Knowledge Representation and
Reasoning
Stuart C. Shapiro
Professor, CSE
Director, SNePS Research Group
Member, Center for Cognitive Science
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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
SNePS
Perceptuo-Motor Level
NL
Sensory-Actuator Level
Vision
Sonar
Proprioception
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Motion
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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Example Cassies
& Worlds
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BlocksWorld
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FEVAHR
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FEVAHRWorld Simulation
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UXO Remediation
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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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.
Also note representation and use of knowledge about words.
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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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Current Research Issues:
Distinguishing Perceptually
Indistinguishable Objects
Ph.D. Dissertation, John F. Santore
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Some robots in a suite of rooms.
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• Are these the same two robots?
• Why do you think so/not?
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Next Steps
• How do people do this?
– Currently doing protocol experiments
• Getting Cassie to do it.
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Current Research Issues:
Belief Revision
in a
Deductively Open Belief Space
Ph.D. Dissertation, Frances L. Johnson
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Belief Revision in a
Deductively Open Belief Space
• Beliefs in a knowledge base must be able to be
changed (belief revision)
– Add & remove beliefs
– Detect and correct errors/conflicts/inconsistencies
• BUT …
– Guaranteeing consistency is an ideal concept
– Real world systems are not ideal
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Belief Revision in a DOBS
Ideal Theories vs. Real World
• Ideal Belief Revision theories assume:
– No reasoning limits (time or storage)
• All derivable beliefs are acquirable (deductive closure)
– All belief credibilities are known and fixed
• Real world
– Reasoning takes time, storage space is finite
• Some implicit beliefs might be currently inaccessible
– Source/belief credibilities can change
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Belief Revision in a DOBS
A Real World KR System
• Must recognize its limitations
– Some knowledge remains implicit
– Inconsistencies might be missed
– A source turns out to be unreliable
– Revision choices might be poor in hindsight
• After further deduction or knowledge acquisition
• Must repair itself
– Catch and correct poor revision choices
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Belief Revision in a DOBS
Theory Example – Reconsideration
Ranking 1 is more credible that Ranking 2.
College A is better than College B. (Source: Ranking 1)
College B is better than College A. (Source: Ranking 2)
Ranking 1 was flawed, so
Ranking 2 is more credible than Ranking 1.
Need to reconsider!
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Next Steps
• Implement reconsideration
• Develop benchmarks for implemented krr
systems.
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Current Research Issues:
Default Reasoning
by
Preferential Ordering of Beliefs
M.S. Thesis, Bharat Bhushan
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Small Knowledge Base
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Birds have wings.
Birds fly.
Penguins are birds.
Penguins don’t fly.
KB Using Default Logic
• x(Bird(x)  Has(x, wings))
• Bird(x): Flies(x)
Flies(x)
• x(Penguin(x)  Bird(x))
• x(Penguin(x)  Flies(x))
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KB Using Preferential Ordering
• x(Bird(x)  Has(x, wings))
• x(Bird(x)  Flies(x))
• x(Penguin(x)  Bird(x))
• x(Penguin(x)  Flies(x))
• Precludes(x(Penguin(x)  Flies(x)),
x(Bird(x)  Flies(x)))
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Next Steps
• Finish theory and implementation.
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Current Research Issues:
Representation & Reasoning
with Arbitrary Objects
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Classical Representation
• Clyde is gray.
– Gray(Clyde)
• All elephants are gray.
– x(Elephant(x)  Gray(x))
• Some elephants are albino.
– x(Elephant(x) & Albino(x))
• Why the difference?
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Representation Using
Arbitrary & Indefinite Objects
• Clyde is gray.
– Gray(Clyde)
• Elephants are gray.
– Gray(any x Elephant(x))
• Some elephants are albino.
– Albino(some x Elephant(x))
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Subsumption Among
Arbitrary & Indefinite Objects
(any x Elephant(x))
(any x Albino(x) & Elephant(x))
(some x Albino(x) & Elephant(x))
(some x Elephant(x))
If x subsumes y, then P(x)  P(y)
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Example (Runs in SNePS 3)
Hungry(any x Elephant(x)
& Eats(x, any y Tall(y)
& Grass(y)
& On(y, Savanna)))

Hungry(any u Albino(u)
& Elephant(u)
& Eats(u, any v Grass(v)
& On(v, Savanna)))
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Next Steps
• Finish theory and implementation of
arbitrary and indefinite objects.
• Extend to other generalized quantifiers
– Such as most, many, few, no, both, 3 of, …
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For More Information
• Shapiro:
http://www.cse.buffalo.edu/~shapiro/
• SNePS Research Group:
http://www.cse.buffalo.edu/sneps/
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