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Page 1304 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews
|[Simon, Andras} (H-AOS; Budapest) Undecidable varieties of semilattice-ordered semigroups, of Boolean algebras with operators, and logics extending Lambek calculus. (English summary) Bull.  ...  Among the corollaries to the main result is that the variety of all Boolean algebras with an associative binary operator has an undecidable equational theory. S.  ...

Multi-Sorted Residuation [chapter]

Wojciech Buszkowski
2014 Lecture Notes in Computer Science
with lattice and boolean operations).  ...  Generalized Lambek Calculus GL involves a finite number of basic operations (with an arbitrary number of arguments) and their residual operations [7] .  ...  The ordered algebras A s are always posets, but some of them can also admit semilattice, lattice, boolean or Heyting operations.  ...

Relevant and substructural logics [chapter]

Greg Restall
2006 Handbook of the History of Logic
This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1  ...  Early antecedents of the frame semantics for substructural logics can be found in Jónnson and Tarski's work on the representation of Boolean algebras with operators [141, 142] .  ...  Then relevant logics are truly systems of modal logic extending classical propositional logic with two modal or intensional operators, ∼ (a one-place operator) and → (a two-place operator).  ...

Relevance Logic [chapter]

J. Michael Dunn, Greg Restall
2002 Handbook of Philosophical Logic
Relevance (and relevant) logic has lost one of its most original and productive proponents. J. Michael Dunn Indiana University Greg Restall Macquarie University  ...  These include Richard Routley and Alasdair Urquhart and especially Nuel D. Belnap, Jr. and Robert K. Meyer, and of course Alan Ross Anderson, to whose memory I dedicate this essay.  ...  The semantic structures of relevance logics have close cousins in the models for the Lambek Calculus and in Relation algebras. Let's consider relation algebras first.  ...

Page 191 of Mathematical Reviews Vol. 28, Issue Index [page]

Mathematical Reviews
varieties of semilattice-ordered semigroups, of Boolean algebras with operators, and logics extending Lambek calculus.  ...  (English summary) 96i:20075 Németi, Istvan (with Sain, Ildiko; Simon, Andras) Undecidability of the equational theory of some classes of residuated Boolean algebras with operators.  ...

Most simple extensions of FL_e are undecidable [article]

Nikolaos Galatos, Gavin St. John
2020 arXiv   pre-print
All known structural extensions of the substructural logic FL_e, Full Lambek calculus with exchange/commutativity, (corresponding to subvarieties of commutative residuated lattices axiomatized by {∨, ·  ...  An even bigger class of extensions is shown to have undecidable deducibility problem (the corresponding varieties of residuated lattices have undecidable word problem); actually with very few exceptions  ...  Substructural logics are defined as extensions of the Full Lambek calculus FL and include among others classical, intuitionistic, linear, relevance, bunched-implication and many-valued logics.  ...

Page 1363 of Mathematical Reviews Vol. 28, Issue Index [page]

Mathematical Reviews
varieties of semilattice-ordered semigroups, of Boolean algebras with operators, and logics extending Lambek calculus.  ...  Comer) 96c:03090 03D35 (03C05, 08B05) — (with Németi, Istvan; Sain, Ildik6) Undecidability of the equational theory of some classes of residuated Boolean algebras with operators.  ...

18. Mathematical Linguistics [chapter]

Trends in Linguistics
Second, traditional boolean algebras are of course IBAs and SIBRs -let us denote them by B.  ...  Therefore, Another way of weakening the Boolean structure is to consider meet semilattices of linear subspaces.  ...