Keywords:many-valued logic, equality logic, completness, prelinear equality∆-algebra , prelinear equality∆ logic
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.
 W. J. Blok, D. Pigozzi, Abstract algebraic logic and the deduction theorem (2001), URL: https://orion.math.iastate.edu/dpigozzi/papers/aaldedth.pdf
 R. Borzooei, F. Zebardast, M. Aaly Kologani, Some types of filters in equality algebras, Categories and General Algebraic Structures with Applications, vol. 7 (Special Issue on the Occasion of Banaschewski's 90th Birthday (II)) (2017), pp. 33–55, DOI: http://dx.doi.org/10.1007/s00500-005-0534-4
 J. R. Büchi, T. M. Owens, Skolem rings and their varieties, [in:] The Collected Works of J. Richard Büchi, Springer (1990), pp. 161–221, DOI: http://dx.doi.org/10.1007/978-1-4613-8928-6-11
 M. Dyba, V. Novák, EQ-logics: Non-commutative fuzzy logics based on fuzzy equality, Fuzzy Sets and Systems, vol. 172(1) (2011), pp. 13–32, DOI: http://dx.doi.org/10.1016/j.fss.2010.11.011
 S. Jenei, L. Kóródi, On the variety of equality algebras, [in:] Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology, Atlantis Press (2011), pp. 153–155, DOI: http://dx.doi.org/10.2991/eusat.2011.1
 V. Novák, EQ-algebras: primary concepts and properties, [in:] Proceedings of International Joint Czech Republic-Japan & Taiwan-Japan Symposium, Kitakyushu, Japan, August 2006 (2006), pp. 219–223.
 R. Suszko, Non-Fregean logic and theories, Analele Universitatii Bucuresti, Acta Logica, vol. 11 (1968), pp. 105–125.
 J. T. Wang, X. L. Xin, Y. B. Jun, Very true operators on equality algebras, Journal of Computational Analysis and Applications, vol. 24(3) (2018), DOI: http://dx.doi.org/10.1515/math-2016-0086
 M. Zarean, R. A. Borzooei, O. Zahiri, On state equality algebras, Quasi-groups and Related Systems, vol. 25(2) (2017), pp. 307–326.
How to Cite
Copyright (c) 2020 Bulletin of the Section of Logic
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.