Combining derivations and refutations for cut-free completeness in bi-intuitionistic logic
R Goré, L Postniece - Journal of Logic and Computation, 2010 - academic.oup.com
Bi-intuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was
introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her
subsequent 'cut-free'sequent calculus has recently been shown to fail cut-elimination. We
present a new cut-free sequent calculus for bi-intuitionistic logic, and prove it sound and
complete with respect to its Kripke semantics. Ensuring completeness is complicated by the
interaction between intuitionistic implication and dual intuitionistic exclusion, similarly to …
introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her
subsequent 'cut-free'sequent calculus has recently been shown to fail cut-elimination. We
present a new cut-free sequent calculus for bi-intuitionistic logic, and prove it sound and
complete with respect to its Kripke semantics. Ensuring completeness is complicated by the
interaction between intuitionistic implication and dual intuitionistic exclusion, similarly to …
Combining Derivations and Refutations for Cut-free Completeness in Bi-intuitionistic Logic
L Postniece - philpapers.org
Bi-intuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was
introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her
subsequent 'cut-free'sequent calculus has recently been shown to fail cut-elimination. We
present a new cut-free sequent calculus for bi-intuitionistic logic, and prove it sound and
complete with respect to its Kripke semantics. Ensuring completeness is complicated by the
interaction between intuitionistic implication and dual intuitionistic exclusion, similarly to …
introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her
subsequent 'cut-free'sequent calculus has recently been shown to fail cut-elimination. We
present a new cut-free sequent calculus for bi-intuitionistic logic, and prove it sound and
complete with respect to its Kripke semantics. Ensuring completeness is complicated by the
interaction between intuitionistic implication and dual intuitionistic exclusion, similarly to …
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