Download presentation

Presentation is loading. Please wait.

Published byErin Davis Modified over 4 years ago

1
Problems of syntax-semantics interface ESSLLI 02 Trento

2
summary The need for lambda calculus From Montague grammar to categorial grammar Lambek calculus Curry-Howard isomorphism Proof-nets Extensions (and restrictions) of L Extended proof-nets

3
Jackendoff Where (narrow) syntax has structural relations such as head-to-complement, head-to-specifier, and head-to-adjunct, conceptual structure has structural relations such as predicate-to- argument, category-to-modifier, and quantifier- to-bound variable. Thus, although conceptual structure undoubtedly constitutes a syntax in the generic sense, its units are not NPs, VPs, etc. […] In particular, unlike syntactic and phonological structures, conceptual structures are purely relational, in the sense that linear order plays no role.

4
recall: Montague grammars Truth-conditional approach: –sentence logical formula (true or false) –noun phrase term (constant, variable, complex term) But what for other linguistic expressions? –verb open atomic formula? –but how to combine? kiss(x,y) composed with p and m gives: kiss(p,m) or kiss(m,p)?

5
fortunately : lambda calculus constants, variables : -terms If M and N are -terms, then (M N) [or M(N)] is a -term,(application) If M is a -term and if x is a variable, then x.M is a -term (abstraction) + -reduction : ( x.M, N) M[N/x]

6
Goal : x (child(x) play(x)) Identical to : ( P.[ x (enfant(x) P(x))] u.play(u)) therefore : every child = P.[ x (child(x) P(x))] Identical to : ( Q. P.[ x (Q(x) P(x))] v.child(v)) therefore: every = Q. P.[ x (Q(x) P(x))] Example : how to extract the « meaning » of quantifiers?

7
other quantifiers a, an = Q. P.[ x (Q(x) P(x))] no = Q. P.[ x (Q(x) P(x))]

8
But we cannot apply anything to anything… x is a -term (x x) is a -term x.(x x) is a -term ( x.(x x) x.(x x)) is a -term But ( x.(x x) x.(x x)) (no end to the reduction : the normalisation process does not stop)

9
« Intransitive verbs » apply to nominal entities (and they give propositions) « Transitive verbs » apply to nominal entities (and they give intransitive verbs…) « Propositional verbs » apply to propositions (and they give propositions) « Adjectives » apply to nominal entities (and they give nominal entities)

10
Typed -calculus Constants and variables of type a are - terms of type a if M is a -term of type and N a - term of type a, then (M N) is a -term of type b If M is a -term of type b and if x is a variable of type a, then x. M is a -term of type

11
In other words:

12
Correspondance syntactic categories – semantic types sentences VP, IV NP, PN TT verbal adverbs VI/VI CN (common noun) sentential adverbs preposition propositional verb intentional verb article t e ou bien, t>,t>, >, >,t>,, >> >, >,, t>>

13
syntax For each syntactic category A, the set P A of all expressions of category A contains at least the set B A of the « dictionary words » of category A, If P A and if P B, then, in some cases to enumerate, F(, ) for some function F belongs to some set P C.

14
Example of rule S2 : if P T/CN and if P CN, then, F 2 (, ) P T, where F 2 (, ) = *, where * = except if is equal to a and if the first word of begins by a vowel, in which case * = an Remark : T is the category of terms, example : a man, an aristocrat

15
Example of rule S4 : if P T and if P VI, then F 4 (, ) P t, where F 4 (, ) = *, where * is obtained from by replacing the first verb by its 3rd person singular form Example : = John, = walk, F 4 (, ) = John walks

16
Montagovian analysis John seeks a unicorn S1 : a T/CN, unicorn CN S2 : F 2 (a, unicorn) = a unicorn T S1 : seek VI/T S5 : F 5 (seek, a unicorn) = seek a unicorn VI S1 : John T S4 : F 4 (John, seek a unicorn) = John seeks a unicorn t

