Equality Logic

Shokoofeh Ghorbani

doi:10.18778/0138-0680.2020.14

Authors

Shokoofeh Ghorbani Shahid Bahonar University of Kerman Faculty of Mathematics and Computer Department of Pure Mathematics Kerman, Iran https://orcid.org/0000-0002-3724-8654

DOI:

https://doi.org/10.18778/0138-0680.2020.14

Keywords:

many-valued logic, equality logic, completness, prelinear equality∆-algebra , prelinear equality∆ logic

Abstract

In this paper, we introduce and study a corresponding logic to equality-algebras and obtain some basic properties of this logic. We prove the soundness and completeness of this logic based on equality-algebras and local deduction theorem. We show that this logic is regularly algebraizable with respect to the variety of equality∆-algebras but it is not Fregean. Then we introduce the concept of (prelinear) equality∆-algebras and investigate some related properties. Also, we study ∆-deductive systems of equality∆-algebras. In particular, we prove that every prelinear equality ∆-algebra is a subdirect product of linearly ordered equality∆-algebras. Finally, we construct prelinear equality ∆ logic and prove the soundness and strong completeness of this logic respect to prelinear equality∆-algebras.

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