José L. Castiglioni

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In this article we provide some results concerning a logic that results from propositional intuitionistic logic when dual negation is added in certain way, producing a paraconsistent logic that has been called da Costa Logic. In particular, we prove the finite model property and strict paraconsistency of this logic.
The (dual) Dold-Kan correspondence says that there is an equivalence of categories K : Ch → Ab between nonnegatively graded cochain complexes and cosimplicial abelian groups, which is inverse to the normalization functor. We show that the restriction of K to DG-rings can be equipped with an associative product and that the resulting functor DGR → Rings,(More)
In [3] we have claimed that finite Heyting algebras with successor only generate a proper subvariety of that of all Heyting algebras with successor, and in particular all finite chains generate a proper subvariety of the latter. As Xavier Caicedo made us notice, this claim is not true. He proved, using techniques of Kripke models, that the intuitionistic(More)
Motivated by an old construction due to J. Kalman that relates distributive lattices and centered Kleene algebras we define the functor K relating integral residuated lattices with 0 (IRL0) with certain involutive residuated lattices. Our work is also based on the results obtained by Cignoli about an adjunction between Heyting and Nelson algebras, which is(More)