Natural deduction system for three-valued Heyting’s logic

2017 ◽  
Vol 72 (3) ◽  
pp. 133-136 ◽  
Author(s):  
Ya. I. Petrukhin
Keyword(s):  
Natural Deduction ◽  
Deduction System ◽  
Natural Deduction System

scholarly journals COMPLETENESS VIA CORRESPONDENCE FOR EXTENSIONS OF THE LOGIC OF PARADOX

2012 ◽  
Vol 5 (4) ◽  
pp. 720-730 ◽  
Author(s):  
BARTELD KOOI ◽  
ALLARD TAMMINGA
Keyword(s):  
Correspondence Analysis ◽  
Natural Deduction ◽  
Correspondence Theory ◽  
Truth Table ◽  
Deduction System ◽  
Natural Deduction System ◽  
Logic Of Paradox

AbstractTaking our inspiration from modal correspondence theory, we present the idea of correspondence analysis for many-valued logics. As a benchmark case, we study truth-functional extensions of the Logic of Paradox (LP). First, we characterize each of the possible truth table entries for unary and binary operators that could be added to LP by an inference scheme. Second, we define a class of natural deduction systems on the basis of these characterizing inference schemes and a natural deduction system for LP. Third, we show that each of the resulting natural deduction systems is sound and complete with respect to its particular semantics.

scholarly journals Normalization as a consequence of cut elimination

2009 ◽  
Vol 86 (100) ◽  
pp. 27-34
Author(s):  
Mirjana Borisavljevic
Keyword(s):  
Intuitionistic Logic ◽  
Natural Deduction ◽  
Cut Elimination ◽  
Deduction System ◽  
Normalization Theorem ◽  
Natural Deduction System

Pairs of systems, which consist of a system of sequents and a natural deduction system for some part of intuitionistic logic, are considered. For each of these pairs of systems the property that the normalization theorem is a consequence of the cut-elimination theorem is presented.

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