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 …

Ordered algebras such as Boolean algebras, Heyting algebras, lattice-ordered groups, and
MV-algebras have long played a decisive role in logic, although perhaps only in recent …

We provide a general method for generating cutfree and/or analytic hypersequent Gentzen-
type calculi for a variety of normal modal logics. The method applies to all modal logics …

In this paper, we introduce hypersequent calculi for some modal logics extending S4 modal
logic. In particular, we uniformly characterize hypersequent calculi for S4, S4. 2, S4. 3, S5 in …

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy
logics that combine the Kripke semantics of modal logic K with the many-valued semantics …

The paper presents a uniform proof-theoretic treatment of several kinds of free logic,
including the logics of existence and definedness applied in constructive mathematics and …

Decidability of the validity problem is established for a family of many-valued modal logics,
notably Gödel modal logics, where propositional connectives are evaluated according to the …

The starting point of this paper are the works of Hájek and Vychodil on the axiomatization of
truth-stressing and-depressing hedges as expansions of Hájek's BL logic by new unary …

S5 is one of the most important modal logic with nice syntactic, semantic and algebraic
properties. In spite of that, a successful (ie cut-free) formalization of S5 on the ground of …

A constructivisation of the cut-elimination proof for sequent calculi for classical, intuitionistic
and minimal infinitary logics with geometric rules—given in earlier work by the second …