The logic determined by Smiley’s matrix for Anderson and Belnap’s first-degree entailment logic

DOI10.1080/11663081.2016.1153930zbMath1398.03109OpenAlexW2480359299MaRDI QIDQ4586153

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Publication date: 12 September 2018

Published in: Journal of Applied Non-Classical Logics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/11663081.2016.1153930

zbMATH Keywords

many-valued logicsmodal logicsrelevant logicsfour-valued logicsSmiley's four-element matrix

Mathematics Subject Classification ID

Modal logic (including the logic of norms) (03B45) Many-valued logic (03B50) Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47) Paraconsistent logics (03B53)

Related Items (5)

EF4, EF4-M and EF4-Ł: A companion to BN4 and two modal four-valued systems without strong Łukasiewicz-type modal paradoxes ⋮ Correspondence analysis and automated proof-searching for first degree entailment ⋮ A class of implicative expansions of Belnap-Dunn logic in which Boolean negation is definable ⋮ A variant with the variable-sharing property of Brady's 4-valued implicative expansion BN4 of Anderson and Belnap's logic FDE ⋮ Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values

Uses Software

• MaTest

Cites Work

• An interpretation of Łukasiewicz's 4-valued modal logic
• The value of the four values
• Intuitive semantics for first-degree entailments and `coupled trees'
• Partiality and its dual
• Reasoning with logical bilattices
• Entailment and relevance¹
• The non-relevant De Morgan minimal logic in Routley-Meyer semantics with no designated points
• What is strict implication?
• A Lattice of Implicative Extensions of Regular Kleene's Logics
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