Paper: Discontinuity And The Lambek Calculus

ACL ID C94-2201
Title Discontinuity And The Lambek Calculus
Venue International Conference on Computational Linguistics
Session Main Conference
Year 1994

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 left-right 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...