Preserving Filtering Unification by Adding Compatible Operations to Some Heyting Algebras

Wojciech Dzik; Sándor Radeleczki

doi:10.18778/0138-0680.45.3.4.08

Authors

Wojciech Dzik University of Silesia, Institute of Mathematics
Sándor Radeleczki University of Miskolc, Institute of Mathematics

DOI:

https://doi.org/10.18778/0138-0680.45.3.4.08

Keywords:

filtering unification, compatible operation, intuitionistic logic, Heyting algebra, residuated lattice

Abstract

We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x ⋁ ¬¬x = 1, preserves filtering (or directed) unification, that is, the property that for every two unifiers there is a unifier more general then both of them. Contrary to that, often adding new operations to algebras results in changing the unification type. To prove the results we apply the theorems of [9] on direct products of l-algebras and filtering unification. We consider examples of frontal Heyting algebras, in particular Heyting algebras with the successor, γ and G operations as well as expansions of some commutative integral residuated lattices with successor operations.

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