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Overview
Midterm results
Midterm solution
Unification examples
Factor
Resolvent
Resolution
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Midterm Results
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CPSC 320 Midterm
Midterm
: 7 (includes two 100โs)
: 8
: 4
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Problem 1
(defun
factorial
(n)
(if
(eq
n
1 (*
n (factorial
(- n
1)))
)
)
syntax: -
content: -
Common mistakes: returning (1), not 1. Infix notation.
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Problem 2
2.1 : Neuroscience, Psychology, Logic, Mathematics, ComputerScience, Cognitive Science, and Philosophy.2.
Strong AI: when we build something intelligent, it will be conscious
Weak AI: regardless of whether it is conscious or not, we canbuild something that acts like human in an intelligent manner.
Turing test can only test for
weak
AI.
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Problem 3.
Space: BFS =
, DFS =
Time: BFS =
, DFS =
BFS: both complete and optimal.
DFS: incomplete and suboptimal.
BFS best when goal is scarce and relatively shallow, and when anoptimal solution is required.
DFS best when there are many shallow goals and optimality doesnot matter much.
Common mistakes: fixed goal depth
does not imply a finite search
tree.
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Problem 3.2 (1)
uses
to choose the best node to
expand (2 points).
Either pushing or enqueueing can be used, because it will besorted anyway. If the list is sorted to begin with, repeated sortingmay not be necessary because we can just insert the new nodeat the right place (2 points).
is optimally efficient,i.e. guaranteed to expand the least
number of nodes (1 point).
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Problem 3.2 (2)
-contour is a contour of nodes within a fixed
-limit, where their
values are all the same (2 points).
IDS uses depth of node, while
uses the
value as a
bound (1 point).
is basically a depth-first search with
serving as the
depth bound, so the space complexity is linear to the path cost tothe goal (2 points).
Common mistakes: (1)
is basically a breadth first, so all expanded
nodes are kept in memory. It does not expand nodes with larger
values if there exist nodes with smaller
values. (2)
can
actually be slower than
because it revisits shallow
contours
again and again (in the worst case).
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Problem 3.
(1)
local maxima, ridge, palteue, spiky terrain, etc (3 points).
because S.A. is probabilistic, it can overcome these localdead-ends (3 points).
(2)
Higher (2 points)
Lower (2 points)
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UNIFY : examples
(unify โ(p x) โ(p (a)))(unify โ(p (a)) โ(p x))(unify โ(p x (g x) (g (b)))
โ(p (f y) z y))
(unify โ(p (g x) (h w) w) โ(p y (h y) (g (a))))(unify โ(p (f x) (g (f (a))) x) โ(p y (g y) (b)))(unify โ(p x) โ(p (a) (b)))(unify โ(p x (f x)) โ(p (f y) y))
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Resolution in Predicate Calculus
Factors
Binary resolvent
Properties of resolution
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Factor of a Clause
Definition
: If two or more literals of a clause
(with the
same
sign)
have a most general unifier
, then
is called a
Factor
of
. If
is a unit clause, it is called a
Unit Factor
of
.
Example
:
.
The first two literals have a unifier
, so
has a
factor
Note
: Factors of a clause are much succint and when two clauses
and
cannot be resoved directly, their factors (letโs call them
and
can be
resolved.
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Resolving Two Clauses
Definition:
Let
and
be two clauses (called
parent clauses
) with
no variables in common, and with complementary literals
and
such that
and
have a most general unifier
. Then the clause
is called a
binary resolvent
of
and
. The literals
and
are called
the literals resolved upon
.
Note
: A clause can be treated as a set of literals.
Example:
Resolve the following (hint:
)
and
.
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Resolvent
Definition:
A
resolvent
of parent clauses
and
is one of the
following binary resolvents:
a binary resolvent of
and
a binary resolvent of
and a factor of
a binary resolvent of a factor of
and
a binary resolvent of a factor of
and a factor of
Example:
resolve the two clauses
and
.
(hint: resolve the factor of
and clause
)
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Property of Resolution for First-Order Logic
Complete
: If a set of clauses
is unsatisfiable, resolution will
eventually
derive
.
Everything that is true can be proved (eventually).
Sound
: If
is derived by resolution, then the original set of
clauses
is unsatisfiable.
Everything that is proved is true
.
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Weakness of Resolution
Basically, resolution tries to derive
Axioms
Theorem =
Is there a
in the axioms? If there is, the whole formula will
always be unsatisfiable no matter what.
Can we tell whether axioms alone can derive
? (generally, this
is not the case)
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Key Points
unification algorithm
factors : definition, and how to derive, why factors are important
resolvent : definition, and how to derive
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