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

Stabler - Lx 185/209 2003
10. Call a truth-valuable expression containing at most one relation-denoting semantic atom a “simple predication.”
In no human language are the simple predications logically independent, in the sense that the
truth values of one are independent of the others.
For example, since it is part of the meaning of the predicate red that red objects are also in the extension
of colored, the truth value of aisredis not independent of the truth value of a is colored.
In propositional prolog, the interpretation of each atomic formula is independent of the others. The importance
of this property has been discussed by Wittgenstein and many other philosophers (Wittgenstein, 1922; Pears, 1981;
Demopoulos and Bell, 1993).
11. Language users can recognize (some) entailment relations among expressions.
Every language includes hyponyms and hypernyms.
Call an expression analytic if it is true simply in virtue of its meaning. Every language includes analytic
expressions.
Perfect synonymy is rare; and perfect (non-trivial) definitions of lexical items are rare.
12. In all languages: Frequent words tend to be short. The most frequent words are grammatical formatives.
The most frequent words tend to denote in high types.
Related facts: affixes and intonation features tend to denote in high types.
13. Quantifiers that are semantic atoms are monotonic.
14. Relation-denoting expressions that are semantic atoms may require argument-denoting expressions to
occur with them, but they never require more than 3.
15. Roughly speaking, specifying for each relation-denoting expression the arguments that are required is
simpler than specifying for each argument-denoting expression the relations it can be associated with. So
we say: verbs “select” their arguments.
16. At least some human languages seem to have truth predicates that apply to expressions in the same
language.
But the semantic paradoxes considered by Russell, Tarski and others show that they cannot apply to all and only the
true expressions. – See for example the papers in (Blackburn and Simmons, 1999).
17. Human languages have patterns that are not (appropriately) described by finite state grammars (FSGs), or
by context free grammars (CFGs). But the patterns can all be described by multiple context free grammars
(MCFGs) and other similar formalisms (a certain simple kind of “minimalist grammars,” MGs, and multicomponent
tree-adjoining grammars, MC-TAGs).
This last idea has been related to Chomsky’s “subjacency” and the “shortest move constraint.”
As we will see, where these problems can be defined reasonably well, only certain kinds of devices can solve
them. And in general, of course, the mechanisms of memory access determine what kinds of patterns can
distinguish the elements of a language, what kinds of problems can be solved.
Propositional prolog lacks most of these properties. We move to a slightly more human-like logic with
respect to properties 7 and 8 in the next section. Many of the other properties mentioned here will be discussed
later.
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