David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Logic, Language and Information 16 (2):141-171 (2007)
We study a multiple-succedent sequent calculus with both of the structural rules Left Weakening and Left Contraction but neither of their counterparts on the right, for possible application to the treatment of multiplicative disjunction (fission, ‘cotensor’, par) against the background of intuitionistic logic. We find that, as Hirokawa dramatically showed in a 1996 paper with respect to the rules for implication, the rules for this connective render derivable some new structural rules, even though, unlike the rules for implication, these rules are what we call ipsilateral: applying such a rule does not make any (sub)formula change sides—from the left to the right of the sequent separator or vice versa. Some possibilities for a semantic characterization of the resulting logic are also explored. The paper concludes with three open questions.
|Keywords||Substructural logics Multiplicative disjunction Fission Structural rules Sequent calculus|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Lloyd Humberstone (2013). Replacement in Logic. Journal of Philosophical Logic 42 (1):49-89.
Similar books and articles
Roy Dyckhoff & Sara Negri (2000). Admissibility of Structural Rules for Contraction-Free Systems of Intuitionistic Logic. Journal of Symbolic Logic 65 (4):1499-1518.
Sharon Shoham & Nissim Francez (2008). Game Semantics for the Lambek-Calculus: Capturing Directionality and the Absence of Structural Rules. Studia Logica 90 (2):161 - 188.
Andreja Prijatelj (1992). Lambek Calculus with Restricted Contraction and Expansion. Studia Logica 51 (1):125 - 143.
Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
Ken-etsu Fujita (1998). On Proof Terms and Embeddings of Classical Substructural Logics. Studia Logica 61 (2):199-221.
Ryo Kashima & Norihiro Kamide (1999). Substructural Implicational Logics Including the Relevant Logic E. Studia Logica 63 (2):181-212.
Sara Negri (2002). Varieties of Linear Calculi. Journal of Philosophical Logic 31 (6):569-590.
Alexej P. Pynko (2009). Distributive-Lattice Semantics of Sequent Calculi with Structural Rules. Logica Universalis 3 (1):59-94.
Sara Negri & Jan von Plato (2001). Sequent Calculus in Natural Deduction Style. Journal of Symbolic Logic 66 (4):1803-1816.
Added to index2009-01-28
Total downloads9 ( #156,922 of 1,100,794 )
Recent downloads (6 months)5 ( #58,660 of 1,100,794 )
How can I increase my downloads?