TY - GEN
T1 - A triple correspondence in canonical calculi
T2 - 3rd International Computer Science Symposium in Russia, CSR 2008
AU - Avron, Arnon
AU - Zamansky, Anna
PY - 2008
Y1 - 2008
N2 - An (n,k)-ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical systems with (n,k)-ary quantifiers form a natural class of Gentzen-type systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a quantifier is introduced. The semantics for these systems is provided using two-valued non-deterministic matrices, a generalization of the classical matrix. In this paper we use a constructive syntactic criterion of coherence to characterize strong cut-elimination in such systems. We show that the following properties of a canonical system G with arbitrary (n,k)-ary quantifiers are equivalent: (i) G is coherent, (ii) G admits strong cut-elimination, and (iii) G has a strongly characteristic two-valued generalized non-deterministic matrix.
AB - An (n,k)-ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical systems with (n,k)-ary quantifiers form a natural class of Gentzen-type systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a quantifier is introduced. The semantics for these systems is provided using two-valued non-deterministic matrices, a generalization of the classical matrix. In this paper we use a constructive syntactic criterion of coherence to characterize strong cut-elimination in such systems. We show that the following properties of a canonical system G with arbitrary (n,k)-ary quantifiers are equivalent: (i) G is coherent, (ii) G admits strong cut-elimination, and (iii) G has a strongly characteristic two-valued generalized non-deterministic matrix.
UR - http://www.scopus.com/inward/record.url?scp=44649084411&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-79709-8_9
DO - 10.1007/978-3-540-79709-8_9
M3 - Conference contribution
AN - SCOPUS:44649084411
SN - 3540797084
SN - 9783540797081
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 52
EP - 63
BT - Computer Science - Theory and Applications - Third International Computer Science Symposium in Russia, CSR 2008, Proceedings
PB - Springer Verlag
Y2 - 7 June 2008 through 12 June 2008
ER -