A Comprehensive Picture of the Decidability of Mereological Theories

Studia Logica 101 (5):987-1012 (2013)
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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References found in this work BETA
Wilfrid Hodges, Model Theory. Stanford Encyclopedia of Philosophy.
Paul Hovda (2009). What Is Classical Mereology? Journal of Philosophical Logic 38 (1):55 - 82.
Andrzej Pietruszczak (2005). Pieces of Mereology. Logic and Logical Philosophy 14 (2):211-234.

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Gabriel Uzquiano (2011). Mereological Harmony. In Karen Bennett & Dean Zimmerman (eds.), Oxford Studies in Metaphysics. Oxford University Press.
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