scholarly journals Natural Deduction System for the Logic of Binary Relations Based on the Algebraic Tradition

2020 ◽  
Author(s):  
Márcia Rosana Cerioli ◽  
Leandro Oliva Suguitani ◽  
Jorge Petrúcio Viana
Keyword(s):  
Natural Deduction ◽  
Binary Relations ◽  
Deduction System ◽  
Natural Deduction System ◽  
The University

We present a proper natural deduction system (ND-system) for a logic of binary relations based on the algebraic tradition. Our system is an evolution from [W. W. Wadge. TCR 5, The University of Warwick, 1975]. We point out some aspects where Wadge's formalism fails as an ND-system and fix them all.

scholarly journals GÖDEL’S NOTRE DAME COURSE

2016 ◽  
Vol 22 (4) ◽  
pp. 469-481 ◽  
Author(s):  
MILOŠ ADŽIĆ ◽  
KOSTA DOŠEN
Keyword(s):  
Proof Theory ◽  
Natural Deduction ◽  
Deduction System ◽  
General Proof ◽  
Natural Deduction System ◽  
University Of Notre Dame ◽  
Proper Perspective ◽  
The University

AbstractThis is a companion to a paper by the authors entitled “Gödel’s natural deduction,” which presented and made comments about the natural deduction system in Gödel’s unpublished notes for the elementary logic course he gave at the University of Notre Dame in 1939. In that earlier paper, which was itself a companion to a paper that examined the links between some philosophical views ascribed to Gödel and general proof theory, one can find a brief summary of Gödel’s notes for the Notre Dame course. In order to put the earlier paper in proper perspective, a more complete summary of these interesting notes, with comments concerning them, is given here.

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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