Information and Computation
Automated deduction for many-valued logics
Handbook of automated reasoning
Using Linear Logic to Reason about Sequent Systems
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Non-deterministic semantics for logics with a consistency operator
International Journal of Approximate Reasoning
Generalized Non-deterministic Matrices and (n,k)-ary Quantifiers
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Canonical Calculi: Invertibility, Axiom Expansion and (Non)-determinism
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Canonical Constructive Systems
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Generic Modal Cut Elimination Applied to Conditional Logics
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Cut elimination in coalgebraic logics
Information and Computation
Strict canonical constructive systems
Fields of logic and computation
Kripke semantics for basic sequent systems
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Cut elimination for shallow modal logics
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Canonical gentzen-type calculi with (n,k)-ary quantifiers
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Non-deterministic semantics for paraconsistent C-systems
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
A formal framework for specifying sequent calculus proof systems
Theoretical Computer Science
Finite-valued Semantics for Canonical Labelled Calculi
Journal of Automated Reasoning
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Canonical propositional Gentzen-type systems are systems which in addition to the standard axioms and structural rules have only pure logical rules which have the subformula property, introduce exactly one occurrence of a connective in their conclusion, and no other occurrence of any connective is mentioned anywhere else in their formulation. We provide a constructive coherence criterion for the non-triviality of such systems, and show that a system of this kind admits cut elimination iff it is coherent. We show also that the semantics of such systems is provided by non-deterministic two-valued matrices (2-Nmatrices). 2- Nmatrices form a natural generalization of the classical two-valued matrix, and every coherent canonical system is sound and complete for one of them. Conversely, with any 2-Nmatrix it is possible to associate a coherent canonical Gentzen-type system which has for each connective at most one introduction rule for each side, and is sound and complete for that 2-Nmatrix. We show also that every coherent canonical Gentzen-type system either defines a fragment of the classical two-valued logic, or a logic which has no finite characteristic matrix.