Fuzzy logics are many-valued logics that are well suited to reasoning in the context of
vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse …

We present two embeddings of Łukasiewicz logic Ł into Meyer and Slaney's Abelian logic A,
the logic of lattice-ordered Abelian groups. We give new analytic proof systems for A and …

In this paper we present the logic FP (Łn, Ł) which allows to reason about the probability of
fuzzy events formalized by means of the notion of state in a MV-algebra. This logic is defined …

Abstract In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue
rules with a simple scheme for betting on the truth of atomic statements, and showed that the …

This paper presents an overview of the methods of hypersequents and display sequents in
the proof theory of non-classical logics. In contrast with existing surveys dedicated to …

An approximate Herbrand theorem is established for first-order infinite-valued Łukasiewicz
Logic and used to obtain a proof-theoretic proof of Skolemization. These results are then …

The difficulty in finding analytic Gentzen sequent calculi for non-classical logics has lead to
the development of many new proof frameworks (proof systems) that have been used to give …

We outline semantic proofs of two related classes theorems of Łukasiewicz logic, one of
which is more difficult to prove than the other in the calculi that we have surveyed. We …

We present a structural proof system, based on the machinery of hypersequent calculi, for a
simple probabilistic modal logic underlying very expressive probabilistic μ-calculi. We prove …

Fuzzy logics based on t-norms and their residua have been investigated extensively from a
semantic perspective but a unifying proof theory for these logics has, until recently, been …