Rules

Lecture notes

Phil/Psych 256
Jan. 21, 1997

Rules (productions):

Q: What is a rule?

	A1: A knowledge structure of form

		IF condition THEN action

Q: What can rules represent?

	A1: logical relationships, e.g.,
		IF eat(x,vegies) THEN peaceful(x) 

	A2: prescriptions for action, e.g.,
		IF threaten(x,y) THEN pay(y,x,money) 

	A3: prescriptions for thought, e.g.,
		IF threaten(x,y) THEN consider(x,bully) 

Q: How are rules related to logic?

	A1: IF-THEN structures are similar to logical implication ( -> )

	A2: logic does not permit actions as components, e.g.,
	pay(y,x,money) 	(English is ambiguous about this)

	A3: logical generalizations are universal, e.g., 
		(x)(eats(x,vegies) -> peaceful(x)) 
	whereas rules may be defaults, e.g.,
		IF eat(x,vegies) THEN peaceful(x) 
	with exceptions, e.g.,
		IF is-a(x,rhino) THEN not peaceful(x) 

	A4: rules form a programming language:
		- easily modeled
		- directly encode search info, e.g.,
		IF you canÕt solve a problem
		THEN find someone who can
			and ask them

Q: What are some linguistic rules?

	A1: Phonology, e.g.,
		IF an English syllable (morpheme) begins with 3 consonants 
		THEN they must be {s}{p,t,k}{l,r} 

	A2: Morphology, e.g.,
		IF you want to pluralize x THEN add "s":
			dog -> dogs, cat -> cats
		NB.  there are exceptions:
			child -> children

	A3: Syntax, e.g.,
		IF you want to form a question from a declarative sentence 
		THEN move the auxiliary verb to the front:
			You are ok -> Are you ok?

		IF that doesn't work 
		THEN place a form of "do" in front:
			That sucks -> Does that suck?

		also:

		S -> NP VP     ART -> the, a
		NP -> ART N    N -> boy, dog, ...
		VP -> V  NP    V ->  hit, feed, ...


Q: How do I plan an extortion?

	A1: "The Operation:"
		IF pay(v,p,m) THEN beat-up(p,v) 

	A2: "The Other Operation:"
		IF not pay(v,p,m) THEN not beat-up(p,v) 

	A3: "The Other Other Operation:"
		IF not pay(v,p,m) THEN beat-up(p,v) 

Phil/Psych 256
Jan. 23, 1997

Q: Can Shimon marry Rebecca?

Database:
	IF related-to(x,y) THEN not marry(x,y)

	IF jewish(z) and father(x,y) and not jewish(x) THEN not related-to(y,z)

	IF mother(x,y) and jewish(x) THEN jewish(y)

	IF jewish(x) and jewish(y) THEN marry(x,y)

GOAL: marry(Shimon,Rebecca)

Database (cont.):
	mother(Rachel,Shimon)
	jewish(Rachel)
	father(Joe,Rebecca)
	not jewish(Joe)

Knowledgebase :
	IF rule(c,not a) THEN rule(not c, a) [search]

	IF rule(c1,a) and rule(c2,a) 
	THEN rule(c1 and c2,a)  [chunking/composition] 

Try this at home!

Q: What about psychological plausibility?

	A1: ChomskyÕs LAD explains rule acquisition despite 
	"poverty of stimulus,"
	e.g., English kiddies learn 
		S --> NP VP (SVO) 
	whereas Gaelic kiddies learn
		S --> VP NP (VSO) 

	A2: Kiddies learn rules despite "Motherese," e.g., go --> goed 
	(Brown and Hanlon)

	A3: In general, systematic errors indicate overgeneralization of rules, 
	e.g.,
		 234	 387	 462	 615	 723
		-153	-124	-234	-351	-258
		-----	-----	-----	-----	-----
		 121	 263	 232	 344	 535
	(VanLehn)

Q: What about implicit learning?

	A1: Implicit learning works better for complex rules (Reber et al.)

	A2: Explicit learning works better for simple rules, e.g., IQ test 
	questions:
		abcbcdcde_

	A3: Implicitly learned rules are difficult to articulate

Q: What are the components of ACT-R? 
(Adaptive Character/Control of Thought - Rationality)

	A1: Production memory - a list of rules that encode skills and 
	implicitly governed behavior

	A2: Declarative memory - a list of facts "committed to memory"

	A3: Working memory - small, short-term storage for retrieval of facts, 
	manipulated by productions; accessible to conscious inspection

Q: How does ACT-R work?

	1. a GOAL is set in working memory

	2. productions that match the contents of working memory "fire"

	3. productions may fire other productions and/or change the contents 
	of working memory; they may also cause the retrieval and storage 
	information from declarative memory

	4. IF the GOAL is not satisfied 
	   THEN go back to step 2.

	(See the addition example in readings)

Q: Is ACT-R psychologically plausible?

	A1: It does model errors of overgeneralization

	A2: It supports some re-use of information 
	(condition-action assymmetry)

	A3: It reflects the "power law of practice" 
	(acquisition, chunking, relevance)

	A4: It has been tested mostly in "safe" domains

	A5: It models "chunking"

	A6: It explains lack of conscious access to skill learning and rules

	A7: It accords with dissociation (amnesiacs)


Q: What about practical applications?

	A1: ACT-R has been used to build tutorial systems

	A2: These instruct by inferring erroneous rules and suggesting better
	ones

Review of rules: 

	1. Database of facts (working and declarative memory

	2. Knowledgebase of procedures (production memory)

	3. Goal expression (working memory)

	4. Derivation strategy (matching and firing, storage and retrieval)

	5. Works well for planning, learning, language acquisition, instruction

	6. Accords with important psychological data

Have a look at the ACT Web page!

Next week:

	- Concepts
	- Minsky

Further materials

• Weddability example
• ACT Web page
• Soar Home Page