Geodesic
Equality Logic
Bulletin of the Section of Logic, Tome 49 (2020) no. 3, pp. 291-324.

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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.
Keywords: many-valued logic, equality logic, completness, prelinear equality∆-algebra, prelinear equality∆ logic 
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Ghorbani, Shokoofeh. Equality Logic. Bulletin of the Section of Logic, Tome 49 (2020) no. 3, pp. 291-324. http://geodesic.mathdoc.fr/item/BSL_2020_49_3_a4/

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