Compositionality, implicational logics, and theories of grammar

1990 ◽  
Vol 13 (4) ◽  
pp. 383-392 ◽  
Author(s):  
Glyn Morrill ◽  
Bob Carpenter
Keyword(s):  
Implicational Logics

Implicational logics in natural deduction systems

1982 ◽  
Vol 47 (1) ◽  
pp. 184-186 ◽  
Author(s):  
E.G.K. López-Escobar
Keyword(s):  
Natural Deduction ◽  
Short Note ◽  
Direct Proof ◽  
Modus Ponens ◽  
Implicational Logics

In 1959 M. Dummett [3] introduced the logic LC obtained by adding the axiom ACpqCqp to the formalization of the intuitionistic prepositional calculus having modus ponens and substitution as its rules of inference. Later on R. A. Bull [1] showed, by quite a roundabout way, that the implicational theses of LC were precisely the theses of the implicational calculus obtained by adding the axiom CCCpqrCCCqprr to the system of positive implication. In 1964 Bull [2] gave another proof, this time using results of Birkhoff concerning subdirectly reducible algebras.The aim of this short note is to emphasize that the use of Gentzen's natural deduction systems (see Prawitz [4]) allows us to give a much more direct proof.

On structural completeness of implicational logics

Studia Logica ◽  
1991 ◽  
Vol 50 (2) ◽  
pp. 275-297 ◽  
Author(s):  
Piotr Wojtylak
Keyword(s):  
Structural Completeness ◽  
Implicational Logics

scholarly journals Computing interpolants in implicational logics

2006 ◽  
Vol 142 (1-3) ◽  
pp. 125-201 ◽  
Author(s):  
Makoto Kanazawa
Keyword(s):  
Implicational Logics

Deduction theorems for weak implicational logics

Studia Logica ◽  
1982 ◽  
Vol 41 (2-3) ◽  
pp. 95-108 ◽  
Author(s):  
M. W. Bunder
Keyword(s):  
Implicational Logics

scholarly journals Super-Łukasiewicz implicational logics

1978 ◽  
Vol 72 ◽  
pp. 127-133 ◽  
Author(s):  
Yuichi Komori
Keyword(s):  
Propositional Logic ◽  
Point Of View ◽  
The Other ◽  
Other Hand ◽  
Implicational Logics

In the traditional study of Łukasiewicz propositional logic, the finite-valued or infinite-valued linearly ordered model exists at the start, and then the axiomatization of the set of all formulas valid in its model are studied. On the other hand, we are in a point of view such that the set of provable formulas is important and models are no more than means to characterize the set.

A Complete Semantics for Implicational Logics

1981 ◽  
Vol 27 (23-24) ◽  
pp. 381-383 ◽  
Author(s):  
Robert E. Kirk
Keyword(s):  
Implicational Logics
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