17
John seeks a unicorn John seek a unicorn a unicorn seek a unicorn

18
Second analysis ! John seeks a unicorn S1 : seek VI/T, he 1 T S5 : F 5 (seek, he 1 ) = seek him 1 VI S4 : F 4 (John, seek him 1 ) = John seeks him 1 t S2 : F 2 (a, unicorn) = a unicorn T S14 : F 14,1 (a unicorn, John seeks him 1 ) = John seeks a unicorn t

19
John seeks a unicorn John John seeks him 1 seek a unicorn aunicorn seek him 1 him 1

20
remark In a « modern» grammar (cf. GPSG in the eighties), syntagmatic rules are put in correspondance with some semantic counterpart, In a « logical » grammar (eg. Lambek grammars), the correspondance automatically follows from a known isomorphism between logical derivations and -terms (Curry-Howard)

21
Syntagmatic grammar S SN SV SN Det N SN Np SV Vi SV Vt SN SV Vp que S SV Vint SV (S) = ( (SN) (SV)) (SN) = ( (Det) (N)) (SN) = (Np) (SV) = (Vi) (SV) = (SN) o (Vt) (SV) = ( (Vp) (S)) (SV) = (SV) o (Vint)

22
Det chaque | tout Det un N enfant | ballon Np stéphane Vi joue Vt cherche Vp dit Vint essaie (tout) = Q. P.[ x (Q(x) P(x))] (un) = Q. P.[ x (Q(x) P(x))] (enfant) = x.enfant(x) (stéphane) = P.P(stéphane) (joue) = x.joue(x) (cherche) = x. y.cherche(x, y) (dit) = P. x. dit(x,P) (essaie) = x. P.essaie(x, P) lexical rules

23
Example : stéphane cherche un ballon SN Det N unballon x. ballon(x) Q. P. x[Q(x) P(x)] ( Q. P. x[Q(x) P(x)] x. ballon(x)) P. x[( x. ballon(x) x) P(x)] P. x[ballon(x) P(x)]

24
Example : stéphane cherche un ballon SN Det N unballon P. x[ballon(x) P(x)] SV Vt x. y. chercher(x,y)

25
Example : stéphane cherche un ballon SN Det N unballon P. x[ballon(x) P(x)] SV Vt x. y. chercher(x,y) Composition : ( x.f(x)) o ( y.g(y)) = z. ( x.f(x), ( y.g(y), z)) z. ( P. x[ballon(x) P(x)],( x. y. chercher(x,y) z)) z. ( P. x[ballon(x) P(x)], y. chercher(z,y)) z. x[ballon(x) ( y. chercher(z,y), x)], z. x[ballon(x) chercher(z,x)]

26
Example : stéphane cherche un ballon SN Det N unballon P. x[ballon(x) P(x)] SV Vt x. y. chercher(x,y) z. x[ballon(x) chercher(z,x)] S SN Np Stéphane P. P(stéphane)

27
Example : stéphane cherche un ballon SN Det N unballon P. x[ballon(x) P(x)] SV Vt x. y. chercher(x,y) z. x[ballon(x) chercher(z,x)] S SN Np Stéphane P. P(stéphane) ( P. P(stéphane) z. x[ballon(x) chercher(z,x)]) ( z. x[ballon(x) chercher(z,x)] stéphane) x[ballon(x) chercher(stéphane,x)]

28
Example : stéphane cherche un ballon SN Det N unballon P. x[ballon(x) P(x)] SV Vt x. y. chercher(x,y) z. x[ballon(x) chercher(z,x)] S SN Np Stéphane P. P(stéphane) x[ballon(x) chercher(stéphane,x)]

Similar presentations

OK

Basic Syntactic Structures of English CSCI-GA.2590 – Lecture 2B Ralph Grishman NYU.

Basic Syntactic Structures of English CSCI-GA.2590 – Lecture 2B Ralph Grishman NYU.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on product specification Ppt on dry fish processing Ppt on young uncle comes to town Ppt on any grammar topic in hindi Ppt on power generation using footsteps prayer Download ppt on teamviewer 9 Seven segment led display ppt on tv Ppt on ms word 2003 Microsoft office ppt online ticket Download ppt on control and coordination of class x