From: AAAI-83 Proceedings. Copyright ©1983, AAAI (www.aaai.org). All rights reserved.
KRYPTON:
Integrating
Terminology
Ronald
Fairchild
Laboratory
J. Brachman
for Artificial
Richard
Xerox
Laboratory
works have intuitive
severely
limited
biguous
readings.
assertionally,
attempted
languages
appeal for forming
assertional
power,
Those based
but are restricted
to overcome
representation
based on frames
system,
to primitive,
called
descriptive
terms and a logic-based
the world.
We here summarize
one for making
the two languages,
have no direct assertional
strictly
for assertions
domain-specific
statements
about
inter-
the TBox and ABox languages,
$2 Two languages
The TBox contains
seems less than perfect
of tasks required
like structures
of a representation
system
are quite popular,
have limited
assertional
‘instantiation’
associated
when confronted
capabilities
and defaults),
or absence
of data
dent predicates;
capabilities,
this limitation
compose new predicates
A productive
but are limited to primitive,
makes
it impossible
sentences
[l].
to capitalize
not typical of the predicate
both styles of repre-
2.1
phrases
that this
version of) “a person with at
from “a person with at most 1 child”.
and disjointness
the implications
predicate
in network
calculus
relationships
among these terms are
owns a car”,
(in the logical sense) of an assertion
terminological
structure,
style, and assertion,
expressed
This distinction
sentation
system:
expressed
that make up
component
to capture the essence of frames withdefinitional framework,
without the
ambiguities
and possible misinterpretations
In particular,
expressions,
common in existing
the TBox supports
which correspond
roughly
to frames,
expressions, the counterparts
of slots. Thus, the language
a small set of Concept- and Role-forming
operators.
form (as in
rep-
In general,
KRYPTON
Concepts
ing other Concepts
in a frame-
and Roles are formed by combining
and Roles. For example,
frame
two types of expressions:
the language
and Role
is defined by
or restrictincludes an
in a form of predicate
yields two main components
a terminological
of the terminological
languages.’
Concept
attempted
and network
of the same facts (as in [3] and [12]). Instead,
calculus.
The language
Our TBox language attempts
in a compositional
and strictly
is
KRYPTON
net marriages
It does not encode logical assertions
like taxonomic
noun
and understands
on the strong points of each. Over
calculus/semantic
14)) nor does it use simultaneous
between
by (the formal
terms and sentences.
of indefinite
the TBox and ABox languages.
to syntactically
While the general idea of a hybrid system is not new,
distinguishes
equivalent
such as this one. Here we review the formal constructs
indepen-
actly this goal in mind.
resentations
the formal
such as “Every person with at least 3 children
and understand
the past year, we have been designing and implementing an experimental knowledge representation
system-called
“KRYPTON’‘-with
ex-
before.
reflect the two kinds of expres-
out of old ones.
view would seem to embrace
in an attempt
KRYPTON
knowledge-(nominal)
based only on their structure and not on any (domain-dependent)
facts.
The ABox, on the other hand, operates with the formal equivalent of
assertions
structures
in
and is disjoint
The subsumption
systems are usually more precise and address a much wider
range of assertional
sentation
frame-
specified,
and tend to allow accidental
that
are being imple-
for representation
is subsumed
least 1 child”,
(e.g., they tend to be limited to
with the mere presence
Logic-based
expression
with the wide range
121. For example,
the operations
and how these operations
such as “a person with at least 3 children”,
represen-
but are often imprecisely
bi-conditionals
of
$1 Introduction
tation
quantified
and
is used
mented.
prover.
styles of knowledge
The ex-
descriptions,
In what follows, we will describe
KRYPTON
The two components
predominant
import.
are available
in
can afford
KRYPTON
Moreover, the ABox language
in more detail
sions it uses to represent
Each of the currently
labor,
in the two languages.
and even universally
have no special definitional
among
theories of domains
are used as structured
import.
of struc-
about those domains.
