Basic proof theory
The method of hypersequents in the proof theory of propositional non-classical logics
Logic: from foundations to applications
Herbrand's Theorem for Prenex Gödel Logic and its Consequences for Theorem Proving
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
On the Undecidability of some Sub-Classical First-Order Logics
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
A Schütte-Tait Style Cut-Elimination Proof for First-Order Gödel Logic
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Hypersequent and the Proof Theory of Intuitionistic Fuzzy Logic
Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
ISMVL '00 Proceedings of the 30th IEEE International Symposium on Multiple-Valued Logic
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Monoidal t-norm based logic MTL is the logic of left continuous t-norms. We introduce two analytic calculi for first-order MTL. These are obtained by lifting two sequent calculi for different fragments of this logic to the hypersequent level with subsequent addition of Avron's communication rule. Our calculi enable to prove the mid(hyper)sequent theorem. As corollaries follow Herbrand's theorem for first-order MTL, the decidability of its ∀∃-fragment and admissibility of Skolemization.