Refutation systems in modal logic (Q1327486)

Refutation systems are deductive systems which infer refutable statements instead of valid statements. Thus, a refutation system is every pair consisting of a set of axioms \(\ldashv\varphi\) and a set of refutation rules: If \(\lvdash\varphi_ 1,\dots,\lvdash \varphi_ k\), \(\ldashv \psi_ 1,\dots,\ldashv \psi_ n\), then \(\ldashv\psi\). The paper contains a historical part on refutation logics and general considerations about such deductive systems. Refutation systems are proposed for various logics. The second part of the paper deals with Gentzen-style refutation rules being a new approach in the area. Besides the cited references, the following technical report may be useful: \textit{Tomasz Skura}: ``Refutation procedures for intuitionistic and modal logics'' [Konstanzer Berichte Logik und Information 37, Universität Konstanz, Zentrum Philosophie und Wissenschaftstheorie].