi - 2016 - Stanford Encyclopedia of Philosophy.
Mereology then and now.Rafał Gruszczyński & Achille C. Varzi - 2015 - Logic and Logical Philosophy 24 (4):409–427.

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References found in this work

Parts: a study in ontology.Peter M. Simons - 1987 - New York: Oxford University Press.
Model theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
What Is Classical Mereology?Paul Hovda - 2009 - Journal of Philosophical Logic 38 (1):55 - 82.

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