Related papers: Fuzzy Topological Systems
There are two kinds of bisimulation, namely crisp and fuzzy, between fuzzy structures such as fuzzy automata, fuzzy labeled transition systems, fuzzy Kripke models and fuzzy interpretations in description logics. Fuzzy bisimulations between…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
The main objective of this paper is to develop a new semantic Network structure, based on the fuzzy sets theory, used in Artificial Intelligent system in order to provide effective on-line assistance to users of new technological systems.…
We introduce two-dimensional logics based on \L{}ukasiewicz and G\"{o}del logics to formalize paraconsistent fuzzy reasoning. The logics are interpreted on matrices, where the common underlying structure is the bi-lattice (twisted) product…
Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…
Categorization systems are widely studied in psychology, sociology, and organization theory as information-structuring devices which are critical to decision-making processes. In the present paper, we introduce a sound and complete…
Cartesian differential categories were introduced to provide an abstract axiomatization of categories of differentiable functions. The fundamental example is the category whose objects are Euclidean spaces and whose arrows are smooth maps.…
A detailed study of graded frame, graded fuzzy topological system and fuzzy topological space with graded inclusion is already done in our earlier paper. The notions of graded fuzzy topological system and fuzzy topological space with graded…
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
We define a stable model semantics for fuzzy propositional formulas, which generalizes both fuzzy propositional logic and the stable model semantics of classical propositional formulas. The syntax of the language is the same as the syntax…
Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for…
Fuzzy closure spaces are an extension of classical closure spaces in topology, where the concept of closure is defined in terms of fuzzy sets. This article introduces interior operators and neighborhood systems in fuzzy closure spaces.…
For a topological space it is well-known that the associated closure and interior operators provide equivalent descriptions of set-theoretic topology; but it is not generally true in other categories, consequently it makes sense to define…
Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator [18] was introduced to formalise programs running in parallel. In other direction, other authors proposed a systematic…
We introduce Riesz Logic, whose models are abelian lattice ordered groups, which generalise Riesz spaces (vector lattices), and show soundness and completeness. Our motivation is to provide a logic for distributional semantics of natural…
This article serves as a preliminary introduction to the design of a new, open-source applied and computational category theory framework, named Categorica, built on top of the Wolfram Language. Categorica allows one to configure and…
The goal of this article is to emphasize the role of cubical sets in enriched categories theory and infinity-categories theory. We show in particular that categories enriched in cubical sets provide a convenient way to describe many…
Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
We develop the basic theory of projective modules and splitting in the more general setting of systems. Systems provide a common language for most tropical algebraic approaches including supertropical algebra, hyperrings (specifically…