Abstract
In this paper we characterize the congruences in classes of algebras that properly include varieties of interest for the logic. These algebras are obtained by weakening the main features of Heyting algebras \((H, \wedge , \vee , \rightarrow ,0, 1)\) but retaining most of their algebraic consequences. The residuation property \(z\le x\rightarrow y\) if and only if \(x \wedge z \le y\) is replaced by the condition: if \(z\le x\rightarrow y\) then \(x \wedge z \le y\). Some of further algebraic conditions of Heyting algebras are required.
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This work was supported by Grants CONICET PIP 112-201101-00636 and UNLP 11/X667.
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The author Hernán Javier San Martín declares that there is no conflict of interest.
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Communicated by A. Di Nola.
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San Martín, H.J. On congruences in weak implicative semi-lattices. Soft Comput 21, 3167–3176 (2017). https://doi.org/10.1007/s00500-016-2188-9
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DOI: https://doi.org/10.1007/s00500-016-2188-9