Related papers: Coalgebraic Fuzzy geometric logic
Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines…
Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with…
We present generalization of the Bloom variety theorem of ordered algebras in fuzzy setting. We introduce algebras with fuzzy orders which consist of sets of functions which are compatible with particular binary fuzzy relations called fuzzy…
Fuzzy logic programming is a growing declarative paradigm aiming to integrate fuzzy logic into logic programming. One of the most difficult tasks when specifying a fuzzy logic program is determining the right weights for each rule, as well…
The purpose of this paper is to study the algorithm FCM and some of its famous innovations, analyse and discover the method of applying hedge algebra theory that uses algebra to represent linguistic-valued variables, to FCM. Then, this…
Motivated by questions like: which spatial structures may be characterized by means of modal logic, what is the logic of space, how to encode in modal logic different geometric relations, topological logic provides a framework for studying…
The AI community is increasingly putting its attention towards combining symbolic and neural approaches, as it is often argued that the strengths and weaknesses of these approaches are complementary. One recent trend in the literature are…
There is a wide range of modal logics whose semantics goes beyond relational structures, and instead involves, e.g., probabilities, multi-player games, weights, or neighbourhood structures. Coalgebraic logic serves as a unifying semantic…
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…
Answering complex First-Order Logical (FOL) queries on large-scale incomplete knowledge graphs (KGs) is an important yet challenging task. Recent advances embed logical queries and KG entities in the same space and conduct query answering…
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…
Temporal logics are an obvious high-level descriptive companion formalism to dynamical systems which model behavior as deterministic evolution of state over time. A wide variety of distinct temporal logics applicable to dynamical systems…
This paper presents a unified differentiable boolean operator for implicit solid shape modeling using Constructive Solid Geometry (CSG). Traditional CSG relies on min, max operators to perform boolean operations on implicit shapes. But…
We apply residuated structures associated with fuzzy logic to develop certain aspects of information processing in quantum computing from a logical perspective. For this purpose, we introduce an axiomatic system whose natural interpretation…
The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient…
This paper initiates the study of picture fuzzy topological spaces. In order to develop a mechanism to construct picture fuzzy topological spaces, we prove some basic results related to picture fuzzy sets together with the introduction of…
Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in…
Closure operators are very useful tools in several areas of classical mathematics and in general category theory. In fuzzy set theory, fuzzy closure operators have been studied by G. Gerla (1966). These works generally define a fuzzy subset…
A new fuzzy optimization framework that extends FCM causality is proposed. This model utilizes the dynamics to map data into metrics and create a framework that examines logical implication and hierarchy of concepts using a multiplex.…
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.