A Note on Gödel-Dummet Logic LC

A Note on the Gödel-Gentzen Translation

Monotone operators on Gödel logic

4 We consider an extension of Gödel logic by a unary operator that enables the addition of nonnegative reals to truth-values. Although its propositional fragment has a simple proof system, first-order validity is Π2-hard. We explain the close connection to Scarpellini’s result on Π2hardness of Łukasiewicz’s logic.

Extending possibilistic logic over Gödel logic

In this paper we present several fuzzy logics trying to capture different notions of necessity (in the sense of Possibility theory) for Gödel logic formulas. Based on different characterizations of necessity measures on fuzzy sets, a group of logics with Kripke style semantics are built over a restricted language, namely a two level language composed of non-modal and modal formulas, the latter ...

A Resolution Mechanism for Prenex Gödel Logic

First order Gödel logic G∞, enriched with the projection operator 4—in contrast to other important t-norm based fuzzy logics, like Lukasiewicz and Product logic—is well known to be recursively axiomatizable. However, unlike in classical logic, testing (1-)unsatisfiability, i.e., checking whether a formula has no interpretation that assigns the designated truth value 1 to it, cannot be straightf...

A connection between Similarity Logic Programming and Gödel Modal Logic

In this paper we relate two logical similarity-based approaches to approximate reasoning. One approach extends the framework of (propositional) classical logic programming by introducing a similarity relation in the alphabet of the language that allows for an extended unification procedure. The second approach is a many-valued modal logic approach where 3p is understood as approximately p. Here...