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Notes from French trip

Splitting concepts

	When a concept turns out to be ambiguous, we may have to
split it, and one method uses a generalized adjective.  A generalized
adjective when APPLIED to and entity gives a MODIFIED entity.  We
may have

app(red,dog)	red dog
app(alleged,criminal)	alleged criminal

So, can we do "John attempted to bribe a public official"?

*****

"Pat knows that Mike is in Luminy"

k(pat,at(mike,luminy))

does pat call him Mike

does pat call it Luminy

Is Pat's notion of "at" the same as ours?

Is Pat's notion of the borders of Luminy the same as ours?

Does it mean "at this instant" or "has his residence" or "is visiting
for 6 weeks"?

Communication among people and among computers uses an imprecise
language and depends on common knowledge and joint knowledge to
disambiguate.

Do people and must computers also use an imprecise internal representation
as well as communicate in an imprecise langaage?  In my opinioh yes.

******

∀p g a s.[holds(wants(p,g) and causes(does(p,a),g) implies does(p,a),s)]

axiom(wants(p,g) and causes(does(p,a),g) implies does(p,a))

*****

	If we minimize expressions rather than predicates, we are no
longer dependent on what predicates and expressions are used.  We can have
an invariant (covariant?) notion.  Is there anything like Lagrange
multipliers?

******

Minimal interpretations w/r a formula with a free variable

1. All interpretations have the same domain.

2 I1 ≤E I2 iff ∀x.[I1[[E]] ≤ I2[[E]]]

We can vary the functions as well as the predicates.

A[phi,psi] ∧ ∀x.(E(phi,psi) ⊃ E(f,p)) ⊃ ∀x(E(f,p) ⊃ E(phi,psi))

A set of formulas is minimally modelable if every model contains a
minimal model.

Open questions:
	1. When are teere minimal models?
	2. When is a circumscription schema equivalent to a single formula?

*****

How about walking to x, being interrupted by a herd of elephants crossing
the streed, each holding the tail of its predecessor in its trunk.

*****

holds(p) ≡ holds(p,nominal)

holds(p,nominal) ∧ ¬prevented(p,w) ⊃ holds(p,w)

at(x,y) ≡ holds(at(x,y)) ≡ holds(at(x,y),nominal)

**

We want a small example of rationality, e.g. a buyer and seller or
passing the salt.

*****

holds(all p.s) ⊃ ∀s.holds(p,s)

holds(succeeds(walks(p,north) until at(p,Chestnut)),s)

	⊃ holds(at(p,Chestnut),result(walks(p,north) until at(p,Chestnut)),s)

What is the limitation on the quantification symbolism?

"He believes that Pat and Mike and the passengers of the bus are the only
witnesses to his crime".

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John knows that if he walks to the car he will be at the car.

causes(e,P) is the proposition that P will be true after e occurs.

holds(k(John, result(does(John,walk(car)),at(John,car))),s)

___

holds(rational(p) and wants(p,g) and k(p,results(does(p,a),g)) implies
does(p,a),a)

___

holds(results(does(p,a),g),s) ≡ holds(g,result(does(p,a),s))

*****