A Natural Deduction System for Sentential Modal Logic

1979 ◽  
Vol 5 ◽  
pp. 611-622
Author(s):  
Howard J. Sobel ◽  
Keyword(s):  
Modal Logic ◽  
Natural Deduction ◽  
Deduction System ◽  
Natural Deduction System

A new S4 classical modal logic in natural deduction

2006 ◽  
Vol 71 (3) ◽  
pp. 799-809 ◽  
Author(s):  
Maria Da Paz N. Medeiros
Keyword(s):  
Modal Logic ◽  
Natural Deduction ◽  
Normalization Procedure ◽  
Deduction System ◽  
Natural Deduction System ◽  
Classical Modal Logic ◽  
New System

AbstractWe show, first, that the normalization procedure for S4 modal logic presented by Dag Prawitz in [5] does not work. We then develop a new natural deduction system for S4 classical modal logic that is logically equivalent to that of Prawitz, and we show that every derivation in this new system can be transformed into a normal derivation.

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.

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