Strong standard completeness for continuous t-norms

Strong non-standard completeness for fuzzy logics

In this paper we are going to introduce the notion of strong non-standard completeness (SNSC) for fuzzy logics. This notion naturally arises from the well known construction by ultraproduct. Roughly speaking, to say that a logic C is strong non-standard complete means that, for any countable theory Γ over C and any formula φ such that Γ 6`C φ, there exists an evaluation e of C-formulas into a C...

Standard fuzzy uniform structures based on continuous t-norms

On strong standard completeness of MTLQ∗ expansions

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. ...

About Strong Standard Completeness of Product Logic

Propositional Product Logic is known to be standard finite-strong complete but not a strong complete, that is, it is complete for deductions only from finite sets of premises with respect to evaluations on the standard product chain over the real unit interval. On the other hand, Montagna has defined a logical system, an axiomatic extension of the Hájek’s Basic Fuzzy Logic BL with an storage op...

Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness results

In this paper we study generic expansions of logics of continuous t-norms with truth-constants, taking advantage of previous results for Lukasiewicz logic and more recent results for Gödel and Product logics. Indeed, we consider algebraic semantics for expansions of logics of continuous t-norms with a set of truth-constants {r | r ∈ C}, for a suitable countable C ⊆ [0, 1], and provide a full de...