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Dual‐Context Sequent Calculus and Strict Implication
Author(s) -
Kikuchi Kentaro
Publication year - 2002
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200201)48:1<87::aid-malq87>3.0.co;2-n
Subject(s) - sequent calculus , sequent , cut elimination theorem , mathematics , natural deduction , calculus (dental) , kripke semantics , dual (grammatical number) , context (archaeology) , proof calculus , modal logic , discrete mathematics , algebra over a field , modal , pure mathematics , mathematical proof , philosophy , linguistics , medicine , paleontology , chemistry , geometry , dentistry , biology , polymer chemistry
We introduce a dual‐context style sequent calculus which is complete with respectto Kripke semantics where implication is interpreted as strict implication in the modal logic K. The cut‐elimination theorem for this calculus is proved by a variant of Gentzen's method.