[T] he framework of ordinary sequents is not capable of handling all interesting logics. There
are logics with nice, simple semantics and obvious interest for which no decent, cut-free …

This is an introductory survey of substructural logics and of residuated lattices which are
algebraic structures for substructural logics. Our survey starts from sequent systems for basic …

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 …

Substructural logics are by now one of the most prominent branches of the research field
usually labelled as" nonclassical logics"-and perhaps of logic tout court. Over the last few …

There are a lot of excellent works in proof theory using various forms of Sequent Calculi (SC)
as the basic formal systems. 1 This book is of a different character. It is not a systematic …

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of
t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy …

We carry out a unified investigation of two prominent topics in proof theory and order
algebra: cut-elimination and completion, in the setting of substructural logics and residuated …

This is an introductory textbook on proof theory and algebra in logic, focusing on both
interrelating and complementary features of these two topics. Proof theory and algebra are …

The first part of this paper provides a comprehensive and self-contained account of the
interrelationships between algebraic properties of varieties and properties of their free …

We present natural deduction systems and associated modal lambda calculi for the
necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in …