Preserving Filtering Unification by Adding Compatible Operations to Some Heyting Algebras

• Autorzy: Wojciech Dzik , Sándor Radeleczki
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2016
• Tom: 45
• Numer: 3/4

Daty

wydano

2016-12-30

Twórcy

autor

Wojciech Dzik

• University of Silesia, Institute of Mathematics

autor

Sándor Radeleczki

• University of Miskolc, Institute of Mathematics

Bibliografia

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Identyfikatory

DOI

10.18778/0138-0680.45.3.4.08