Decidability of General Extensional Mereology

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

Authors
Hsing-Chien Tsai
National Chung Cheng University
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
Keywords Mereology  Boolean algebra  Decidability  General extensional mereology  Classical extensional mereology  Classical mereology
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s11225-012-9400-4
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 47,330
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Parts: A Study in Ontology.Peter Simons - 1987 - 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.

View all 12 references / Add more references

Citations of this work BETA

Mereology Then and Now.Rafał Gruszczyński & Achille C. Varzi - 2015 - Logic and Logical Philosophy 24 (4):409.

Add more citations

Similar books and articles

Analytics

Added to PP index
2012-07-25

Total views
52 ( #172,173 of 2,291,076 )

Recent downloads (6 months)
1 ( #832,027 of 2,291,076 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature