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  1.  13
    Decidability of General Extensional Mereology.Hsing-Chien Tsai - 2013 - Studia Logica 101 (3):619-636.
    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 (...)
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  2.  27
    Decidability of mereological theories.Hsing-Chien Tsai - 2009 - Logic and Logical Philosophy 18 (1):45-63.
    Mereological theories are theories based on a binary predicate ‘being a part of’. It is believed that such a predicate must at least define a partial ordering. A mereological theory can be obtained by adding on top of the basic axioms of partial orderings some of the other axioms posited based on pertinent philosophical insights. Though mereological theories have aroused quite a few philosophers’ interest recently, not much has been said about their meta-logical properties. In this paper, I will look (...)
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  3.  16
    A Comprehensive Picture of the Decidability of Mereological Theories.Hsing-Chien Tsai - 2013 - Studia Logica 101 (5):987-1012.
    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 (...)
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  4.  17
    More on The Decidability of Mereological Theories.Hsing-Chien Tsai - 2011 - Logic and Logical Philosophy 20 (3):251-265.
    Quite a few results concerning the decidability of mereological theories have been given in my previous paper. But many mereological theories are still left unaccounted for. In this paper I will refine a general method for proving the undecidability of a theory and then by making use of it, I will show that most mereological theories that are strictly weaker than CEM are finitely inseparable and hence undecidable. The same results might be carried over to some extensions of those weak (...)
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  5.  27
    Atoms, Gunk, and the Limits of ‘Composition’.Hsing-Chien Tsai & Achille C. Varzi - 2016 - Erkenntnis 81 (2):231-235.
    It is customary practice to define ‘x is composed of the ys’ as ‘x is a sum of the ys and the ys are pairwise disjoint ’. This predicate has played a central role in the debate on the special composition question and on related metaphysical issues concerning the mereological structure of objects. In this note we show that the customary characterization is nonetheless inadequate. We do so by constructing a mereological model where everything qualifies as composed of atoms even (...)
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  6.  7
    General Extensional Mereology is Finitely Axiomatizable.Hsing-Chien Tsai - 2018 - Studia Logica 106 (4):809-826.
    Mereology is the theory of the relation “being a part of”. The first exact formulation of mereology is due to the Polish logician Stanisław Leśniewski. But Leśniewski’s mereology is not first-order axiomatizable, for it requires every subset of the domain to have a fusion. In recent literature, a first-order theory named General Extensional Mereology can be thought of as a first-order approximation of Leśniewski’s theory, in the sense that GEM guarantees that every definable subset of the domain has a fusion, (...)
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  7.  14
    On the Decidability of Axiomatized Mereotopological Theories.Hsing-Chien Tsai - 2015 - Notre Dame Journal of Formal Logic 56 (2):287-306.
    The signature of the formal language of mereotopology contains two predicates $P$ and $C$, which stand for “being a part of” and “contact,” respectively. This paper will deal with the decidability issue of the mereotopological theories which can be formed by the axioms found in the literature. Three main results to be given are as follows: all axiomatized mereotopological theories are separable; all mereotopological theories up to $\mathbf{ACEMT}$, $\mathbf{SACEMT}$, or $\mathbf{SACEMT}^{\prime}$ are finitely inseparable; all axiomatized mereotopological theories except $\mathbf{SAX}$, $\mathbf{SAX}^{\prime}$, (...)
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  8.  2
    An addendum to: “Notes on models of first-order mereological theories”.Hsing-Chien Tsai - 2015 - Logic and Logical Philosophy 24 (4):483.
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  9.  17
    On the effective universality of mereological theories.Nikolay Bazhenov & Hsing-Chien Tsai - 2022 - Mathematical Logic Quarterly 68 (1):48-66.
    Mereological theories are based on the binary relation “being a part of”. The systematic investigations of mereology were initiated by Leśniewski. More recent authors (including Simons, Casati and Varzi, Hovda) formulated a series of first‐order mereological axioms. These axioms give rise to a plenitude of theories, which are of great philosophical interest. The paper considers first‐order mereological theories from the point of view of computable (or effective) algebra. Following the approach of Hirschfeldt, Khoussainov, Shore, and Slinko, we isolate two important (...)
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  10.  8
    Finitely inseparable first-order axiomatized mereotopological theories.Hsing-Chien Tsai - 2013 - Logic and Logical Philosophy 22 (3):347-363.
    This paper will first introduce first-order mereotopological axioms and axiomatized theories which can be found in some recent literature and it will also give a survey of decidability, undecidability as well as other relevant notions. Then the main result to be given in this paper will be the finite inseparability of any mereotopological theory up to atomic general mereotopology (AGEMT) or strong atomic general mereotopology (SAGEMT). Besides, a more comprehensive summary will also be given via making observations about other properties (...)
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  11.  1
    Notes on models of first-order mereological theories.Hsing-Chien Tsai - 2015 - Logic and Logical Philosophy 24 (4).