perm filename LANG1.AI[ESS,JMC] blob
sn#005529 filedate 1971-10-31 generic text, type T, neo UTF8
00100 This is an attempt to delimit a small part of what is
00200 expressed in ordinary language and to give a formal semantics for it.
00300 The idea is that it may be more fruitful to do a small part
00400 completely rather than spend one's time thinking and arguing about
00500 difficult cases. We therefore accept the following limitations:
00600
00700 1. All sentences are descriptive of a certain situation. The
00800 sentences do not describe events, meanings of words, wishes,
00900 assertions that people know things. Some examples of allowed
01000 sentences are:
01100
01200 a. The book is on the table.
01300 b. John is Mary's brother.
01400 c. John is a student.
01500 d. Stanford University is in California.
01600 e. Kansas is between New York and California.
01700 f. Topeka is in Kansas.
01800 g. Topeka is between New York and California.
01900
02000 2. All the above sentences can be expressed by atomic
02100 formulas of first order logic and our intention is to do so. Thus
02200 they may be replaced by:
02300
02400 a. on(Book1,Table1)
02500 b. brother(John1, Mary1)
02600 c. student(John1)
02700 d. in(StanfordU, California)
02800 e. between(NewYork,Kansas,California)
02900 f. in(Topeka,Kansas)
03000 g. between(NewYork,Topeka,California).
03100
03200 I wrote John1, etc. because many people are named John. I suppose
03300 that there is only one California. Names designating unique objects
03400 are written beginning with capital letters. I have not yet decided
03500 whether I should have written the words on, brother, student, between
03600 and in beginning with capitals.
03700
03800 3. We shall allow the use of variables, propositional,
03900 connectives and quantifiers in constructing sentences. The problem
04000 we shall consider first is how to express enough of the facts about
04100 the world so that consequences that anyone would admit in English
04200 will follow formally. Thus sentence g follows from e, f, and the
04300 universal sentence
04400
04500 (∀ w x y z) (between(x,y,z) ∧ in(w,y) ⊃ between(x,w,z)).
04600
04700 4. We shall not worry about ambiguity of words. English
04800 words will come with tags designating the number of the sense
04900 intended. No pronouns will be used and no descriptive phrases.
05000
05100 5. Even accepting all these restrictions, there is still a lot
05200 of work to be done. First of all, we need to axiomatize concepts
05300 of spacial location (in, between, adjoining, near, etc.), concepts
05400 of mass (some sugar, a quart of molasses).
05500 posession (John has a book), relationship(John is Mary's brother),
05600 state of action(John loves or is loving Mary) [no distinction since
05700 we are not treating events in time],
05800 predication (this book is red, crows are black),