Related papers: Distributive abstract logics and the Esakia dualit…
In this paper we make a contribution to the unification of formal models of defeasible reasoning. We present several translations between formal argumentation frameworks and nonmonotonic logics for reasoning with plausible assumptions. More…
We review the close relationship between abstract machines for (call-by-name or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing the…
We introduce and study the Scott adjunction, relating accessible categories with directed colimits to topoi. Our focus is twofold, we study both its applications to formal model theory and its geometric interpretation. From the geometric…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
In this article we determine the implicational fragments of most of the known subintuitionistic logics.
We connect Priestley duality for distributive lattices and its generalization to distributive meet-semilattices to Hofmann-Mislove-Stralka duality for semilattices. Among other things, this involves consideration of various morphisms…
We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz…
We identify and highlight certain landmark results in Samson Abramsky's work which we believe are fundamental to current developments and future trends. In particular, we focus on the use of (i) topological duality methods to solve problems…
We present three different functional interpretations of intuitionistic linear logic ILL and show how these correspond to well-known functional interpretations of intuitionistic logic IL via embeddings of IL into ILL. The main difference…
We provide, explicitly, equivalences and dual equivalences between categories of abstract quadratic forms theories and subcategories of multifields and multirings, that will bring new perspectives and methods to the abstract theories of…
This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science. Our target audience are graduate students and researchers in mathematics and computer science. Our aim is to get in a…
This paper presents a novel treatment of the canonical extension of a bounded lattice, in the spirit of thetheory of natural dualities. At the level of objects, this can be achieved by exploiting the topological representation due to M.…
The notion of support provides an analogue of Stone duality, relating lattices to topological spaces. This note aims to explain in lattice theoretic terms what has been developed in the context of triangulated categories. In particular, the…
In a previous work we introduced a non-associative non-commutative logic extended by multimodalities, called subexponentials, licensing local application of structural rules. Here, we further explore this system, considering a classical…
Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic…
Plonka sums consist of an algebraic construction similar, in some sense to direct limits, which allows to represent classes of algebras defined by means of regular identities (namely those equations where the same set of variables appears…
In this paper, a subclass of bounded distributive lattices, that is, finitely disjunctive distributive lattices (FDD-lattices) have been introduced. Then we apply it to establish a Stone duality for Lawson compact algebraic L-domains.…
In [Ben13], the notion of logically distributive category has been introduced to provide a sound and complete semantics to multi-sorted first-order logical theories based on intuitionistic logic. In this note, it will be shown that the…
Intuitionistic dependence logic was introduced by Abramsky and Vaananen (2009) as a variant of dependence logic under a general construction of Hodges' (trump) team semantics. It was proven that there is a translation from intuitionistic…
It is shown that propositional intuitionistic logic is the maximal (with respect to expressive power) abstract logic satisfying a certain topological property reminiscent of compactness, the Tarski union property and preservation under…