David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Logic, Language and Information 9 (3):339-352 (2000)
An axiomatics of the product-free syntactic calculus L ofLambek has been presented whose only rule is the cut rule. It was alsoproved that there is no finite axiomatics of that kind. The proofs weresubsequently simplified. Analogous results for the nonassociativevariant NL of L were obtained by Kandulski. InLambek's original version of the calculus, sequent antecedents arerequired to be nonempty. By removing this restriction, we obtain theextensions L 0 and NL 0 ofL and NL, respectively. Later, the finiteaxiomatization problem for L 0 andNL 0 was partially solved, viz., for formulas withoutleft (or, equivalently, right) division and an (infinite) cut-ruleaxiomatics for the whole of L 0 has been given. Thepresent paper yields an analogous axiomatics forNL 0. Like in the author's previous work, the notionof rank of an axiom is introduced which, although inessentialfor the results given below, may be useful for the expectednonfinite-axiomatizability proof.
|Keywords||axiomatizability cut rule Lambek 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
No citations found.
Similar books and articles
Martin Amerbauer (1996). Cut-Free Tableau Calculi for Some Propositional Normal Modal Logics. Studia Logica 57 (2-3):359 - 372.
Rajeev Gore & Revantha Ramanayake (2012). Valentini's Cut-Elimination for Provability Logic Resolved. Review of Symbolic Logic 5 (2):212-238.
Roy Dyckhoff & Luis Pinto (1998). Cut-Elimination and a Permutation-Free Sequent Calculus for Intuitionistic Logic. Studia Logica 60 (1):107-118.
Rajeev Gore, Linda Postniece & Alwen Tiu, Cut-Elimination and Proof-Search for Bi-Intuitionistic Logic Using Nested Sequents.
Brian Hill & Francesca Poggiolesi (2010). A Contraction-Free and Cut-Free Sequent Calculus for Propositional Dynamic Logic. Studia Logica 94 (1):47 - 72.
Wojciech Zielonka (1990). Linear Axiomatics of Commutative Product-Free Lambek Calculus. Studia Logica 49 (4):515 - 522.
Wojciech Zielonka (1989). A Simple and General Method of Solving the Finite Axiomatizability Problems for Lambek's Syntactic Calculi. Studia Logica 48 (1):35 - 39.
Wojciech Zielonka (2002). On Reduction Systems Equivalent to the Lambek Calculus with the Empty String. Studia Logica 71 (1):31-46.
Wojciech Zielonka (2001). Cut-Rule Axiomatization of the Syntactic Calculus L. Journal of Logic, Language and Information 10 (2):339-352.
Added to index2009-01-28
Total downloads5 ( #234,982 of 1,100,097 )
Recent downloads (6 months)4 ( #90,386 of 1,100,097 )
How can I increase my downloads?