scholarly journals Algebras of Relations and Relevance Logic

2008 ◽  
Vol 19 (2) ◽  
pp. 305-321 ◽  
Author(s):  
S. Mikulas
Keyword(s):  
Relevance Logic ◽  
Algebras Of Relations

On Algebras of Relations with Operations of Left and Right Reflexive Product

2020 ◽  
Vol 41 (2) ◽  
pp. 160-167 ◽  
Author(s):  
D. A. Bredikhin
Keyword(s):  
Algebras Of Relations ◽  
Left And Right

RELEVANCE LOGIC AND THE CALCULUS OF RELATIONS

2010 ◽  
Vol 3 (1) ◽  
pp. 41-70 ◽  
Author(s):  
ROGER D. MADDUX
Keyword(s):  
Propositional Logic ◽  
Relevance Logic ◽  
Binary Relations ◽  
Classical Propositional Logic

Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.

scholarly journals POSITIVE FRAGMENTS OF RELEVANCE LOGIC AND ALGEBRAS OF BINARY RELATIONS

2010 ◽  
Vol 4 (1) ◽  
pp. 81-105 ◽  
Author(s):  
ROBIN HIRSCH ◽  
SZABOLCS MIKULÁS
Keyword(s):  
Equational Theory ◽  
Relevance Logic ◽  
Binary Relations ◽  
Finitely Based ◽  
Similarity Type ◽  
Relation Composition

We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.

Note on algebraic models for relevance logic

1990 ◽  
Vol 36 (6) ◽  
pp. 535-540 ◽  
Author(s):  
Josep M. Font ◽  
Gonzalo Rodríguez
Keyword(s):  
Relevance Logic ◽  
Algebraic Models

Multiplicative conjunction and an algebraic meaning of contraction and weakening

1998 ◽  
Vol 63 (3) ◽  
pp. 831-859 ◽  
Author(s):  
A. Avron
Keyword(s):  
Classical Logic ◽  
Linear Logic ◽  
Substructural Logics ◽  
Interesting Property ◽  
Relevance Logic ◽  
Proper Subset ◽  
Algebraic Structures ◽  
Elimination Rule ◽  
First Case ◽  
Soundness And Completeness

AbstractWe show that the elimination rule for the multiplicative (or intensional) conjunction Λ is admissible in many important multiplicative substructural logics. These include LLm (the multiplicative fragment of Linear Logic) and RMIm (the system obtained from LLm by adding the contraction axiom and its converse, the mingle axiom.) An exception is Rm (the intensional fragment of the relevance logic R, which is LLm together with the contraction axiom). Let SLLm and SRm be, respectively, the systems which are obtained from LLm and Rm by adding this rule as a new rule of inference. The set of theorems of SRm is a proper extension of that of Rm, but a proper subset of the set of theorems of RMIm. Hence it still has the variable-sharing property. SRm has also the interesting property that classical logic has a strong translation into it. We next introduce general algebraic structures, called strong multiplicative structures, and prove strong soundness and completeness of SLLm relative to them. We show that in the framework of these structures, the addition of the weakening axiom to SLLm corresponds to the condition that there will be exactly one designated element, while the addition of the contraction axiom corresponds to the condition that there will be exactly one nondesignated element (in the first case we get the system BCKm, in the second - the system SRm). Various other systems in which multiplicative conjunction functions as a true conjunction are studied, together with their algebraic counterparts.

Relevance logic, classical logic, and disjunctive syllogism

1975 ◽  
Vol 27 (6) ◽  
pp. 361-376 ◽  
Author(s):  
John A. Barker
Keyword(s):  
Classical Logic ◽  
Relevance Logic ◽  
Disjunctive Syllogism

Categorical Propositions In Relevance Logic

1989 ◽  
pp. 197-203
Author(s):  
John Bacon
Keyword(s):  
Relevance Logic
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