Knowledge Representation and
Reasoning
Stuart C. Shapiro
Professor, CSE
Director, SNePS Research Group
Member, Center for Cognitive Science
Fellow, AAAI
Chair, ACM/SIGART, 1991-1995
President, KR., Inc., 1998-2000
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Introduction
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Long-Term Goal
• Theory and Implementation of
Natural-Language-Competent
Computerized Cognitive Agent
• and Supporting Research in
Artificial Intelligence
Cognitive Science
Computational Linguistics.
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Research Areas
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Knowledge Representation and Reasoning
Cognitive Robotics
Natural-Language Understanding
Natural-Language Generation.
Goal
• A computational cognitive agent that can:
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Understand and communicate in English;
Discuss specific, generic, and “rule-like” information;
Reason;
Discuss acts and plans;
Sense;
Act;
Remember and report what it has sensed and done.
Cassie
• A computational cognitive agent
– Embodied in hardware
– or Software-Simulated
– Based on SNePS and GLAIR.
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GLAIR Architecture
Grounded Layered Architecture with Integrated Reasoning
Knowledge Level
NL
SNePS
Perceptuo-Motor Level
Sensory-Actuator Level
Vision
Sonar
Motion
Proprioception
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SNePS
• Knowledge Representation and Reasoning
– Propositions as Terms
• SNIP: SNePS Inference Package
– Specialized connectives and quantifiers
• SNeBR: SNePS Belief Revision
• SNeRE: SNePS Rational Engine
• Interface Languages
– SNePSUL: Lisp-Like
– SNePSLOG: Logic-Like
– GATN for Fragments of English.
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Interaction with Cassie
English
(Statement, Question, Command)
(New Belief)
[SNePS]
(Current) Set of Beliefs
[SNePS]
Reasoning
Clarification Dialogue
GATN Parser
Looking in World
Answer
Actions (Updated) Set
of Beliefs
[SNIP]
[SNeRE]
[SNePS]
GATN
Generator
Reasoning
English sentence expressing
new belief answering question reporting actions
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Example Cassies
& Worlds
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Cassie, the BlocksWorld Robot
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FEVAHR: Award-Winning
Embodied Cassie Project
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FEVAHRWorld Simulation
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UXO Remediation Cassie
Corner flag
Field
UXO
Drop-off zone
NonUXO object
Battery
meter
Corner flag
Recharging
Station
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Corner flag
Cassie
Safe zone
Crystal Space Environment
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UB Virtual Site Museum
• The 9th-Century BC Northwest Palace at Nimrud-Iraq
is the best preserved and documented of all the
Assyrian palaces.
• Its audience halls were originally created as the
backdrop for differing royal activities.
• Completely immersive re-creation of this palace with
animated characters and interactive story boards.
• T. Kesavadas & S. Paley
Modeling of King - Animation in Real time VR
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Sample Research Issues
Intensional Entities
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Intensional Entities 1
• Rather than represent “objects in the world,”
represent mental entities.
• Includes Imaginary and Fictional Entities.
• Multiple mental entities may correspond to
one world object.
– Intensional entities may be co-extensional.
– But must be kept separate.
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Intensional Entities 2
: The morning star is the evening star.
I understand that the morning star is the evening
star.
: The evening star is Venus.
I understand that Venus is the evening star.
: Clark Kent is Superman.
I understand that Superman is Clark Kent.
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Intensional Entities 3
: Lois Lane saw Clark Kent.
I understand that Lois Lane saw Clark Kent.
: Did Lois Lane see Superman?
I don't know.
: Did Lois Lane see Clark Kent?
Yes, Lois Lane saw Clark Kent.
Note Open World Assumption.
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Intensional Entities 4
: Superman went to the morning star.
I understand that Superman went to Venus.
: Did Clark Kent go to Venus?
Yes, Superman went to Venus.
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Intensional Entities 5
: Buck Rogers went to the evening star.
I understand that Buck Rogers went to Venus.
: Who went to Venus?
Buck Rogers went to Venus
and Superman went to Venus.
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Intensional Entities 6
The morning star
The evening star
Go to
Go to
Superman
Clark Kent
See
Lois Lane
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Venus
Buck Rogers
Sample Research Issues
Complex Categories
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Complex Categories 1
• Noun Phrases:
<Det> {N | Adj}* N
Understanding of the modification must
be left to reasoning.
Example:
orange juice seat
Representation must be left vague.
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Complex Categories 2
: Kevin went to the orange juice seat.
I understand that Kevin went to the orange juice
seat.
: Did Kevin go to a seat?
Yes, Kevin went to the orange juice seat.
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Complex Categories 3
: Pat is an excellent teacher.
I understand that Pat is an excellent teacher.
: Is Pat a teacher?
Yes, Pat is a teacher.
: Lucy is a former teacher.
I understand that Lucy is a former teacher.
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Complex Categories 4
: `former' is a negative adjective.
I understand that `former' is a negative adjective.
: Is Lucy a teacher?
No, Lucy is not a teacher.
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PseudoRepresentation of
Complex Categories
• Isa(B30, CompCat(orange, CompCat(juice, seat)))
• Isa(Pat, CompCat(excellent, teacher))
• Isa(Lucy, CompCat(former, teacher))
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Sample Research Issues
Possession
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Possession 1
• “One man’s meat is another man’s poison.”
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Possession 2
: Richard's meat is Henry's poison.
I understand that Henry's poison is Richard's
meat.
: Edward ate Richard's meat.
