Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
non-demonstrative and defeasible, that is, prone to error and correction. In fact these inferences are widely
regarded as fundamentally beyond the analytical tools available now. See, e.g., Chomsky (1968, p6), Chomsky
(1975, p138), Partee (1975, p80), Kamp (1984, p39), Fodor (1983), Putnam (1986, p222), and many others. 51
Putnam argues that
…deciding – at least in hard cases – whether two terms have the same meaning or whether they
have the same reference or whether they could have the same reference may involve deciding what
is and what is not a good scientific explanation.
For the moment, then, we will not consider these parts of the problem, but see the further discussion of these
matters in §16.5.1 and in §?? below.
Fortunately, we do not need the actual semantic values of expressions in order to recognize many entailment
relations among them, just as we do not need to actually interpret the sentences of propositional logic or of
prolog to prove theorems with them.
16.3 Meaning postulates
To prove the theorems we want, theorems of the sort shown on 232, we often need to know more than just
thetypeofsemanticobjectwearedealingwith. Totake a simple example, we have allowed coordinators to
combine sentences that express truth values, so both and and or presumably have the type t → t → t, butthey
are importantly different. To capture the difference, we need some additional information that is specific to
each of these lexical items. 52 Among the important inferences that the language user should be able to make
are these, which a logician will find familiar. For all structures ∆, Γ :
C(∆) C(Γ )
C(and,C(∆),C(Γ ))
C(and,C(∆),C(Γ )
C(∆)
C(∆)
C(or,C(∆),C(Γ ))
C(and,C(∆),C(Γ )
C(Γ )
C(Γ )
C(or,C(∆),C(Γ ))
For the quantifiers, we can can generalize Aristotle’s syllogistic approach to a more general reasoning with
monotonicity properties in intransitive sentences. Here we just leave out the functional categories, and use
51 Philosophers, trying to make sense of how language could be learned and how the claims we make in language are related to
reality have worried about the two error-prone steps in the picture above: the assessment of what the speaker intends and then the
assessment of what things actually are charging in the intended sense. Are these possible sources of error always present? Suppose
that instead of interpreting what someone else said, you are interpreting what you said to yourself, or what you just wrote in your
diary, or some such thing. In the typical case, this would reduce the uncertainty about what was intended. (But does it remove it?
What about self-deception, memory lapses, etc?) And suppose that instead of talking about something abstract like charging (in any
sense), we are talking about something more concrete and directly observable. Then we could perhaps reduce the uncertainty about
the actual extensions of our predicates. (But again, can the uncertainty be removed? Even in claims about your own sensations, this
is far from clear. And furthermore, even if the uncertainty were reduced for certain perceptual reports that you make to yourself, it
is very unclear how the more interesting things you know about could perch on these perceptual reports for their foundation.) The
search for a secure empirical foundation upon which human knowledge could rest is often associated with the “positivist tradition” in
philosophy of science, in the work of Carnap, Reichenbach and others in the mid 1900’s. These attempts are now generally regarded as
unsuccessful (Quine, 1951b; Fodor, 1998, for example), but some closely related views are still defended (Boghossian, 1996; Peacocke,
1993, for example).
52 Logicians and philosophers have sometimes assumed that the rules for quantifiers and for the propositional operators would not
need to be given in this lexically specific fashion, but that they might be “structural” in the sense that the validity of the inferences
would follow from their semantic type alone. In our grammar, though, we have not found any motivation for distinguishing semantic
types for each of the coordinators. This kind of proposal was anticipated and discussed in the philosophical literature, for example in
the following passage:
…with the exception of inferences involving substitution of sentences with the same truth value, none of the standard
inferences involving sentential connectives is structurally valid. Briefly, the sentences ‘P and Q’ and ‘P or Q’ have the same
structure; the former’s entailing P is due to the special variation the word ‘and’ plays upon a theme it has in common with
‘or’. Quantifiers are more complicated but they too can be seen as falling into a single semantic category…(Evans, 1976,
pp64-66)
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