More on the decidability of mereological theories

Hsing-chien Tsai



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 theories by adding the fusion axiom schema. Most of the proofs to be presented in this paper take finite lattices as the base models when applying the refined method. However, I shall also point out the limitation of this kind of reduction and make some observations and conjectures concerning the decidability of stronger mereological theories.


mereology; mereological theories; part-whole relation; decidability; undecidability

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Casati, R., and A.C. Varzi 1999, Parts and Places, The MIT Press. Clay, R.E., 1974, “Relation of Leśniewski’s Mereology to Boolean Algebras’, Journal of Symbolic Logic 39: 638–648.

Enderton, H.B., 1972, A Mathematical Introduction to Logic, San Diego: Academic Press.

Grzegorcyk, A., 1955, “The systems of Leśniewski in relation to contemporary logical research”, Studia Logica 3: 77–95.

Monk, J.D., 1976, Mathematical Logic, New York: Springer-Verlag.

Simons, P., 1987, Parts: A Study in Ontology, Oxford: Clarendon Press. Tarski, A., 1949, “Arithmetical classes and types of Boolean algebras”, Bull. Amer. Math. Soc 55: 64.

Tarski, A., 1956, “On the foundations of Boolean algebra’, pages 320–341 in: Logic, Semantics, Metamathematics, Clarendon Press, Oxford.

Tsai, Hsing-chien, 2009, “Decidability of mereological theoreis”, Logic and Logical Philosophy 18: 45–63.

Financed by MNiSW on the basis of agreement no. 706/P-DUN/2018 (dated 10/05/18). Project 1: “Preparation of articles in English for eight editions of the journal Logic and Logical Philosophy over the period 2018–19; Vol. 27, No. 1–4 (2018), Vol. 28, No. 1–4 (2019)”; amount from the DUN grant: 64800 zł. Project 4: “Digitalisation of eight editions of the journal Logic and Logical Philosophy over the period 2018-19; Vol. 27, No. 1–4 (2018), Vol. 28, No. 1–4 (2019)”; amount from the DUN grant: 18600 zł.

ISSN: 1425-3305 (print version)
ISSN: 2300-9802 (electronic version)

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