Lecture Notes Supplement, 22 Sep 2010
Last Update: 23 September 2010
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§1.3: Predicates & Quantifiers (cont'd)
Knowledge Representation & Translation:
- How to Represent "Toy Gun", etc.:
In class today, I represented
"Mark Twain was a wise man" in FOL as
"Wise(mark-twain) ∧ Man(mark-twain)".
But I pointed out that this doesn't work for all Adjective+Noun
E.g., "Dumbo is a small elephant" shouldn't be represented as
"Small(dumbo) ∧ Elephant(dumbo)",
because it would logically follow
that Dumbo is small
(but we assume that all elephants are large).
Similarly, "x is a toy gun" shouldn't be represented as
"Toy(x) ∧ Gun(x)",
because—although toy guns are
toys—they aren't guns.
Similarly, "Fred is an alleged murderer" shouldn't be represented as
"Alleged(fred) ∧ Murderer(fred)",
because—although Fred may be
alleged to be something—he might not be a murderer.
- And how should we represent "Ann swam quickly"?
- It's not that we can't figure out some way to represent these.
Rather, the problem is that our language for FOL is not rich enough to
represent these in such a way that we can reason correctly about them.
We need to extend FOL, just as FOL was itself an extension of
earlier lecture, I described some of those extensions.
One of them,
"modal" logic, can be used to handle "swimming quickly".
extensions can handle the other cases.
To read more about this, take a look at:
Parsons, Terence (1970),
"Some Problems concerning the Logic of Grammatical Modifiers",
Synthese 21: 320–334.
"The Meaning of Noun Phrases"
- Part of a longer document called "Common Sense Problem Page":
"Commonsense reasoning is a central part of intelligent
behavior. In contrast to expert knowledge, which is usually explicit,
most commonsense knowledge is implicit. One of the prerequisites to
developing commonsense systems is making this knowledge explicit. The
goal of the formal commonsense reasoning community is to encode this
knowledge using formal logic."
Text copyright © 2010 by William J. Rapaport
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