2 1. Understanding the meaning(use) of programming languages
3 helps understanding the meaning(use) of natural langauges
5 1. Richard Montague. 1970. Universal Grammar. _Theoria_ 34:375--98.
6 "There is in my opinion no important theoretical difference
7 between natural languages and the artificial languages of
8 logicians; indeed, I consider it possible to comprehend the
9 syntax and semantics of both kinds of languages within a
10 single natural and mathematically precise theory."
14 Function/argument structure:
19 John is his own worst enemy
21 foreach x in [1..10] print x
22 Print every number from 1 to 10
24 3. Possible differences:
28 ?It was four plus seven that John computed 3 multiplied by
29 (compare: John computed 3 multiplied by four plus seven)
32 Time flies like and arrow, fruit flies like a banana.
35 A cloud near the mountain
36 Unbounded numbers of distinct pronouns:
37 f(x1) + f(x2) + f(x3) + ...
38 He saw her put it in ...
39 [In ASL, dividing up the signing space...]
42 2. Standard methods in linguistics are limited.
44 1. First-order predicate calculus
46 Invented for reasoning about mathematics (Frege's quantification)
48 Alethic, order insensitive: phi & psi == psi & phi
49 But: John left and Mary left too /= Mary left too and John left
51 2. Simply-typed lambda calculus
53 Can't express the Y combinator
56 3. Meaning is computation.
58 1. Semantics is programming
60 2. Good programming is good semantics
64 1. Programming technique
70 2. Application to linguistics
81 presupposition failure
82 build into meaning of innocent predicates?