Consistency of Finite Theory in Three Types of Many-Valued Propositional Logic Systems

2009 ◽  
Author(s):  
Li-Feng Li
Keyword(s):  
Propositional Logic ◽  
Finite Theory ◽  
Logic Systems

scholarly journals Consistency Degrees of Theories in Łukasiewicz Fuzzy andn-Valued Propositional Logic Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-7
Author(s):  
Jiancheng Zhang
Keyword(s):  
Propositional Logic ◽  
Necessary Conditions ◽  
New Concepts ◽  
Polar Index ◽  
Sufficient And Necessary Conditions ◽  
Logic Systems ◽  
Completeness Theorems ◽  
Truth Degrees

By means of theory of truth degrees of formulas, according to deduction theorems and completeness theorems, the new concepts of consistency degrees and polar index for general theories in Łukasewicz fuzzy andn-valued propositional logic systems are introduced. Moreover, sufficient and necessary conditions for a theoryΓto be consistent, inconsistent, and fully divergent are obtained. Finally, some important properties of truth degrees of formulas are proposed.

Hilbert-style proof Calculus for Propositional Logic in ABC notation

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Propositional Logic ◽  
Inference Rule ◽  
Modus Ponens ◽  
Axiomatic System ◽  
First Contact

All nine axioms and a single inference rule of logic (Modus Ponens) within the Hilbert axiomatic system are presented using capital letters (ABC) in order to familiarize the beginner student in hers/his first contact with the topic.

Reducing Separation Formulas to Propositional Logic

2003 ◽  
Author(s):  
Ofer Strichman ◽  
Sanjit A. Seshia ◽  
Randal E. Bryant
Keyword(s):  
Propositional Logic
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