The Loś-Tarski Theorem and the ChangLoś-Susko Theorem, two classical results in Model Theory, are extended to the infinitevalued Lukasiewicz logic. The latter is used to settle a characterisation of the class of generic structures introduced in the framework of model theoretic forcing for Lukasiewicz logic [1]. Key-words: First Order Many-Valued Logic, Lukasiewicz logic, Model Theory.

The multi-valued logic of Lukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation elimination, [DNE]. However, our understanding of Lukasiewicz logic can be improved by separating its classical and intuitionistic aspects. The intuitionistic aspect of Lukasiewicz logic ...

In the framework of propositional Lukasiewicz logic, a suitable notion of implicit definability, tailored to the intended real-valued semantics and referring to the elements of its domain, is introduced. Several variants of implicitly defining each of the rational elements in the standard semantics are explored, and based on that, a faithful interpretation of theories in Rational Pavelka logic ...

We investigate admissible rules of Lukasiewicz multi-valued propositional logic. We show that admissibility of multiple-conclusion rules in Lukasiewicz logic, as well as validity of universal sentences in free MV -algebras, is decidable (in PSPACE ).

We construct explicit bases of single-conclusion and multiple-conclusion admissible rules of propositional Lukasiewicz logic, and we prove that every formula has an admissibly saturated approximation. We also show that Lukasiewicz logic has no finite basis of admissible rules.

We show that the set of valid formulas in Lukasiewicz predicate logic is a complete Π 2 set. We also show that the classically valid formulas are exactly those formulas in the classical language whose fuzzy value is 1/2. Lukasiewicz’ infinite valued logic can be seen as a particular “implementation” of fuzzy logic. The set of possible “truth values” (or, in another interpretation, degrees of ce...

In this work we investigate bounded Lukasiewicz logics, characterised as the intersection of the k-valued Lukasiewicz logics for k = 2, . . . , n (n ≥ 2). These logics formalise a generalisation of Ulam’s game with applications in Information Theory. Here we provide an analytic proof calculus G LBn for each bounded Lukasiewicz logic, obtained by adding a single rule to G L, a hypersequent calcu...

We connect Lukasiewicz logic, a well-established many-valued logic, with weighted logics, recently introduced by Droste and Gastin. We use this connection to show that for formal series with coefficients in semirings derived from MValgebras, recognizability and definability in a fragment of second order Lukasiewicz logic coincide.

Recently there have been some unexpected results concerning Fuzzy Description Logics (FDLs) with General Concept Inclusions (GCIs). They show that, unlike the classical case, the DL ALC with GCIs does not have the finite model property under Lukasiewicz Logic or Product Logic and, specifically, knowledge base satisfiability is an undecidable problem for Product Logic. We complete here the analy...

The paper explores properties of the Lukasiewicz μ-calculus, or Lμ for short, an extension of Lukasiewicz logic with scalar multiplication and least and greatest fixed-point operators (for monotone formulas). We observe that Lμ terms, with n variables, define monotone piecewise linear functions from [0, 1]n to [0, 1]. Two effective procedures for calculating the output of Lμ terms on rational i...