# One can write arbitrary comments in this file after hashes, # but keep in mind that students will be able to see such comments. # The first non-comment line of the file is the title of the # assignment. Homework 3: Generalized Quantifiers # Next, typing conventions are entered. If no typing conventions # are given, some defaults are used. constants of type e : a b c constants of type n : k variables of type e : x-z variables of type <'a,'b> : d-f variables of type : P-Q X-Z variables of type : R-W # The following directive instructs the program to # interpret multiple-letter constants and variables # properly. multiple letter identifiers # "use rule" directives are for tree evaluation exercises. # They indicate which composition rules are available # at nonterminals. use rule function application use rule non-branching nodes use rule predicate modification use rule lambda abstraction # Next, lexical entries provided to the student are given. # A word (i.e. "sleep") can be given any number of lexical # entry choices by repeating the "define" directive multiple # times. Students are able to add their own lexical entries # as well. define happy : Lx.happy(x) define boy,boys : Lx.boy(x) define girl,girls : Lx.girl(x) define love, loves : LyLx.love(x,y) define someone, somebody : LP.Ex[P(x)] define everyone, everybody : Lf.Ax[f(x)] define no-one, nobody : LP.~Ex[P(x)] define some,a : LP.LQ.Ex[P(x) & Q(x)] define some,a : LP.LR.Ly.Ex[P(x) & R(x)(y)] define every : LP.LQ.P << Q define every : LP.LQ.{x | P(x)} << {x | Q(x)} define every : LP.LR.Ly.{x | P(x)} << {x | R(x)(y)} define most : LP.LQ.[|P ^^ Q| >= k*|P|] define most : LP.LQ.[|{x | P(x)} ^^ {x | Q(x)}| >= k*|{x|P(x)}|] define no : LP.LQ.~Ex[P(x) & Q(x)] define no : LP.LQ.P ^^ Q = \emptyset define no : LP.LQ.|P ^^ Q| = 0 define Alice : a define Betty : b define Connor : c # Finally, the exercises themselves are entered. exercise tree title Formulating NatLg denotations as lambda-expressions directions Do the derivation. [.S [.NP everyone] [.VP (is) [.VP happy] ] ] [.S [.NP every boy] [.VP (is) [.VP happy] ] ] [.S [.NP every boy] [.VP loves [.NP some girl ] ] ] [.S [.NP every boy] [.VP loves [.NP every girl ] ] ] [.S [.NP some boy] [.VP loves [.NP some girl ] ] ] [.S [.NP some boy] [.VP loves [.NP every girl ] ] ] [.S [.NP most boys] [.VP love [.NP some girl ] ] ] [.S [.NP no boy] [.VP loves [.NP a girl ] ] ] [.S [.NP no boy] [.VP loves [.NP every girl ] ] ]