TY - JOUR
T1 - Canonical signed calculi with multi-ary quantifiers
AU - Zamansky, Anna
AU - Avron, Arnon
PY - 2012/7
Y1 - 2012/7
N2 - Canonical Gentzen-type calculi are a natural class of systems, which in addition to the standard axioms and structural rules have only logical rules introducing exactly one connective. There is a strong connection in such systems between a syntactic constructive criterion of . coherence, the existence of a two-valued non-deterministic semantics for them and strong cut-elimination. In this paper we extend the theory of canonical systems to . signed calculi with multi-ary quantifiers. We show that the extended criterion of coherence fully characterizes strong . analytic cut-elimination in such calculi, and use finite . non-deterministic matrices to provide modular semantics for every coherent canonical signed calculus.
AB - Canonical Gentzen-type calculi are a natural class of systems, which in addition to the standard axioms and structural rules have only logical rules introducing exactly one connective. There is a strong connection in such systems between a syntactic constructive criterion of . coherence, the existence of a two-valued non-deterministic semantics for them and strong cut-elimination. In this paper we extend the theory of canonical systems to . signed calculi with multi-ary quantifiers. We show that the extended criterion of coherence fully characterizes strong . analytic cut-elimination in such calculi, and use finite . non-deterministic matrices to provide modular semantics for every coherent canonical signed calculus.
KW - Cut-elimination
KW - Generalized quantifiers
KW - Non-deterministic matrices
KW - Proof theory
KW - Signed calculi
UR - http://www.scopus.com/inward/record.url?scp=84857372072&partnerID=8YFLogxK
U2 - 10.1016/j.apal.2011.09.006
DO - 10.1016/j.apal.2011.09.006
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AN - SCOPUS:84857372072
SN - 0168-0072
VL - 163
SP - 951
EP - 960
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 7
ER -