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On Generalization of Definitional Equivalence to Languages with Non-Disjoint Signatures

Lefever, Koen and Székely, Gergely (2018) On Generalization of Definitional Equivalence to Languages with Non-Disjoint Signatures. [Preprint]

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Abstract

For simplicity, most of the literature introduces the concept of definitional equivalence only to languages with disjoint signatures. In a recent paper, Barrett and Halvorson introduce a straightforward generalization to languages with non-disjoint signatures and they show that their generalization is not equivalent to intertranslatability in general. In this paper,we show that their generalization is not transitive and hence it is not an equivalence relation. Then we introduce the Andréka and Németi generalization as one of the many equivalent formulations for languages with disjoint signatures. We show that the Andréka-Németi generalization is the smallest equivalence relation containing the Barrett–Halvorson generalization and it is equivalent to intertranslatability even for languages with non-disjoint signatures. Finally,we investigate which definitions for definitional equivalences remain equivalent when we generalize them for theories with non-disjoint signatures.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Lefever, Koenkoen.lefever@vub.be0000-0001-7836-4734
Székely, Gergelyszekely.gergely@renyi.mta.hu
Keywords: First-Order Logic, Definability Theory, Definitional Equivalence, Logical Translation, Logical Interpretation
Subjects: Specific Sciences > Mathematics > Logic
Depositing User: Dr. Koen Lefever
Date Deposited: 24 Feb 2018 17:33
Last Modified: 24 Feb 2018 17:33
Item ID: 14402
Subjects: Specific Sciences > Mathematics > Logic
Date: February 2018
URI: http://philsci-archive.pitt.edu/id/eprint/14402

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