Related papers: Fuzzy Topological Systems
The paper explores categorical interconnections between lattice-valued Relational systems and algebras of Fitting's lattice-valued modal logic. We define lattice-valued boolean systems, and then we study co-adjointness, adjointness of…
The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…
This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…
We develop category-theoretic framework for universal homogeneous objects, with some applications in the theory of Banach spaces, linear orderings, and in topology of compact spaces.
In this paper we present the N-norms/N-conorms in neutrosophic logic and set as extensions of T-norms/T-conorms in fuzzy logic and set. Also, as an extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic Topologies.
We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism spaces of this category, and prove that it is equivalent to an existing algebraic spherical category.
This is a short survey illustrating some of the essential aspects of the theory of canonical extensions. In addition some topological results about canonical extensions of lattices with additional operations in finitely generated varieties…
We define a symmetric monoidal category modelling fuzzy concepts and fuzzy conceptual reasoning within G\"ardenfors' framework of conceptual (convex) spaces. We propose log-concave functions as models of fuzzy concepts, showing that these…
In the paper we define the convergence of compact fuzzy sets as a convergence of alpha-cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy variables and show relations with…
We introduce a two-sort weighted modal logic for possibilistic reasoning with fuzzy formal contexts. The syntax of the logic includes two types of weighted modal operators corresponding to classical necessity ($\Box$) and sufficiency…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
The definition of the complement of a fuzzy subset is algebraic in nature and when it is used in the context of fuzzy topological spaces it does not share any similarity with the usual property of topological spaces that the complement of…
We describe a notion of categorical model for unitless fragments of (multiplicative) linear logic. The basic definition uses promonoidal categories, and we also give an equivalent elementary axiomatisation.
We introduce the notion of a G\"odel fibration, which is a fibration categorically embodying both the logical principle of traditional Skolemization (we can exchange the order of quantifiers paying the price of a functional) and the…
We present a logic for reasoning with if-then formulas which involve constants for rational truth degrees from the unit interval. We introduce graded semantic and syntactic entailment of formulas. We prove the logic is complete in Pavelka…
Limits and colimits of diagrams, defined by maps between sets, are universal constructions fundamental in different mathematical domains and key concepts in theoretical computer science. Its importance in semantic modeling is described by…
We construct a left semi-model category of "marked strict $\infty$-categories" for which the fibrant objects are those whose marked arrows satisfy natural closure properties and are weakly invertible. The canonical model structure on strict…
The Distributional Compositional Categorical (DisCoCat) model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings…
Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable…
In a recent paper as an alternative to models based on the notion of ideal mathematical point, characterized by a property of separatedness, we considered a viewpoint based on the notion of continuous change, making use of elements of a…