Product L ukasiewicz Logic

Preservation theorems in {L}ukasiewicz \model theory

We present some model theoretic results for {L}ukasiewiczpredicate logic by using the methods of continuous model theorydeveloped by Chang and Keisler.We prove compactness theorem with respect to the class of allstructures taking values in the {L}ukasiewicz $texttt{BL}$-algebra.We also prove some appropriate preservation theorems concerning universal and inductive theories.Finally, Skolemizatio...

Classical Indeterminacy , Many - Valued Logic

The problem of representing 3-valued supervaluational languages by 2-dimensional product languages is pursued in [3], [8], and [4]. A solution is presented here that attempts to incorporate into such a representation familiar and plausible intuitive principles from traditional many-valued theories. In particular, it is argued in Sections II and III that the concept of classical indeterminacy, w...

Querying with ?ukasiewicz logic

Implicit Operations in MV-Algebras and the Connectives of Lukasiewicz Logic

It is shown that a conservative expansion of in…nite valued ×ukasiewicz logic by new connectives univocally determined by their axioms does not necessarily have a complete semantics in the real interval [0,1]. However, such extensions are always complete with respect to valuations in a family of MV-chains, Rational ×ukasiewicz logic being the largest one that has a complete semantics in [0,1]. ...

Querying with ?ukasiewicz logic