I understand that Edward ate Richard's meat.
: Did Edward eat Henry's poison?
Yes, Edward ate Henry's poison.
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Possession 3
: Did Edward eat Henry’s meat?
I don’t know.
: Did Edward eat Richard's poison?
I don’t know.
Moral: Possession is a three-place relation.
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PseudoRepresentation of
Possession
• Has(Richard, meat, B35)
• Has(Henry, poison, B37)
• Equiv(B35, B37)
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Sample Research Issues
Propositions about Propositions
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Propositions about Propositions 1
• Propositions are “first-class” mental entities.
• They can be discussed, just like other mental
entities.
• And must be represented like other mental
entities.
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Propositions about Propositions 2
: That Bill is sweet is Mary's favorite proposition.
I understand that Mary's favorite proposition is
that Bill is sweet.
: Mike believes Mary's favorite proposition.
I understand that Mike believes that Bill is sweet.
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Propositions about Propositions 3
: That Mary's favorite proposition is that Bill is
sweet is cute.
I understand that that Mary's favorite proposition
is that Bill is sweet is cute.
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Representing Propositions
• Representation of Proposition
– Not by a Logical Sentence
– But by a Functional Term
– Denoting a Proposition.
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PseudoRepresentation of
Propositions about Propositions
• Has(Mary, CompCat(favorite, proposition),
HasProp(Bill, sweet))
• Believes(Mike, HasProp(Bill, sweet))
• HasProp(Has(Mary,
CompCat(favorite, proposition),
HasProp(Bill, sweet)),
cute)
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Sample Research Issues
Conditional Plans
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Conditional Plans
If a block is on a support then a plan to achieve
that the support is clear is to pick up the block
and then put the block on the table.
all(x, y)
({Block(x), Support(y), On(x, y)}
&=> {GoalPlan(Clear(y),
Snsequence(Pickup(x),
Put(x, Table)))})
STRIPS-like representation: No times
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Use of Conditional Plan
GoalPlan(Clear(B),
Snsequence(Pickup(A),
Put(A, Table)))
Remember (cache) derived propositions.
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Use of Conditional Plan
GoalPlan(Clear(B),
Snsequence(Pickup(A),
Put(A, Table)))???
SNeBR to the rescue!
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Sample Research Issues
Indexicals
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Representation and Use of Indexicals
• Words whose meanings are determined by
occasion of use
• E.g. I, you, now, then, here, there
• Deictic Center <*I, *YOU, *NOW>
• *I: SNePS term representing Cassie
• *YOU: person Cassie is talking with
• *NOW: current time.
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Analysis of Indexicals
(in input)
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First person pronouns: *YOU
Second person pronouns: *I
“here”: location of *YOU
Present/Past relative to *NOW.
Generation of Indexicals
• *I: First person pronouns
• *YOU: Second person pronouns
• *NOW: used to determine tense and aspect.
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Use of Indexicals 1
Come here.
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Use of Indexicals 2
Come here.
I came to you, Stu.
I am near you.
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Use of Indexicals 3
Who am I?
Your name is ‘Stu’
and you are a person.
Who have you talked to?
I am talking to you.
Talk to Bill.
I am talking to you, Bill.
Come here.
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Use of Indexicals 4
Come here.
I found you.
I am looking at you.
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Use of Indexicals 5
Come here.
I found you.
I am looking at you.
I came to you.
I am near you.
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Use of Indexicals 6
Who am I?
Your name is ‘Bill’
and you are a person.
Who are you?
I am the FEVAHR
and my name is ‘Cassie’.
Who have you talked to?
I talked to Stu
and I am talking to you.
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Sample Research Issues
Time
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Motivating Joke
9:30:00 AM (Door-to-Door Salesman):
May I interest you in a brush?
9:30:02 AM (Homeowner): Not now.
9:30:03 AM (Salesman): Now?
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A Personal Sense of Time
• *NOW contains SNePS term representing
current time.
• *NOW moves when Cassie acts or
perceives a change of state.
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The Pacemaker
• PML process periodically increments
variable COUNT.
• *COUNT = some PML integer.
• Reset to 0 when NOW moves.
• Provides bodily “feel” of passing time.
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Quantizing Time
Cannot conceptualize fine distinctions in time
intervals.
So quantize, e.g. into half orders of magnitude
(Hobbs, 2000).
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Movement of Time with
Pacemaker
!
time
t1
before
!
duration
after
q
t2
KL
PML
hom
NOW
COUNT
n
0
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The Vagueness of “now”
I’m now giving a talk.
I’m now on sabbatical.
I’m now living in East Amherst.
I’m now at UB.
Multiple now’s at different granularities.
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NOW-MTF
Maximal Temporal Frame based on *NOW
NOW
Semi-lattice of times, all of which contain *NOW,
any of which could be meant by “now”
Finite---only conceptualized times of conceptualized states
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Moving NOW with MTF
NOW
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Current
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Current Students
• Bharat Bhushan, M.S. Candidate
• Preferential Ordering of Beliefs for Default Reasoning
• Debra T. Burhans, Ph.D. Candidate
• A Question-Answering Interpretation of Resolution Refutation
• Frances L. Johnson, Ph.D. Candidate
• Belief Revision in a Deductively Open Belief Space
• John F. Santore, Ph.D. Candidate
• Distinguishing Perceptually Indistinguishable Objects
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For More Information
• URL: http://www.cse.buffalo.edu/~shapiro/
• Group: http://www.cse.buffalo.edu/sneps/
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