ACL Anthology Network (All About NLP) (beta) The Association Of Computational Linguistics Anthology Network 
ACL ID  C942201 

Title  Discontinuity And The Lambek Calculus 
Venue  International Conference on Computational Linguistics 
Session  Main Conference 
Year  1994 
Authors 

Natural deduction rules labelled in this way are as follows: (2) a/B:a B:b [B:v] /E A:a a : (~b) ~ /I A/B : X:v.a B:b BA :(~ [B :v] A : (b~) l E~ ___A :a ~ /3A :,~v.a We can eusure that only deductions appropriate to (implicational) L are made by requiring that the label that results with any inference is a term satisfying Buszkowski's three conditions. To facilitate testing this requirement, I use a flmction E, which maps from label terms to the string of their free variables occurring in the leftright order that follows from type directionality (giving what I call a marker term). A notion of 'string equivalence' ( ~) for marker terms is definecl by the axioms: (~.1) *,(>z)±(x.y).z (2) .~.. (.3) .~x.c E is recursively specified by the following clauses (where PV returns the set of...