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Some remarks on distributive semilattices

Sergio A. Celani, Ismael Calomino (2013)

Commentationes Mathematicae Universitatis Carolinae

In this paper we shall give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we will present some new ones through annihilators and relative maximal filters. We shall also simplify the topological representation for distributive semilattices given in Celani S.A., Topological representation of distributive semilattices, Sci. Math. Japonicae online 8 (2003), 41–51, and show that the meet-relations are closed under composition....

States on basic algebras

Ivan Chajda, Helmut Länger (2017)

Mathematica Bohemica

States on commutative basic algebras were considered in the literature as generalizations of states on MV-algebras. It was a natural question if states exist also on basic algebras which are not commutative. We answer this question in the positive and give several examples of such basic algebras and their states. We prove elementary properties of states on basic algebras. Moreover, we introduce the concept of a state-morphism and characterize it among states. For basic algebras which are the certain...

Strong completeness of the Lambek Calculus with respect to Relational Semantics

Szabolcs Mikulás (1993)

Banach Center Publications

In [vB88], Johan van Benthem introduces Relational Semantics (RelSem for short), and states Soundness Theorem for Lambek Calculus (LC) w.r.t. RelSem. After doing this, he writes: "it would be very interesting to have the converse too", i.e., to have Completeness Theorem. The same question is in [vB91, p. 235]. In the following, we state Strong Completeness Theorems for different versions of LC.

Strong functors and interleaving fixpoints in game semantics

Pierre Clairambault (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We describe a sequent calculus μLJ with primitives for inductive and coinductive datatypes and equip it with reduction rules allowing a sound translation of Gödel’s system T. We introduce the notion of a μ-closed category, relying on a uniform interpretation of open μLJ formulas as strong functors. We show that any μ-closed category is a sound model for μLJ. We then turn to the construction of a concrete μ-closed category based on Hyland-Ong game semantics. The model relies on three main ingredients:...

Structuration cognitive et logique intrinsèque

Pascal Boldini (1993)

Mathématiques et Sciences Humaines

À travers l'étude d'un modèle de représentation des connaissances comme catégorie de faisceaux de traits localement définis ; ce texte montre que la théorie des topoï permet de décrire formellement l'émergence d'une logique intrinsèque à partir d'une approche relationnelle, qu'elle soit structurale ou cognitive. On peut alors caractériser mathématiquement le défaut d'intensionnalité des modèles classiques, et montrer qu'une solution est dans la mathématisation de structures entièrement relationnelles....

Subdirectly irreducible MV-algebras

Hernando Gaitan (2003)

Czechoslovak Mathematical Journal

In this note we characterize the one-generated subdirectly irreducible MV-algebras and use this characterization to prove that a quasivariety of MV-algebras has the relative congruence extension property if and only if it is a variety.

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