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Natural Language and Logic:Some Difficulties
John Barnden
Professor of Artificial Intelligence
School of Computer Science
Substances
Do you like peanut butter? What exactly is it you like?
likes(student123, peanut-butter) ???
.x ( likes(student123, x) is-peanut-butter(x) ) ???
Object Identity
What is a river? The water is constantly exchanged. And are the banks included?
So what would a logic constant like the-nile stand for???
Lincoln’s ax(e): Repaired bit by bit over years. Is it the same axe at the end?
What would lincolns-ax stand for?
Subtlety of Common Actions
“Tesco sells pineapples”
What does this mean, exactly?And does it actually matter?
sells(Tesco, pineapples) ?????Simple representation, but what inferences can
be drawn ??
Subtlety of Prepositions
“There’s a banana in the bowl”The banana need not be within the volume of
the bowl.
“There’s a mirror on my ceiling”The mirror is below the ceiling!
“Vanessa Granola is at her desk”
Context Often Needed for Precise Meaning:
Some Examples
Pronouns. Ambiguous words.
Prepositional phrase attachment. “Hank saw Vanessa with a telescope”
Did Hank use a telescope? Or did Vanessa have a telescope?
Quantification: Context-Sensitive
“When Hank arrived everyone laughed” …. .x (is-person(x) laughed(x)) would be wrong
“When Hank arrived everyone sat down to dinner.”
“Hank doesn’t believe anything Vanessa tells him”
Vague Quantification
Most, a few, several, many, ….
Most.x (is-person(x) anxious(x)) ????
But what inferences could you draw, and how?
Embedding of Propositions, Situations, etc.
“Vanessa fell over because Hank bumped into her”
In ordinary first-order logic, can’t write things like
cause( bumpinto(H,V), fallover(V) ) because formulas (e.g. bumpinto(H,V) )
can’t be arguments in applications of predicate symbols etc.
One method: take situations, events, etc. to be objects, just as e.g. people are.
f,b (is-fallover-event(f,V) is-bumpinto-event(b,H,V)
cause(b,f))
Situations, events, etc. are treated as objects in ordinary language anyway.
Embedding contd.: Another example -- Belief
“Vanessa believes that Hank is lying.”
Can’t write following in ordinary first-order logic if lying is a predicate symbol:
believes(Vanessa, lying(Hank))
“Honorary” Object Types
fake X, alleged X, imitation X, plastic tree, toy X, model boat, ...
a fake gun is not actually a gun, so it would be bad to write something like
fake (g) is-gun(g)
but it would be nasty to have to use fake-gun(g)
Figurative Language
Metonymy: “He was listening to Bach”
Metaphor: “The suspicion grabbed me by the back of
my neck.”
Variety of Types of Difficulty
May need context in order to pin precise meaning down.
Precise meaning may be difficult to pin down even when context fully known.
Precise meaning may be difficult to express in logic, or to do so usefully.
Final Remarks
This presentation has shown just a selection of the problems of expressing the meaning of natural language utterances in logic.
There are many approaches to the problems, but no-one has a complete solution to all of them and some remain puzzling.
Feel like doing a PhD on the issues??!
