Interval-valued fuzzy set theory is an increasingly popular extension of fuzzy set theory where traditional [0, 1]-valued membership degrees are replaced by intervals in [0, 1] that approximate the (unknown) membership degrees. To construct suitable graded logical connectives in this extended setting, it is both natural and appropriate to “reuse” ingredients from classical fuzzy set theory. In ...

Abstract Inferentialism is a theory in the philosophy of language which claims that meanings expressions are constituted by inferential roles or relations. Instead traditional model-theoretic semantics, it naturally lends itself to proof-theoretic where meaning understood terms inference rules with proof system. Most work semantics has focused on logical constants, comparatively little non-logi...

In order to analyze the logical foundation of fuzzy reasoning, this paper first introduces the concept of generalized roots of theories in Łukasiewicz propositional fuzzy logic Łuk, Gödel propositional fuzzy logic Göd, Product propositional fuzzy logic P, and nilpotent minimum logic NM (the R0-propositional fuzzy logic L ). Next, it is proved that all consequences of a theory C, named D(C), are...

Distributional representations have recently been proposed as a general-purpose representation of natural language meaning, to replace logical form. There is, however, one important difference between logical and distributional representations: Logical languages have a clear semantics, while distributional representations do not. In this paper, we propose a semantics for distributional represen...

Models of fuzzy Petri net (FPN) are defined based on generating rules of knowledge base and the Petri nets semantics description of logical rules are presented. Two kinds of reasoning patterns are considered. First, the beliefs of initial propositions are known and their beliefs of noninitial propositions need to be computed. Second, the beliefs of initial propositions are known and the beliefs...

Algebraical fixpoint theory is an invaluable instrument for studying semantics of logics. For example, all major semantics of logic programming, autoepistemic logic, default logic and more recently, abstract argumentation have been shown to be induced by the different types of fixpoints defined in approximation fixpoint theory (AFT). In this paper, we add a new type of fixpoint to AFT: a ground...