Within the mathematical logic field, much effort has been devoted to prove completeness of different axiomatizations with respect to classes of algebras defined on the real unit interval [0, 1] (see for instance [1] and [2]), but in general, what has been mainly achieved are axiomatizations and results concerning fini-tary completeness, that is, for deductions from a finite number of premises. ...

Extensions of monoidal t-norm logic MTL and related fuzzy logics with truth stresser modalities such as globalization and “very true” are presented here both algebraically in the framework of residuated lattices and proof-theoretically as hypersequent calculi. Completeness with respect to standard algebras based on t-norms, embeddings between logics, decidability, and the finite embedding prope...

A subresiduated lattice ordered commutative monoid (or srl-monoid for short) is a with particular subalgebra which contains residuated implication. The srl-monoids can be regarded as algebras that generalize lattices and respectively. In this paper we prove the class of forms variety. We show congruences any isomorphic to its strongly convex subalgebras also give description generated by subset...

We discuss a formal many-valued logic called EQlogic which is based on a recently introduced special class of algebras called EQ-algebras. The latter have three basic binary operations (meet, multiplication, fuzzy equality) and a top element and, in a certain sense, generalize residuated lattices. The goal of EQ-logics is to present a possible direction in the development of mathematical logics...

In 1950, B.A. Trakhtenbrot showed that the set of first-order tautologies associated to finite models is not recursively enumerable. In 1999, P. Hájek generalized this result to the first-order versions of Lukasiewicz, Gödel and Product logics, w.r.t. their standard algebras. In this talk we extend the analysis to the first-order versions of axiomatic extensions of MTL. Our main result is the f...

This talk is a contribution towards the project of developing discrete representability for the algebraic semantics of various non-classical logics. Discrete duality is a type of duality where a class of abstract relational systems is a dual counterpart to a class of algebras. These relational systems are referred to as ‘frames’ following the terminology of non-classical logics. There is no top...

Since all the algebras connected to logic have, more or less explicitely, an associated order relation, it follows that they have two presentations, dual to each other. We classify these dual presentations in ”left” and ”right” ones and we consider that, when dealing with several algebras in the same research, it is useful to present them unitarily, either as ”left” algebras or as ”right” algeb...

Since all the algebras connected to logic have, more or less explicitely, an associated order relation, it follows that they have two presentations, dual to each other. We classify these dual presentations in ”left” and ”right” ones and we consider that, when dealing with several algebras in the same research, it is useful to present them unitarily, either as ”left” algebras or as ”right” algeb...