The variety of RDP-algebras forms the algebraic semantics of RDP-logic, the many-valued propositional logic of the revised drastic product left-continuous triangular norm and its residual. We prove a Priestley duality for finite RDP-algebras, and obtain an explicit description of co- products of finite RDP-algebras. In this light, we give a combinatorial representation of free finitely generated RDP-algebras, which we exploit to construct normal forms, strongest deductive interpolants, and most general unifiers. We prove that RDP-unification is unitary, and that the tautology problem for RDP-logic is coNP-complete.
Finite RDP-algebras : duality, coproducts and logic / S. Bova, D. Valota. - In: JOURNAL OF LOGIC AND COMPUTATION. - ISSN 0955-792X. - 22:3(2012 Jun), pp. 417-450.
Finite RDP-algebras : duality, coproducts and logic
S. BovaPrimo
;D. ValotaUltimo
2012
Abstract
The variety of RDP-algebras forms the algebraic semantics of RDP-logic, the many-valued propositional logic of the revised drastic product left-continuous triangular norm and its residual. We prove a Priestley duality for finite RDP-algebras, and obtain an explicit description of co- products of finite RDP-algebras. In this light, we give a combinatorial representation of free finitely generated RDP-algebras, which we exploit to construct normal forms, strongest deductive interpolants, and most general unifiers. We prove that RDP-unification is unitary, and that the tautology problem for RDP-logic is coNP-complete.Pubblicazioni consigliate
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