In recent years there has been a revitalised interest in nonclassical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry’s paradox. This can be adapted to provide a proof theoretic analysis of the ω-inconsistency in Lukasiewicz’s continuum valued logic, allowing us to better evaluate which logics are suitable for ...

Modal fuzzy logics is a research topic that has attracted increasing attention in the last years. Several papers have been published treating different aspects, see for instance [6] for a modal expansion of Lukasiewicz logic, [3, 4, 2] for modal expansions of Gödel fuzzy logic, [1] for modal logics over finite residuated lattices, and more recently [7] for a modal expansion of Product fuzzy log...

We present n-valued rst-order logics with a purely proba-bilistic semantics. We then introduce a new probabilistic semantics of n-valued rst-order logics that lies between the purely probabilistic semantics and the truth-functional semantics of the n-valued Lukasiewicz logics Ln. Within this semantics, closed formulas of classical rst-order logics that are logically equivalent in the classical ...

The aim of this paper is to explore the class of intermediate logics between the truth-preserving Lukasiewicz logic L and its degree-preserving companion L≤. From a syntactical point of view, we introduce some families of inference rules (that generalize the explosion rule) that are admissible in L≤ and derivable in L and we characterize the corresponding intermediate logics. From a semantical ...

In this paper I study Lukasiewicz-style refutation procedures (cf. [8], also [3]) for intermediate logics as a method of obtaining decidability results. This method proves to be more general than Harrop’s criterion (cf. [4]) saying that every finitely axiomatizable logic with the finite model property is decidable. There are 2א0 intermediate logics without the f.m.p. (cf. [1], [2]). I give a mo...

Chris Fermüller has recently put forward a convincing interpretation of Lukasiewicz real valued logic based on Giles’s games (see, eg. Fermüller and Metcalfe, 2009; Fermüller, 2010). As the latter are based on probability, this solution can be seen as muddling up the clear and widely endorsed distinction between degrees of truth and degrees of belief. I argue that the distinction need not be gi...

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli in [FT, 82] on the basis of a seminal paper of Landauer [La, 61] are extended to d–valued logics, with a special attention to three–valued logics. Different approaches to d–valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typic...

We investigate what happens if PA LTr2, a co-inductive language, formalizes itself. We analyze the truth concept in fuzzy logics by formalizing truth degree theory in the framework of truth theories in fuzzy logics. Hájek-Paris-Shepherdson’s paradox [HPS00] involves that so called truth degrees do not represent the degrees of truthhood (defined by the truth predicate) correctly in Lukasiewicz i...

This paper presents a hybrid method to construct concise and comprehensible fuzzy rules from training data. The construction procedure consists of a genetic algorithm, which determines the rulebase, and a gradient based optimization for the tuning of the membership functions. An approximation of the well-known Lukasiewicz logic is used to describe both the fuzzy connectives and the memberships,...