Related papers: On the relationship between fuzzy logic and four-v…
In this paper we present a propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is…
A classical logic exhibits a threefold inner structure comprising an algebra of propositions `A', a space of ``truth values'' `V', and a distinguished family of mappings `phi' from propositions to truth values. Classically A is a Boolean…
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…
Justification Logics provide a framework for reasoning about justifications and evidences. Most of the accounts of justification logics are crisp in the sense that agent's justifications for a statement is convincing or is not. In this…
This paper mainly focuses on (1) a generalized treatment of fuzzy sets of type $n$, where $n$ is an integer larger than or equal to $1$, with an example, mathematical discussions, and real-life interpretation of the given mathematical…
This paper examines attribute dependencies in data that involve grades, such as a grade to which an object is red or a grade to which two objects are similar. We thus extend the classical agenda by allowing graded, or fuzzy, attributes…
In this paper, we present the interval neutrosophic logics which generalizes the fuzzy logic, paraconsistent logic, intuitionistic fuzzy logic and many other non-classical and non-standard logics. We will give the formal definition of…
This paper presents a five-valued representation of bifuzzy sets. This representation is related to a five-valued logic that uses the following values: true, false, inconsistent, incomplete and ambiguous. In the framework of five-valued…
This paper develops a category-theoretic approach to uncertainty, informativeness and decision-making problems. It is based on appropriate first order fuzzy logic in which not only logical connectives but also quantifiers have fuzzy…
In this article, we describe the fuzzy logic, fuzzy language and algorithms as the basis of fuzzy reasoning, one of the intelligent information processing method, and then describe the general fuzzy reasoning method.
We propose a matrix model for two- and many-valued logic using families of observables in Hilbert space, the eigenvalues give the truth values of logical propositions where the atomic input proposition cases are represented by the…
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…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
The article demonstrates that logic is not necessarily singleton and does not always have the standard interpretation of negation. Appropriate generalizations of logic are suggested. Positive logic and multivalued negation operations are…
Combining symbolic and neural approaches has gained considerable attention in the AI community, as it is often argued that the strengths and weaknesses of these approaches are complementary. One such trend in the literature are weakly…
Transportation Problem is an important aspect which has been widely studied in Operations Research domain. It has been studied to simulate different real life problems. In particular, application of this Problem in NP- Hard Problems has a…
Within the possibilistic approach to uncertainty modeling, the paper presents a modal logical system to reason about qualitative (comparative) statements of the possibility (and necessity) of fuzzy propositions. We relate this qualitative…
In this paper, a short survey about the concepts underlying general logics is given. In particular, a novel rigorous definition of a fuzzy negation as an operation acting on a lattice to render it into a fuzzy logic is presented. According…
The fuzzy modality `probably` is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is…
We explore the problem of explaining observations in contexts involving statements with truth degrees such as `the lift is loaded', `the symptoms are severe', etc. To formalise these contexts, we consider infinitely-valued {\L}ukasiewicz…