An algebraic view of super-Belnap logics

DOI10.1007/s11225-017-9739-7zbMath1417.03175OpenAlexW2741242605MaRDI QIDQ1685564

Umberto Rivieccio, Adam Přenosil, Hugo Albuquerque

Publication date: 14 December 2017

Published in: Studia Logica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11225-017-9739-7

zbMATH Keywords

abstract algebraic logicfour-valued logicLeibniz filtersparaconsistent logicexactly true logicBelnap-Dunn logicKleene logicDe Morgan algebrasFDElogic of paradoxstrong versions of logicssuper-Belnap logics

Mathematics Subject Classification ID

Many-valued logic (03B50) Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47) Paraconsistent logics (03B53) Abstract algebraic logic (03G27)

Related Items (17)

THE LATTICE OF SUPER-BELNAP LOGICS ⋮ Representation of De Morgan and (semi-)Kleene lattices ⋮ Between Hilbert and Gentzen: four-valued consequence systems and structural reasoning ⋮ The strong version of a sentential logic ⋮ Locally tabular \(\neq \) locally finite ⋮ Cut elimination, identity elimination, and interpolation in super-Belnap logics ⋮ The value of the one value: \textit{exactly true logic} revisited ⋮ A deterministic weakening of Belnap-Dunn logic ⋮ Abstract algebraic logic. An introductory chapter ⋮ Logics of upsets of De Morgan lattices ⋮ A sound and complete tableaux calculus for Reichenbach's quantum mechanics logic ⋮ First-Degree Entailment and Structural Reasoning ⋮ A capacity-based framework encompassing Belnap-Dunn logic for reasoning about multisource information ⋮ The \textsc{Fmla-Fmla} axiomatizations of the exactly true and non-falsity logics and some of their cousins ⋮ Hilbert-style axiomatization of first-degree entailment and a family of its extensions ⋮ Countably many weakenings of Belnap-Dunn logic ⋮ Containment logics: algebraic completeness and axiomatization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The proof by cases property and its variants in structural consequence relations
• Selfextensional logics with a conjunction
• Theory of logical calculi. Basic theory of consequence operations
• A Kripke-style semantics for R-mingle using a binary accessibility relation
• The logic of paradox
• Implicational classes of De Morgan lattices
• Lattices of quasivarieties of 3-element algebras
• Algebraic semantics for deductive systems
• The strong version of a sentential logic
• A non-finitely based quasi-variety of De Morgan algebras
• Intuitive semantics for first-degree entailments and `coupled trees'
• Partiality and its dual
• A note on freedom from detachment in the logic of paradox
• Nothing but the truth
• A calculus of antinomics
• COMPATIBILITY OPERATORS IN ABSTRACT ALGEBRAIC LOGIC
• ASSERTIONALLY EQUIVALENT QUASIVARIETIES
• Algebraizable logics
• Coproducts of De Morgan algebras
• Belnap's Four-Valued Logic and De Morgan Lattices
• Subprevarieties versus extensions. Application to the logic of paradox
• Outline of a Theory of Truth
• An infinity of super-Belnap logics
• Assertional logics, truth-equational logics, and the hierarchies of abstract algebraic logic
• Characterizing Belnap's Logic via De Morgan's Laws
• On Priest's logic of paradox
• Lattices With Involution
• On notation for ordinal numbers
• THE LATTICE OF SUPER-BELNAP LOGICS
• Protoalgebraic logics
• Leibniz filters and the strong version of a protoalgebraic logic

This page was built for publication: An algebraic view of super-Belnap logics