Refutation systems are axiomatic systems applied to non-valid formulas (or sequents). A refutation system consists of refutation axioms and refutation rules. We say that a formula A is refutable iff A is derivable from refutation axioms by refutation rules (or, dually, A multiple-conclusion entails some refutation axioms). The concept was introduced by Łukasiewcz, but the idea of refutation was already known to Aristotle. This approach is complementary to standard proof methods. Although refutation systems are not widely known, we believe that the method has potential and can produce results that are both interesting and useful.
The goal of this conference is to explain key concepts and techniques, and present new results on refutation systems. But we also expect exchanging ideas and posing interesting questions. We are interested in the following aspects of refutation systems:
- Constructive Completeness Proofs;
- Complementary Gentzen Systems;
- Decision Procedures;
- Non-monotonic Logic;
- Hybrid Rules;
- Non-classical Logics via Refutability;
- Philosophical Aspects of Refutation.