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Preserving filtering unification by adding compatible operations to some Heyting algebras. (English) Zbl 1423.06031
Summary: We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law $$\neg x \vee\neg\neg x = 1$$, 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 [the authors, J. Mult.-Val. Log. Soft Comput. 28, No. 2–3, 189–215 (2017; Zbl 1398.08007)] on direct products of $$l$$-algebras and filtering unification. We consider examples of frontal Heyting algebras, in particular Heyting algebras with the successor, $$\gamma$$ and $$G$$ operations as well as expansions of some commutative integral residuated lattices with successor operations.
##### MSC:
 06D20 Heyting algebras (lattice-theoretic aspects) 03G25 Other algebras related to logic
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