TY - JOUR
T1 - Uniqueness of axiomatic extensions of cut-free classical propositional logic
AU - Piazza, Mario
AU - Pulcini, Gabriele
N1 - Sem PDF.
FAPESP, Sao Paulo State, Brazil (2013/22371-0)
PY - 2016/10
Y1 - 2016/10
N2 - In this article, we prove that, for any cluster of extra-logical assumptions, there exists exactly one axiomatic (i.e. minimal) extension of classical propositional logic that admits cut elimination. As a corollary, it follows that classically equivalent formulas share the same axiomatization. The moral is that cut elimination "flattens" the specific information encoded by the logical structure of proper axioms.
AB - In this article, we prove that, for any cluster of extra-logical assumptions, there exists exactly one axiomatic (i.e. minimal) extension of classical propositional logic that admits cut elimination. As a corollary, it follows that classically equivalent formulas share the same axiomatization. The moral is that cut elimination "flattens" the specific information encoded by the logical structure of proper axioms.
KW - Axiomatic extensions
KW - Cut elimination with proper axioms
KW - Logic of pivotal assumptions
KW - Proof theory
UR - http://www.scopus.com/inward/record.url?scp=84995790173&partnerID=8YFLogxK
U2 - 10.1093/jigpal/jzw032
DO - 10.1093/jigpal/jzw032
M3 - Article
AN - SCOPUS:84995790173
SN - 1367-0751
VL - 24
SP - 708
EP - 718
JO - Logic Journal of the IGPL
JF - Logic Journal of the IGPL
IS - 5
ER -