Refutation systems are systems of formal, syntactic derivations, designed to derive the non-
valid formulas or logical consequences of a given logic. Here we provide an overview with …

A kind of a bi-intuitionistic propositional logic is introduced that combines verification and its
dual. This logic, 2Int, is motivated by a certain dualization of the natural deduction rules for …

Proofs and countermodels are the two sides of completeness proofs, but, in general, failure
to find one does not automatically give the other. The limitation is encountered also for …

• Rauszer's cut-elimination fails (Uustalu 2006)• Some proofs require cut rule (bad for proof-
search)• Crolard's calculus uses cuts (Crolard 2001)• Goré's display calculus is not suitable …

Bi-intuitionistic logic is a conservative extension of intuitionistic logic with a connective dual
to implication, called exclusion. We present a sound and complete cut-free labelled sequent …

Bi-intuitionistic logic, also known as Heyting-Brouwer logic or subtractive logic, is extended
in various ways by a strong negation connective used to express commitments arising from …

As anyone who reads the literature on bi-intuitionistic logic will know, the numerous papers
by Cecylia Rauszer are foundational but confusing. For example: these papers claim and …

We identify a large family of fully structural propositional sequent systems, which we call
basic systems. We present a general uniform method for providing (potentially …

A novel countermodel-producing decision procedure that applies to several multi-modal
logics, both intuitionistic and classical, is presented. Based on backwards search in labeled …

In this paper we present LSJ, a contraction-free sequent calculus for Intuitionistic
propositional logic whose proofs are linearly bounded in the length of the formula to be …