Studia Logica 101 (5):987-1012 (2013)

Authors
Hsing-Chien Tsai
National Chung Cheng University
Abstract
The signature of the formal language of mereology contains only one binary predicate which stands for the relation “being a part of” and it has been strongly suggested that such a predicate must at least define a partial ordering. Mereological theories owe their origin to Leśniewski. However, some more recent authors, such as Simons as well as Casati and Varzi, have reformulated mereology in a way most logicians today are familiar with. It turns out that any theory which can be formed by using the reformulated mereological axioms or axiom schemas is in a sense a subtheory of the elementary theory of Boolean algebras or of the theory of infinite atomic Boolean algebras. It is known that the theory of partial orderings is undecidable while the elementary theory of Boolean algebras and the theory of infinite atomic Boolean algebras are decidable. In this paper, I will look into the behaviors in terms of decidability of those mereological theories located in between. More precisely, I will give a comprehensive picture of the said issue by offering solutions to the open problems which I have raised in some of my papers published previously
Keywords Mereology  Boolean algebra  Decidability  Undecidability  Separability  Inseparability
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DOI 10.1007/s11225-012-9405-z
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References found in this work BETA

Parts: A Study in Ontology.Peter Simons - 1987 - Oxford University Press.
Mathematical Logic.Joseph R. Shoenfield - 1967 - Reading, Mass., Addison-Wesley Pub. Co..
Undecidable Theories.Alfred Tarski - 1968 - Amsterdam: North-Holland Pub. Co..

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Citations of this work BETA

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.
On the Decidability of Axiomatized Mereotopological Theories.Hsing-Chien Tsai - 2015 - Notre Dame Journal of Formal Logic 56 (2):287-306.
Notes on Models of First-Order Mereological Theories.Hsing-Chien Tsai - 2015 - Logic and Logical Philosophy 24 (4).

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