view of the constructs
pressions in the TBox language
We have
a functional
theorem
and to answer questions
to take a strict
knowledge
in terms of a taxonomy
with a first-order
relationships
about analytical
Given its division of representational
has two rep-
KRYPTON
one for forming
and an implementation
frames and its interaction
terms.
taxonomies
tured terms and answer questions
of interest
logic are less limited
unrelated
Research
one (or ‘ABox’). The TBox allows us to establish
net-
with am-
in a new, hybrid
“KRYPTON”.
a frame-based
fraught
Intelligence
these terms; the ABox allows us to build descriptive
but tend to have
and are often
these limitations
languages,
face to the system,
descriptions
on first-order
resentation
or semantic
Center
J. Levesque
for Artificial
The demands placed on a knowledge representation
scheme by a knowledge-based system are generally not all met by any of today’s canRepresentation
Research
E. Fikes
Abstract
didates.
Intelligence
Palo Alto Research
Hector
Fairchild
and Assertion
for our repre-
‘The TBox is, in large part, a distillation of KL-ONE
[13], which accounts
use below of terms like “value restriction”
and “differentiation”.
one (or ‘TBox’) and an assertional
31
for our
operator
ConjGenerIc
ber of Concepts,
junction.
(‘conjoined
(assuming
(ConjGeneric
it the expression
auy num-
faam i!Jr :
pi
man)
unmarried-person
Taking
can also be formed
operator
by restricting
that
person
ted generic’)
child
operator
(‘value-restricted
who is a man, a mother
a father
some number
of children,
TON
of “a social structure
this frame as a description
other things,
all persons”,
also has an NRGeneric
that restricts
(PrimGeneric
(ConjGeneric
(NRGeneric
(VRGeneric
social-structure
father man)
(NRGeneric
(VRGeneric
social-structure
mother
father
of the set of fillers
person child 1 3) for “a person
(VRGeneric
can be defined as specializations
One basic Role specialization
takes a Role r and a Concept
tive Role corresponding
operator
VRDWRoie
operator
would be appropriate
Another
Role-forming
as (VRDiffRole
RoleChain,
operator,
(‘value-restricted
We have considered
c, and defines the derivason, given already
for defining
terms child (a Role) and man (a Concept),
tionally composed so that (RoleChain
guage;
All of the term-forming
operators
brother-in-law)
can be composed
a wide range of operators
ones in the current
unmarried-person
Interpretation
Expression
(ConjGeneric
(VRGeneric
could be
cl . . . e,)
cl r ~2)
(NRGeneric
e r nl rz2)
(PrimGeneric
c i)
(DecompGeneric
c ii
in the obvious
sibling man)
(NRGeneric
person (RoleChain
can be read as “a bachelor
or, more literally,
them, between
conjunction
value restriction
“a c with between nr and n2 r’s”
“a e of the i-th kind”
“a c of the i-th type from the
number restriction
primitive Concept
decomposition
j-th
facilities
Concept
Concepts
“an r that is a c”
Uan rn of . . . of an rrn
“an r of the k-th kind”
differentiation
composition
primitive Role
(DecompRole
“an r of the Cth type from the
j-th [disjoint] decomposition”
decomposition
r i J’
die joint?)
To this end,
if something
Concept
is described
of a Concept
have, among
(DecompGeneric
by it. However,
To introduce
the
ABox language
a pair of Concepts
decomposition
compositionally
quite different from those motivating
by its
As discussed
sub-
plete
language
knowledge
to motivate
of the
operators,
however, are
the ones for forming TBox terms.
in [2], the issue of expressive
resentation
the sentences
from simpler ones. The
behind the choice of sentence-forming
concerns
power in an assertional
rep-
is really the issue of the extent to which incom-
can be represented.
the standard
Moreover,
logical sentential
this issue can be seen
constructs
of disjunction,
(or Roles)
negation
operators
ability to deal systematically
with incomplete knowledge and to compensate for the fact that the TBox has been purged of any assertional
and existential
quantification
ability, our ABox language
relate to a more traditional
the following description
of the TBox language,
are constructed
and
are given for detertwo primitive
component
of a
would be used.
