Search Results - "Galatos, Nikolaos"

Gluing Residuated Lattices by Galatos, Nikolaos, Ugolini, Sara

“…We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or…”
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The structure of generalized BI-algebras and weakening relation algebras by Galatos, Nikolaos, Jipsen, Peter

“…Generalized bunched implication algebras (GBI-algebras) are defined as residuated lattices with a Heyting implication, and are positioned between Boolean…”
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Unilinear residuated lattices: axiomatization, varieties and FEP by Galatos, Nikolaos, Zhuang, Xiao

“…We characterize all residuated lattices that have height equal to 3 and show that the variety they generate has continuum-many subvarieties. More generally, we…”
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Residuated frames with applications to decidability by GALATOS, NIKOLAOS, JIPSEN, PETER

“…Residuated frames provide relational semantics for substructural logics and are a natural generalization of Kripke frames in intuitionistic and modal logic,…”
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Algebraic proof theory for substructural logics: Cut-elimination and completions by Ciabattoni, Agata, Galatos, Nikolaos, Terui, Kazushige

“…We carry out a unified investigation of two prominent topics in proof theory and order algebra: cut-elimination and completion, in the setting of substructural…”
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Algebraic proof theory: Hypersequents and hypercompletions by Ciabattoni, Agata, Galatos, Nikolaos, Terui, Kazushige

“…We continue our program of establishing connections between proof-theoretic and order-algebraic properties in the setting of substructural logics and…”
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Cut elimination and strong separation for substructural logics: An algebraic approach by Galatos, Nikolaos, Ono, Hiroakira

“…We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study…”
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From Axioms to Analytic Rules in Nonclassical Logics by Ciabattoni, A., Galatos, N., Terui, K.

“…We introduce a systematic procedure to transform large classes of (Hilbert) axioms into equivalent inference rules in sequent and hypersequent calculi. This…”
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Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics over FL by Galatos, Nikolaos, Ono, Hiroakira

“…Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of…”
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Decidability of Lattice Equations by Galatos, Nikolaos

“…We provide an alternative proof of the decidability of the equational theory of lattices. The proof presented here is quite short and elementary…”
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Semiconic Idempotent Logic II: Beth Definability and Deductive Interpolation by Fussner, Wesley, Galatos, Nikolaos

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Semiconic idempotent logic I: Structure and local deduction theorems by Fussner, Wesley, Galatos, Nikolaos

“…Semiconic idempotent logic is a common generalization of intuitionistic logic, relevance logic with mingle, and semilinear idempotent logic. It is an…”
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Distributive ℓ-pregroups: Generation and decidability by Galatos, Nikolaos, Gallardo, Isis A.

“…We show that every distributive lattice-ordered pregroup can be embedded into a functional algebra over an integral chain, thus improving the existing…”
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Distributive residuated frames and generalized bunched implication algebras by Galatos, Nikolaos, Jipsen, Peter

“…We show that all extensions of the (non-associative) Gentzen system for distributive full Lambek calculus by simple structural rules have the cut elimination…”
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Densification via polynomials, languages, and frames by Galatos, Nikolaos, Horčík, Rostislav

“…It is known that every countable totally ordered set can be embedded into a countable dense one. We extend this result to totally ordered commutative monoids…”
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From distributive ℓ-monoids to ℓ-groups, and back again by Colacito, Almudena, Galatos, Nikolaos, Metcalfe, George, Santschi, Simon

“…We prove that an inverse-free equation is valid in the variety LG of lattice-ordered groups (ℓ-groups) if and only if it is valid in the variety DLM of…”
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Proof theory for lattice-ordered groups by Galatos, Nikolaos, Metcalfe, George

“…Proof-theoretic methods are developed and exploited to establish properties of the variety of lattice-ordered groups. In particular, a hypersequent calculus…”
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The FEP for some varieties of fully distributive knotted residuated lattices by Cardona, Riquelmi, Galatos, Nikolaos

“…We prove the finite embeddability property for a wide range of varieties of fully distributive residuated lattices and FL-algebras. Part of the axiomatization…”
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Twist Structures and Nelson Conuclei by Busaniche, Manuela, Galatos, Nikolaos, Marcos, Miguel Andrés

“…Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization…”
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Equivalence of consequence relations: an order-theoretic and categorical perspective by Galatos, Nikolaos, Tsinakis, Constantine

“…Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations…”
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