Bridging the data integration gap: from theory to implementation
ACM SIGSOFT Software Engineering Notes
Basic proof theory
Non-deterministic Multiple-valued Structures
Journal of Logic and Computation
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Combining Derivations and Refutations for Cut-free Completeness in Bi-intuitionistic Logic
Journal 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
Negative Modalities, Consistency and Determinedness
Electronic Notes in Theoretical Computer Science (ENTCS)
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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.