On the logic foundation of fuzzy reasoning
Information Sciences: an International Journal
A triangular-norm-based propositional fuzzy logic
Fuzzy Sets and Systems - Logic and algebra
Integrated semantics and logic metric spaces
Fuzzy Sets and Systems - Logic and algebra
The extensions Ln of the formal system Ln and their completeness
Information Sciences: an International Journal
Formalized theory of general fuzzy reasoning
Information Sciences—Informatics and Computer Science: An International Journal
Unified forms of fully implicational restriction methods for fuzzy reasoning
Information Sciences: an International Journal
Unified full implication algorithms of fuzzy reasoning
Information Sciences: an International Journal
Triple I method based on pointwise sustaining degrees
Computers & Mathematics with Applications
Unified forms of Triple I method
Computers & Mathematics with Applications
A new theory consistency index based on deduction theorems in several logic systems
Fuzzy Sets and Systems
Consistency degrees of theories in some systems of propositional fuzzy logic
Fuzzy Sets and Systems
A Duality Theorem for Quantitative Semantics
Electronic Notes in Theoretical Computer Science (ENTCS)
Information Sciences: an International Journal
Computers & Mathematics with Applications
Fast decision procedure for propositional Dummett logic based on a multiple premise tableau calculus
Information Sciences: an International Journal
Some properties of fuzzy reasoning in propositional fuzzy logic systems
Information Sciences: an International Journal
Rough Truth Degrees of Formulas and Approximate Reasoning in Rough Logic
Fundamenta Informaticae
Rough Truth Degrees of Formulas and Approximate Reasoning in Rough Logic
Fundamenta Informaticae
Theory of truth degrees in three valued formed system RSL
RSKT'12 Proceedings of the 7th international conference on Rough Sets and Knowledge Technology
Hierarchical structure and applications of fuzzy logical systems
International Journal of Approximate Reasoning
Generalized Bosbach and Riečan states on nucleus-based-Glivenko residuated lattices
Archive for Mathematical Logic
On the rough consistency measures of logic theories and approximate reasoning in rough logic
International Journal of Approximate Reasoning
Truth degree analysis of fuzzy reasoning
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Approximation reasoning models based on random variables sequence
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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In this paper, we introduce the concept of the degree of the truth in the framework of so called many-valued propositional logic systems with the intention of measuring to what extent a given formula is true. Such a concept can indeed induce, in a very natural way, the degree of the similarity as well as to induce a pseudo-metric among formulas as the 'graded' version of the notion of the logical equivalence. The basic properties of such induced logic metric space hence are investigated in this paper. We further introduce different concepts of the degree of the divergence and the degree of the consistency in order to grade the extent of the consistency of a logic theory. To the end, all the basic logic notions are graded. Lastly, we propose in this paper three patterns of 'approximate reasoning' so far as the many-valued propositional logic systems are concerned. Hence, we can claim that we have laid the foundation for the ''quantitative logic''. Since this theory has touched upon several key concepts of similarity, comparison, measurements, etc. in information theory, we are convinced that the theory may have profound impact in contemporary information technology. In addition, quantitative logic can be regarded as a highly representative example of mathematics of uncertainty capable of handling vagueness.