TY - CHAP

T1 - RM and its Nice Properties

AU - Avron, Arnon

N1 - Publisher Copyright:
© 2016, Springer International Publishing Switzerland.

PY - 2016

Y1 - 2016

N2 - Dunn–McCall logic RM is by far the best understood and the most well-behaved logic in the family of logics developed by the school of Anderson and Belnap. However, it is not considered to be a relevant logic by the relevant logicians, since it fails to have the variable-sharing property. Instead, RM is usually characterized as being “semi-relevant,” without explaining what this notion means. In this paper we suggest a plausible definition of semi-relevance, and show that according to it, RM is a strongly maximal semi-relevant logic having a conjunction, a disjunction, and an implication. We also review and prove the most important nice properties of RM, especially strong completeness results about it (the full proofs of which are difficult to find in the literature).

AB - Dunn–McCall logic RM is by far the best understood and the most well-behaved logic in the family of logics developed by the school of Anderson and Belnap. However, it is not considered to be a relevant logic by the relevant logicians, since it fails to have the variable-sharing property. Instead, RM is usually characterized as being “semi-relevant,” without explaining what this notion means. In this paper we suggest a plausible definition of semi-relevance, and show that according to it, RM is a strongly maximal semi-relevant logic having a conjunction, a disjunction, and an implication. We also review and prove the most important nice properties of RM, especially strong completeness results about it (the full proofs of which are difficult to find in the literature).

KW - Degrees of truth

KW - Fuzzy logics

KW - Paraconsistent logics

KW - Relevant logics

KW - Semi-relevance

UR - http://www.scopus.com/inward/record.url?scp=85043980473&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-29300-4_2

DO - 10.1007/978-3-319-29300-4_2

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AN - SCOPUS:85043980473

T3 - Outstanding Contributions to Logic

SP - 15

EP - 43

BT - Outstanding Contributions to Logic

PB - Springer

ER -