Basic Quasi-Boolean Expansions of Relevance Logics

Structural Completeness in Relevance Logics

Studia Logica ◽

10.1007/s11225-015-9644-x ◽

2015 ◽

Vol 104 (3) ◽

pp. 381-387 ◽

Cited By ~ 3

Author(s):

J. G. Raftery ◽

K. Świrydowicz

Keyword(s):

Relevance Logics ◽

Structural Completeness

Some relevance logics from the point of view of relational semantics

Logic Journal of IGPL ◽

10.1093/jigpal/jzw003 ◽

2016 ◽

Vol 24 (3) ◽

pp. 268-287

Author(s):

Katalin Bimbó

Keyword(s):

Point Of View ◽

Relational Semantics ◽

Relevance Logics

Modal and Relevance Logics: 1977

Modern Logic — A Survey ◽

10.1007/978-94-009-9056-2_8 ◽

1981 ◽

pp. 131-151 ◽

Cited By ~ 3

Author(s):

Nuel D. Belnap

Keyword(s):

Relevance Logics

Semantic Discovery for Relevance Logics

Directions in Relevant Logic ◽

10.1007/978-94-009-1005-8_18 ◽

1989 ◽

pp. 241-267 ◽

Cited By ~ 1

Author(s):

Charles G. Morgan

Keyword(s):

Relevance Logics ◽

Semantic Discovery

Gaggle Theory Applied to Intuitionistic, Modal, and Relevance Logics

Logik und Mathematik ◽

10.1515/9783110887792.335 ◽

1995 ◽

pp. 335-368 ◽

Cited By ~ 1

Keyword(s):

Relevance Logics ◽

Gaggle Theory

Algorithmic Correspondence for Relevance Logics I. The Algorithm $$\mathsf {PEARL}$$

10.1007/978-3-030-71430-7_4 ◽

2021 ◽

pp. 163-211

Author(s):

Willem Conradie ◽

Valentin Goranko

Keyword(s):

Relevance Logics

Gentzen formulations of two positive relevance logics

Studia Logica ◽

10.1007/bf02584063 ◽

1981 ◽

Vol 40 (3) ◽

pp. 311-311 ◽

Cited By ~ 1

Author(s):

Aleksandar Kron

Keyword(s):

Relevance Logics ◽

Positive Relevance

Incompleteness for Quantified Relevance Logics

Directions in Relevant Logic ◽

10.1007/978-94-009-1005-8_16 ◽

1989 ◽

pp. 205-225 ◽

Cited By ~ 9

Author(s):

Kit Fine

Keyword(s):

Relevance Logics

Philosophy of Logic ◽

10.1016/b978-044451541-4/50022-1 ◽

2007 ◽

pp. 723-789 ◽

Cited By ~ 7

Keyword(s):

Relevance Logics

RELEVANCE LOGICS AND RELATION ALGEBRAS

The Review of Symbolic Logic ◽

10.1017/s1755020309090145 ◽

2009 ◽

Vol 2 (1) ◽

pp. 102-131 ◽

Cited By ~ 6

Author(s):

KATALIN BIMBÓ ◽

J. MICHAEL DUNN ◽

ROGER D. MADDUX

Keyword(s):

Dynamic Semantics ◽

Relational Semantics ◽

Relation Algebras ◽

Sequent Calculi ◽

Accessibility Relation ◽

Cut Rule ◽

Relevance Logics

Relevance logics are known to be sound and complete for relational semantics with a ternary accessibility relation. This paper investigates the problem of adequacy with respect to special kinds of dynamic semantics (i.e., proper relation algebras and relevant families of relations). We prove several soundness results here. We also prove the completeness of a certain positive fragment of R as well as of the first-degree fragment of relevance logics. These results show that some core ideas are shared between relevance logics and relation algebras. Some details of certain incompleteness results, however, pinpoint where relevance logics and relation algebras diverge. To carry out these semantic investigations, we define a new tableaux formalization and new sequent calculi (with the single cut rule admissible) for various relevance logics.