Transcript Data Modeling - Hiram College

(FO) Inference Methods
CPSC 386 Artificial Intelligence
Ellen Walker
Hiram College
Inference Methods
• Unification (prerequisite)
• Forward Chaining
– Production Systems
– RETE Method (OPS)
• Backward Chaining
– Logic Programming (Prolog)
• Resolution
– Transform to CNF
– Generalization of Prop. Logic resolution
Forward Chaining
• Given a new fact, generate all consequences
• Assumes all rules are of the form
– C1 and c2 and c3 and…. --> result
• Each rule & binding generates a new fact
• This new fact will “trigger” other rules
• Keep going until the desired fact is generated
• (Semi-decidable as is FOL in general)
Efficient Forward Chaining
• Order conjuncts appropriately
– E.g. most constrained variable
• Don’t generate redundant facts; each new
fact should depend on at least one newly
generated fact.
– Production systems
– RETE matching
– CLIPS (on CS)
OPS
• Facts
– Type, attributes & values
– (goal put-on yellow-block red-block)
• Rules
–
–
–
–
If conditions, then action.
Variables (<x>, <y>, etc) can be bound
If (goal put-on <x> <y>) AND
(clear <x>) THEN add (goal clear <y>)
RETE Network
• Based only on Left Sides (conditions) of rules
• Each condition (test) appears once in the
network
• Tests with “AND” are connected with “JOIN”
– Join means all tests work with same bindings
Example Rules
1. If (goal put-on <x> <y>) AND
(clear <x>) AND (clear <y>) THEN
add (on <x> <y>) delete (clear <y>)
2. If (goal clear <x>) AND (on <y> <x>) AND (clear <y>) THEN
add (clear <x>) add (on <y> table) delete (on <y> <x>)
3. If (goal clear <x>) AND (on <y> <x>) THEN
add (goal clear <y>)
4. If (goal put-on <x> <y>) AND (clear <x>) THEN
add (goal clear <y>)
5. If (goal put-on <x> <y>) AND (clear <y>) THEN
add (goal clear <x>)
RETE Network
type is on?
bind x and y (1)
type is goal?
goal type is put-on?
goal-type is clear?
bind x and y (3)
bind x (2)
type is clear?
bind x (4) bind y (5)
JOIN
report rule 1
is satisfied
JOIN
report rule 3
is satisfied
JOIN
JOIN
report rule 5
report rule 2 is satisfied
is satisfied
JOIN
report rule 4
is satisfied
Using the RETE Network
• Each time a fact comes in…
– Update bindings for the relevant node (s)
– Update join(s) below those bindings
– Note new rules satisfied
• Each processing cycle
– Choose a satisfied rule
Example (Facts)
1. (goal put-on yellow-block red-block)
2. (on blue-block yellow-block)
3. (on yellow-block table)
4. (on red-block table)
5. (clear red-block)
6. (clear blue-block)
Why RETE is Efficient
• Rules are “pre-compiled”
• Facts are dealt with as they come in
– Only rules connected to a matching node are
considered
– Once a test fails, no nodes below are considered
– Similar rules share structure
• In a typical system, when rules “fire”, new
facts are created / deleted incrementally
– This incrementally adds / deletes rules (with
bindings) to the conflict set
CLIPS
• CLIPS is a forward-chaining production system that
uses the RETE method.
• Important commands
–
–
–
–
–
–
–
(assert fact) (deffacts fact1 fact2 … )
(defrule rule-name rule)
(reset) - eliminates all facts except “initial-fact”
(load file) (load-facts file)
(run)
(watch all)
(exit)
CLIPS Rule Example
(defrule putting-on
?g <- (goal put-on ?x ?y)
(clear ?x)
?bottomclear <- (clear ?y)
==>
(assert (on ?x ?y))
(retract ?g)
(retract ?bottomclear)
)
Blocks example
•
•
•
•
•
•
•
•
•
(load “blocks.clp”)
(assert (on blue table))
(assert (clear blue))
(assert (on red table))
(assert (on green red))
(assert (clear green)
(assert (goal put-on red blue))
(watch all)
(run)
Backward Chaining
• Consider the item to be proven a goal
• Find a rule whose head is the goal (and
bindings)
• Apply bindings to the body, and prove these
(subgoals) in turn
• If you prove all the subgoals, increasing the
binding set as you go, you will prove the item.
• Logic Programming (gprolog, on CS)
Prolog Rules
• Rule Example
– puton(X,Y) :- cleartop(X), cleartop(Y),takeoff(X,Y).
• Capital letters are variables
• Three parts to the rule
– Head (thing to prove)
– Neck :– Body (subgoals, separated by ,)
• Rules end with .
Prolog Environment
• SWI-Prolog on windows – to start, double-click plwin
• To read a file, consult(‘file’).
• To enter data directly, consult(user). Type control-D
when done.
• Every statement must end in a period. If you forget,
put it on the next line.
• To prove a fact, enter the fact directly at the
command line. gprolog will respond Yes, No, or give
you a binding set. If you want another answer, type ;
otherwise return.
• Trace(predicate) or trace(all) will allow you to watch
the backward chaining process.
Monkey and Banana in Prolog
movedTo(X,Y) :- at(X,Y,Z).
movedTo(monkey,Y) :- at(monkey,X,floor), write('Walk
to '), write(Y), nl.
movedTo(ladder,Y) :- at(ladder,X,floor),
movedTo(monkey,X),
write('Drag ladder to '), write(Y), nl.
reachable(X) :- at(X,Y,ceiling), movedTo(ladder,Y),
movedTo(monkey,Y).
reach(X) :- reachable(X), write('Reach for '), write(X), nl.
Running the Monkey & Banana
consult(user).
compiling user for byte code...
at(monkey,corner,floor).
at(monkey,corner,floor).
at(ladder,left,floor).
at(ladder,left,floor).
at(banana,center,ceiling).
at(banana,center,ceiling).
Control-D
reach(banana).
In-class assignment
• Try the following in both Prolog and Clips:
– Define the concept of a prerequisite, and at least
the following facts:
• Prerequisite of 172 is 171
• Prerequisite of 400 is 201
Prerequisite of 201 is 172
Prerequisite of 386 is 172
– Create a rule that a course cannot be taken unless
its prerequisite has been taken
– Create facts to indicate that Mary has taken 172
and 171.
– Prove the following in your system:
• Mary can take 386, Mary cannot take 400