Research in
Knowledge Representation
and Reasoning
Stuart C. Shapiro
Department of Computer Science & Engineering
Center for MultiSource Information Fusion
Center for Cognitive Science
University at Buffalo, The State University of New York
MGLAIR Agent Architecture
Mind
Body
KL (SNePS)
Independent
of lower-body
implementation
PMLa
PMLb
I/P s o c k e t s
Dependent
on lower-body
implementation
PMLc
Proprioception
Speech
W
O
R
L
D
Hearing
SAL
Vision
Motion
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SNePS
SNePS is a
Logic-Based
Frame-Based
Network-Based
knowledge representation, reasoning,
and acting system.
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SNePS Is Logic-Based
wff1!: all(x)(Isa(x,dog) => Property(x,four-legged))
wff2!: Isa(Toto,dog)
: Property(Toto,?x)?
wff3!: Property(Toto,four-legged)
: Isa(Fala,dog)!
wff6!: Property(Fala,four-legged)
wff5!: Isa(Fala,dog)
: askwh Property(?x,four-legged)
Fala: Fala
Toto: Toto
: list-wffs
wff6!: Property(Fala,four-legged)
wff5!: Isa(Fala,dog)
wff3!: Property(Toto,four-legged)
wff2!: Isa(Toto,dog)
wff1!: all(x)(Isa(x,dog) => Property(x,four-legged))
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SNePS Is Frame-Based
: %(describe *nodes)
(m6! (a1 Fala) (a2 four-legged) (r Property))
(m5! (a1 Fala) (a2 dog)
(r Isa))
(m3! (a1 Toto) (a2 four-legged) (r Property))
(m2! (a1 Toto) (a2 dog)
(r Isa))
(m1! (forall v1) (ant (p1 (a1 v1) (a2 dog) (r Isa)))
(cq (p2 (a1 v1) (a2 four-legged) (r Property))))
: %(describe (assert r Isa
a1 (Fido Rover Lassie)
a2 (dog pet)))
(m7! (a1 Lassie Rover Fido) (a2 pet dog) (r Isa))
wff7!: Isa({Lassie,Rover,Fido},{pet,dog})
: Property(Rover, ?x)?
wff8!: Property(Rover,four-legged)
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SNePS Is Network-Based
: define-frame Ako(nil subclass superclass)
Ako(x1, x2) will be represented by {<subclass, x1>, <superclass, x2>}
: Ako({man, dog}, mammal).
wff1!: Ako({dog,man},mammal)
: Ako({mammal, fish}, vertebrate).
wff2!: Ako({fish,mammal},vertebrate)
: Ako(vertebrate, animal).
wff3!: Ako(vertebrate,animal)
: %(define-path subclass
(compose subclass
(kstar (compose superclass- ! subclass))))
...
: askwh Ako(?x, animal)
vertebrate: vertebrate
fish: fish
mammal: mammal
dog: dog
man: man
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Procedural Attachment
A predicate or function symbol
may be attached to a user-written procedure
so instances may be computed
in the underlying programming language.
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Example of Procedural Attachment
: Diff(7,3,?x)?
wff24!: Diff(7,3,4)
: Diff(10,?x,7)?
wff25!: Diff(10,3,7)
: Diff(?x,5,7)?
wff26!: Diff(12,5,7)
: Diff(15,8,7)?
wff314!: Diff(15,8,7)
: Diff(15,8,9)?
wff316!: ~Diff(15,8,9)
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Building Domain
all(x)(onFloor(x)
=> {(<(x,3) => location(belowGround)),
(<(2,x) => location(aboveGround))}).
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Primitive Acts
A version of procedural attachment
for implementing intelligent agents:
: perform say(Welcome, "to you all.")
Welcome to you all.
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Policies
Connect propositions and acts:
wheneverdo(location(belowGround),
withsome(f, onFloor(f),
say("It's dark here on floor",f),
say("Where am I?",""))).
wheneverdo(location(aboveGround),
withsome(f, onFloor(f),
say("It's sunny outside floor",f),
say("Where am I?",""))).
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SNeBR:
Belief Revision/
Assumption-Based Truth Maintenance
• Identify possible culprits of contradictions.
• Disbelieve implications of disbelieved hypotheses.
• Use state constraints to adjust beliefs:
andor(1,1){onFloor(1),onFloor(2),onFloor(3),onFloor(4)}.
andor(1,1){location(belowGround),location(aboveGround)}.
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Combined Use of
SNeBR & Procedural Attachment
: perform believe(onFloor(1))
It's dark here on floor 1
: location(?x)?
wff24!: ~location(aboveGround)
wff6!: location(belowGround)
: perform believe(onFloor(4))
It's sunny outside floor 4
: location(?x)?
wff33!: ~location(belowGround)
wff7!: location(aboveGround)
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BR with Multiple Sources
wff1: all(x)(andor(0,1){mammal(x),fish(x)})
wff2: all(x)(fish(x) <=> has(x,scales))
wff4: all(x)(whale(x) => fish(x))
wff5: Source(Melville,all(x)(whale(x) => fish(x)))
wff6: all(x)(whale(x) => mammal(x))
wff7: Source(Darwin,all(x)(whale(x) => mammal(x)))
wff8:
Sgreater(Darwin,Melville)
wff11: free(Willy) and whale(Willy)
Note: Source & Sgreater props are regular object-language props.
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Finding the Contradiction
: has(Willy, scales)?
I infer
fish(Willy)
I infer
has(Willy,scales)
I infer
mammal(Willy)
I infer it is not the case that wff14: fish(Willy)
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Using Source Credibility
A contradiction was detected within context default-defaultct.
The contradiction involves the newly derived proposition:
wff17: ~fish(Willy) {<der,{wff1,wff6,wff11}>}
and the previously existing proposition:
wff14: fish(Willy) {<der,{wff4,wff11}>}
The least believed hypothesis:
(wff4)
The most common hypothesis:
(nil)
The hypothesis supporting the fewest wffs: (wff1)
I
removed the following belief:
wff4: all(x)(whale(x) => fish(x))
I no longer believe the following 2 propositions:
wff14: fish(Willy)
wff13: has(Willy,scales)
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Conclusions
• MGLAIR is an agent architecture
– For connecting reasoning with sensing and acting
• SNePS is a
–
–
–
–
Logic-based
Frame-based
Network-based
Knowledge representation, reasoning, and acting system.
• Procedural attachment provides
– Sensing, acting, computing at the “subcognitive” layers
• SNeBR does belief revision & truth maintenance.
• Source meta-knowledge may be entered and used.
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