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Finitely Inseparable First-Order Axiomatized Mereotopological Theories

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Tsai H.-c.

Logic and Logical Philosophy

2013

vol. 22

issue 3

347-363

This paper will first introduce first-order mereotopological ax- ioms and axiomatized theories which can be found in some recent litera- ture 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 stronger than undecidability.

More on The Decidability of Mereological Theories

100%

Tsai H.-c.

Logic and Logical Philosophy

2011

vol. 20

issue 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 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.

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2 Logic and Logical Philosophy

2 Tsai H.-c.

1 2013

1 2011

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Finitely Inseparable First-Order Axiomatized Mereotopological Theories

More on The Decidability of Mereological Theories