Nikolaos Galatos
نویسندگان
چکیده
Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.
منابع مشابه
Nikolaos GALATOS , Jeffrey S . OLSON and James G . RAFTERY IRREDUCIBLE
A b s t r a c t. This paper deals with axiomatization problems for varieties of residuated meet semilattice-ordered monoids (RSs). An internal characterization of the finitely subdirectly irreducible RSs is proved, and it is used to investigate the varieties of RSs within which the finitely based subvarieties are closed under finite joins. It is shown that a variety has this closure property if...
متن کاملVanderbilt University Department of Mathematics Shanks Workshop on Proof Theory and Algebra Booklet
متن کامل
Algebraic proof theory: Hypersequents and hypercompletions
Article history: Received 9 June 2014 Received in revised form 31 January 2016 Accepted 14 October 2016 Available online xxxx MSC: 03B47 03G10 03F05
متن کاملMacNeille Completions of FL-algebras
We show that a large number of equations are preserved by DedekindMacNeille completions when applied to subdirectly irreducible FL-algebras/residuated lattices. These equations are identified in a systematic way, based on proof-theoretic ideas and techniques in substructural logics. It follows that a large class of varieties of Heyting algebras and FL-algebras admits completions.
متن کامل