José Luis Castiglioni

Compatible Operations on Residuated Lattices

This work extend to residuated lattices the results of [7]. It also provides a possible generalization to this context of frontal operators in the sense of [9].Let L be a residuated lattice, and f : Lk → L a function. We give a necessary and sufficient condition for f to be compatible with respect to every congruence on L. We use this characterization of compatible functions in order to prove that the variety of residuated lattices is locally affine complete.We study some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P(x, y) and Q(x, y) on a residuated lattice L which imply that the function

Strict paraconsistency of truth-degree preserving intuitionistic logic with dual negation

{x \mapsto min\{y \in L : P(x, y) \leq Q(x, y)\}}

On a Definition of a Variety of Monadic ℓ-Groups

when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators.

On frontal operators in Hilbert algebras

Let L be a commutative residuated lattice and let f : Lk → L a function. We give a necessary and sufficient condition for f to be compatible with respect to every congruence on L. We use this characterization of compatible functions in order to prove that the variety of commutative residuated lattices is locally affine complete. Then, we find conditions on a not necessarily polynomial function P(x, y) in L that imply that the function x ↦ min{y є L | P(x, y) ⪯ y} is compatible when defined. In particular, Pn(x, y) = yn → x, for natural number n, defines a family, Sn, of compatible functions on some commutative residuated lattices. We show through examples that S1> and S2, defined respectively from P1 and P2, are independent as operations over this variety; i.e. neither S1 is definable as a polynomial in the language of L enriched with S2 nor S2 in that enriched with S1.

On some Classes of Heyting Algebras with Successor that have the Amalgamation Property

Fil: Castiglioni, Jose Luis. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - La Plata; Argentina

The left adjoint of Spec from a category of lattice-ordered groups

In this paper, we study the universal central extension of a Lie–Rinehart algebra and we give a description of it. Then we study the lifting of automorphisms and derivations to central extensions. We also give a definition of a non-abelian tensor product in Lie–Rinehart algebras based on the construction of Ellis of non-abelian tensor product of Lie algebras. We relate this non-abelian tensor product to the universal central extension.

On products of posets and coproducts of KM-algebras

In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL0 of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor