Bonds Between $$L$$ -Fuzzy Contexts Over Different Structures of Truth-Degrees

2015 ◽  
pp. 81-96
Author(s):  
Jan Konecny
Keyword(s):  
Truth Degrees

scholarly journals Truth Degrees Theory and Approximate Reasoning in 3-Valued Propositional Pre-Rough Logic

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yingcang Ma ◽  
Juanjuan Zhang ◽  
Huan Liu
Keyword(s):  
Approximate Reasoning ◽  
Logical Formula ◽  
Concept Of Truth ◽  
Truth Degrees ◽  
Truth Degree

By means of the function induced by a logical formulaA, the concept of truth degree of the logical formulaAis introduced in the 3-valued pre-rough logic in this paper. Moreover, similarity degrees among formulas are proposed and a pseudometric is defined on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in 3-value logic pre-rough logic is established.

Rough Truth Degrees of Formulas and Approximate Reasoning in Rough Logic

2011 ◽  
Vol 107 (1) ◽  
pp. 67-83 ◽  
Author(s):  
Yanhong She ◽  
Xiaoli He ◽  
Guojun Wang
Keyword(s):  
Approximate Reasoning ◽  
Truth Degrees

Theory of Truth Degrees in Four Valued Pre-rough Logic

2012 ◽  
Vol 4 (15) ◽  
pp. 462-469
Author(s):  
Yingcang Ma ◽  
Huan Liu
Keyword(s):  
Truth Degrees

Fuzzy Logic and Mathematics

2017 ◽  
Author(s):  
Radim Belohlavek ◽  
Joseph W. Dauben ◽  
George J. Klir
Keyword(s):  
Fuzzy Logic ◽  
Common Ground ◽  
Fundamental Principle ◽  
Paradigm Shifts ◽  
Human Beings ◽  
Truth Values ◽  
Logical Connectives ◽  
Broad Variety ◽  
And Mathematics ◽  
Truth Degrees

The term “fuzzy logic” (FL) is a generic one, which stands for a broad variety of logical systems. Their common ground is the rejection of the most fundamental principle of classical logic—the principle of bivalence—according to which each declarative sentence has exactly two possible truth values—true and false. Each logical system subsumed under FL allows for additional, intermediary truth values, which are interpreted as degrees of truth. These systems are distinguished from one another by the set of truth degrees employed, its algebraic structure, truth functions chosen for logical connectives, and other properties. The book examines from the historical perspective two areas of research on fuzzy logic known as fuzzy logic in the narrow sense (FLN) and fuzzy logic in the broad sense (FLB), which have distinct research agendas. The agenda of FLN is the development of propositional, predicate, and other fuzzy logic calculi. The agenda of FLB is to emulate commonsense human reasoning in natural language and other unique capabilities of human beings. In addition to FL, the book also examines mathematics based on FL. One chapter in the book is devoted to overviewing successful applications of FL and the associated mathematics in various areas of human affairs. The principal aim of the book is to assess the significance of FL and especially its significance for mathematics. For this purpose, the notions of paradigms and paradigm shifts in science, mathematics, and other areas are introduced and employed as useful metaphors.

Mathematics Based on Fuzzy Logic

2017 ◽  
Author(s):  
Radim Bělohlávek ◽  
Joseph W. Dauben ◽  
George J. Klir
Keyword(s):  
Fuzzy Logic ◽  
Mathematical Analysis ◽  
Classical Logic ◽  
Mathematical Reasoning ◽  
Narrow Sense ◽  
And Mathematics ◽  
Truth Degrees

Mathematical reasoning is governed by the laws of classical logic, based on the principle of bivalence. With the acceptance of intermediate truth degrees, the situation changed substantially. This chapter begins with a characterization of mathematics based on fuzzy logic, an identification of principal issues of its development, and an outline of this development. It then examines the role of fuzzy logic in the narrow sense for developing mathematics based on fuzzy logic and the main approaches developed toward its foundations. Next, some selected areas of mathematics based on fuzzy logic are presented, such as the theory of sets and relations, algebra, topology, quantities and mathematical analysis, probability, and geometry. The chapter concludes by examining various semantic questions regarding fuzzy logic and mathematics based on it.

M: AN APPROXIMATE REASONING SYSTEM

1993 ◽  
Vol 07 (03) ◽  
pp. 431-440
Author(s):  
QINPING ZHAO ◽  
BO LI
Keyword(s):  
Solution Algorithm ◽  
Approximate Reasoning ◽  
Inference Rules ◽  
Multivalued Logic ◽  
Reasoning System ◽  
Sld Resolution ◽  
Truth Value ◽  
Truth Degrees

A system of multivalued logical equations and its solution algorithm are put forward in this paper. Based on this work we generalize SLD-resolution into multivalued logic and establish the corresponding truth value calculus. As a result, M, an approximate reasoning system, is built. We present the language and inference rules of M. Furthermore, we analyse inconsistency of assignments to truth degrees and give the solving strategies of M.

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