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Erschienen in:
18.05.2016 | Foundations
On congruences in weak implicative semi-lattices
Erschienen in: Soft Computing | Ausgabe 12/2017
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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.