TY - JOUR
T1 - A unified semantic framework for fully structural propositional sequent systems
AU - Lahav, Ori
AU - Avron, Arnon
PY - 2013/11
Y1 - 2013/11
N2 - We identify a large family of fully structural propositional sequent systems, which we call basic systems. We present a general uniform method for providing (potentially, nondeterministic) strongly sound and complete Kripke-style semantics, which is applicable for every system of this family. In addition, this method can also be applied when: (i) some formulas are not allowed to appear in derivations, (ii) some formulas are not allowed to serve as cut formulas, and (iii) some instances of the identity axiom are not allowed to be used. This naturally leads to new semantic characterizations of analyticity (global subformula property), cut admissibility and axiom expansion in basic systems. We provide a large variety of examples showing that many soundness and completeness theorems for different sequent systems, as well as analyticity, cut admissibility, and axiom expansion results, easily follow using the general method of this article.
AB - We identify a large family of fully structural propositional sequent systems, which we call basic systems. We present a general uniform method for providing (potentially, nondeterministic) strongly sound and complete Kripke-style semantics, which is applicable for every system of this family. In addition, this method can also be applied when: (i) some formulas are not allowed to appear in derivations, (ii) some formulas are not allowed to serve as cut formulas, and (iii) some instances of the identity axiom are not allowed to be used. This naturally leads to new semantic characterizations of analyticity (global subformula property), cut admissibility and axiom expansion in basic systems. We provide a large variety of examples showing that many soundness and completeness theorems for different sequent systems, as well as analyticity, cut admissibility, and axiom expansion results, easily follow using the general method of this article.
KW - Analyticity
KW - Axiom expansion
KW - Cut admissibility
KW - Kripke semantics
KW - Logic
KW - Nondeterministic semantics
KW - Proof theory
KW - Semantic characterization
KW - Sequent calculi
UR - http://www.scopus.com/inward/record.url?scp=84890337944&partnerID=8YFLogxK
U2 - 10.1145/2528930
DO - 10.1145/2528930
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AN - SCOPUS:84890337944
SN - 1529-3785
VL - 14
JO - ACM Transactions on Computational Logic
JF - ACM Transactions on Computational Logic
IS - 4
M1 - 27
ER -