On the constructive nature of natural language quantifiers. Allan Ramsay School of Computer Science, University of Manchester, Manchester M13 9PL, UK

Transcription

1 On the constructive nature of natural language quantifiers Allan Ramsay School of Computer Science, University of Manchester, Manchester M13 9PL, UK 1

2 What does saying that NL should be treated constructively mean? Where s the evidence that this is the right way to go? What difference does it make to computational treatments? 2

3 What does saying that NL should be treated constructively mean? Classical: language is about describing the world. You do this in order to have some effect on some other person(s), but the primary task of semantics is to see how language can be used to describe the world. Constructive: language is about having some effect on some other person(s). To do this, what you say must describe the world, but the primary task of semantics is to see how language can be used to affect other people. Semantics is pragmatics. Allan Ramsay, -3-What does saying that NL should be treated constructively mean?

4 Where s the evidence that this is the right way to go? This distinction makes very little difference when you are thinking about quantifier-free sentences.... language is about describing the world...,...what you say must describe the world... There is a link to the question of whether such words should be characterised by their extensions (green = grass, leaves,...) or their intensions (green = reflects light with a wavelength between in the range nm)... I have never seen a quantifier-free sentence of natural language Allan Ramsay, -4- Where s the evidence that this is the right way to go?

5 But it does make a difference when you want to think about quantifiers and logical connectives (1) If I m at home in Buxton then my cat has green hair Classical P Q is true if P is false or Q is true. Er, I m in Toulouse Allan Ramsay, -5- Where s the evidence that this is the right way to go?

6 But it does make a difference when you want to think about quantifiers and logical connectives (1) If I m at home in Buxton then my cat has green hair Classical P Q is true if P is false or Q is true. Er, I m in Toulouse Constructive P Q means that you can prove Q by assuming P. Imagine I m at home in Buxton. Could you prove that my cat has green hair? Does it make any practical difference? Maybe not, because you wouldn t be able to prove anything using the classical notion unless I was at home in Buxton, which I m not. But it s deeply unsatisfying. Allan Ramsay, -6- Where s the evidence that this is the right way to go?

7 (2) A man and a woman came into the room. The man was shouting angrily and waving his arms around, the woman was looking embarrassed and trying to pretend she didn t know him. Classical There is exactly one man and exactly one woman. [[man]] I = 1, [[woman]] I = 1 Then I has to be specified with respect to the context. What context? Constructive There is exactly one thing that can proved to be a man using the information currently available. Likewise woman. the information currently available = the minutes of the conversation + what you think everyone involved knows. Allan Ramsay, -7- Where s the evidence that this is the right way to go?

8 Invoking the minutes explains how you can easily refer to something whose existence you doubt/disbelieve, indeed to something whose existence you explicitly doubt/disbelieve. (3) A: My boyfriend bought me a Ferarri for my birthday B: I don t believe you A: He did, he did B: Go on then, what colour is it? Allan Ramsay, -8- Where s the evidence that this is the right way to go?

9 (4) Most people think that the study of semantics is an esoteric waste of time. Classical Over half the set of people think semantics is a waste of time person semantics waste of time person > 0.5 What set of people? Everyone there is? Everyone there ever has been? Everyone I know? Allan Ramsay, -9- Where s the evidence that this is the right way to go?

10 (4) Most people think that the study of semantics is an esoteric waste of time. Classical Over half the set of people think semantics is a waste of time person semantics waste of time semantics waste of time What set of people? Everyone there is? Everyone there ever has been? Everyone I know? > 0.5 Constructive If X is a person, it would be reasonable to infer that X thinks semantics is a waste of time. How would you prove it? Try to imagine a conversation that you would have in the pub. Have you ever persuaded a non-specialist that what you do is of any value? Allan Ramsay, -10- Where s the evidence that this is the right way to go?

11 (5) Tania is a farmer. She owns a donkey which she looks after very nicely. We ve introduced a female farmer into the conversation. After that, we can easily use she to refer to her. Allan Ramsay, -11- Where s the evidence that this is the right way to go?

12 (5) Tania is a farmer. She owns a donkey which she looks after very nicely. We ve introduced a female farmer into the conversation. After that, we can easily use she to refer to her. (6) If a farmer owns a donkey she looks after it very nicely. Why is it weird? By the time we get to she, we have already introduced a farmer into the conversation, and along with that we have made use of the general rule that Most farmers are male (which probably isn t even true) to visualise this farmer as male. Allan Ramsay, -12- Where s the evidence that this is the right way to go?

13 What difference does it make to computational treatments? At one level, none at all. There is no point in having a program that can construct meaning representations unless you also have a program that can do something with them. That s constructive: what matters is what you can do. (that s not to say that there no point in trying to work out what the truth conditions of a sentence are as a philosophical exercise. Just no point writing a program to do it) Allan Ramsay, -13- What difference does it make to computational treatments?

14 But at a finer granularity it does have consequences: it affects what kind of inference engine you build it affects what kind of meaning representation you use it affects what you use it for Allan Ramsay, -14- What difference does it make to computational treatments?

15 It affects what kind of inference engine you build You can t do proof by contradiction: so you can t use resolution, simple tableaux. So you can t just pinch Vampire,...You shouldn t anyway: natural languages are not first-order, not even if you use a first-order modal logic I use SATCHMO with extensions defaults, epistemic & temporal contexts, fine-grained intensionality, asymmetric approximate unification; but basic SATCHMO is so simple that extensions are easy. Allan Ramsay, -15- It affects what kind of inference engine you build

16 prove(p, LABEL) :- P. prove(p & Q, LABEL) :- prove(p, LABEL), prove(q, LABEL). prove(p or Q, LABEL) :- prove(p, LABEL); prove(q, LABEL). prove(not(p), LABEL) :- prove(p ==> absurd, LABEL). prove(p ==> Q, LABEL) :- assert(p), (prove(q, LABEL) -> (used(p, LABEL), %% Relevance logic retract(p); (retract(p), fail)). Allan Ramsay, -16- It affects what kind of inference engine you build

17 It affects what kind of meaning representation you use Classical Translate into some suitable meaning representation (not first-order logic!) Apply normal-form (forwards inference) rules: negation normal form, quantifier free form, clausal form,... Every word and phrase has a translation, and hence we know what they mean Allan Ramsay, -17- It affects what kind of meaning representation you use

18 It affects what kind of meaning representation you use Classical Translate into some suitable meaning representation (not first-order logic!) Apply normal-form (forwards inference) rules: negation normal form, quantifier free form, clausal form,... Every word and phrase has a translation, and hence we know what they mean Constructive Natural language is the most suitable meaning representation. Nothing goes missing, nothing gets accidentally added. Apply normal-form (forwards inference) rules: polarity marking,..., negation normal form, quantifier free form, clausal form,... No need to annotate a grammar with semantic interpretations. No need to have a grammar! Allan Ramsay, -18- It affects what kind of meaning representation you use

19 It affects what you use it for If what you are given is a simple statement, you ground it and use it to extend the minutes by doing a bit (???) of model building. If what you are given is a rule (i) you ground the antecedent;(ii) use it to make temporary extension of the minutes; (iii) ground the consequent; (iv) then unextend the minutes. Allan Ramsay, -19- It affects what you use it for

20 THE END! What does it mean to say that NL is constructive, why do I think it s a way of thinking about it, what kind of meaning rep and inference engine do you need to proceed in this way. Allan Ramsay, -20- It affects what you use it for