The lattice of modal logics: an algebraic investigation

DOI10.2307/2273184zbMath0436.03010OpenAlexW1983453585MaRDI QIDQ3875896

Willem J. Blok

Publication date: 1980

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2273184

zbMATH Keywords

modal logicKripke semanticssubdirectly irreduciblemodal operatorvarieties of modal algebras

Mathematics Subject Classification ID

Lattices of varieties (08B15) Modal logic (including the logic of norms) (03B45) Other algebras related to logic (03G25)

Related Items

THE LATTICE OF SUPER-BELNAP LOGICS ⋮ Bjarni Jónsson's contributions in algebra ⋮ What is the upper part of the lattice of bimodal logics? ⋮ On the canonicity of Sahlqvist identities ⋮ Algebraic aspects of deduction theorems ⋮ Matching topological and frame products of modal logics ⋮ On varieties of cylindric algebras with applications to logic ⋮ Varieties of complex algebras ⋮ The structure of lattices of subframe logics ⋮ Total tense algebras and symmetric semiassociative relation algebras ⋮ An axiomatization of the modal theory of the veiled recession frame ⋮ Involutions defined by monadic terms ⋮ Ideal Related Algebras and Their Logics Extended Abstract ⋮ Tense logics over lattices ⋮ Universal algebraic methods for non-classical logics ⋮ Varieties with equationally definable principal congruences ⋮ Deduction theorem in congruential modal logics ⋮ The lattice of varieties of modal algebras is not strongly atomic ⋮ In memory of Willem Johannes Blok 1947-2003 ⋮ Willem Blok and modal logic ⋮ How many varieties of cylindric algebras are there ⋮ Some Computational Constraints in Epistemic Logic ⋮ Mathematical modal logic: A view of its evolution ⋮ Post complete and 0-axiomatizable modal logics ⋮ Some descending chains of incomplete modal logics ⋮ CANONICAL FORMULAS FOR wK4 ⋮ Topological soft algebra and its application ⋮ Algebraization of quantifier logics, an introductory overview ⋮ Interpolation in weakly transitive modal logics ⋮ Bounded lattice expansions ⋮ Erdős Graphs Resolve Fine's Canonicity Problem ⋮ A splitting logic in NExt(KTB) ⋮ Kripke incomplete logics containing KTB ⋮ Decidability of Some Interpolation Properties for Weakly Transitive Modal Logics ⋮ Varieties of semiassociative relation algebras and tense algebras ⋮ AN ALGEBRAIC APPROACH TO CANONICAL FORMULAS: INTUITIONISTIC CASE ⋮ Unnamed Item ⋮ On the structure of varieties with equationally definable principal congruences. I ⋮ A note on the fixed point for the polynomials of a Boolean algebra with an operator of endomorphism ⋮ On the Semilattice of Modal Operators and Decompositions of the Discriminator ⋮ An effective representation for finitely generated free interior algebras ⋮ An almost general splitting theorem for modal logic

Cites Work

• Some embedding theorems for modal logic
• An incomplete logic containing S4
• An incompleteness theorem in modal logic
• Algebraic semantics for modal logics I
• Algebras Whose Congruence Lattices are Distributive.