To see how some of the TBox operators
of frames, consider
specializations
of the assertional
As with the expressions
includes
disjoint nor do they neces-
KRYPTON
or DecompRole)
but not
KRYPTON
is one that is subsumed
are not by definition
that do have these properties,
hypothetical
have grand-
The PrimGeneric
but where no sufficient conditions
1. The TBox Language.
and a man all of
to be able to give necessary
‘only-if’ definitions.
sarily exhaust that Concept.
language
person
are used to form primitive
or Role. A primitive
superconcept,
mining
one wants
operators
decomposition”
(VRDiflRole
c r)
(RoleChain
rl . . . r,)
(PrimRole
r i)
2.2 The language
for a definition.
for specifying
PrimRole
whose brothers
“an unmarried
are men are persons whose children
In many domains
[disjoint]
child child) 1 co)).
1 and co children”.
sufficient conditions
Description
“a el and . . . and a c,,”
“a er any r of which is a es*
disjoint?)
man)
(VRDiffRole
whose siblings that
in
Concepts:
T&e
children”
are summarized
Roles:
(ConjGeneric
This expression
for the TBox lan-
version
defined
way, as in, for example,
(VRGeneric
the principal
child man).
of uncle.
used as the definition
child person))).
Table 1.
allows Roles to be func-
parent
social-structure
woman)
1 1)
of other Roles.
“an r that is a c”. Thus, this
to the phrase
1 1)
mother
with at least 1 and not more than 3 children”.
differentiation’),
and
KRYP-
we might express it in
as
(‘number-restric-
the cardinality
for a given Role, as in (NRGeneric
Roles, like Concepts,
with, among
who is a woman,
“a cl all of whose r’s are Q’S”, as in
bachelor) for “a person all of whose children
The language
are bachelors”.
using
cl, a Role r, and a Concept
takes a Concept
cz, and yields the term meaning
(VRGeneric
other Concepts
has a VRGeneric
KRYPTON
For example,
generic’)
social-structure
as Concepts).
Concepts
Roles.
lea
to their con-
and man had appropriate
that the symbols unmarried-person
definitions
which takes
corresponding
could be used to define the symbol2 bachelor
This operator
by assigning
generic’).
and forms the Concept
der predicate
of a family (in a
operators
‘framese’):
calculus
2As we will describe below, expressions can be assigned as definitions to atomic
symbols.
This use of defined symbols, however, is purely for the convenience of
the user.
32
is structured
language.
compositionally
between
our ABox language
logical one lies in the atomic
symbols of a standard
logical language-that
(and function
if any)-are
symbols,
like a first or-
In other words, the sentence-forming
are the usual ones: Not, Or, ThereExists,
The major difference
first order
(see also 191). So to provide the
sentences.
and so on.
and a standard
The non-logical
is, the predicate
taken to be independent,
symbols
primitive,
domain-dependent
specifying
terms.
a collection
Our approach,
therefore,
a facility
In our case, there is already
of domain-dependent
terms,
is to make the non-logical
for
by
namely the TBox.
TELL:
ABox:
Sentence
language
be the terms of the TBox language. As observed by Hayes [5]
and Nilsson [lo], when the language of frames and slots is ‘translated’
into predicate
calculus,
place predicates
respectively.
are suggesting
primitive
the frames
and slots become
The main difference
any theory expressed
related
18 sentence
As for the TBox, the TELL
between what they
operation
the knowledge
of
asks whether
includes
the symbol,
We have focused on two ASKoperations:
one TBox term subsumes
one TBox term is conceptually
another,
disjoint
it
The effect is to change
base into one whose vocabulary
defined by the term.
in the ABox language).3
true?
takes a symbol and associates
with a TBox term (Concept or Role expression).
are not
to each other (independent
is true.
ASK: KB x SENTENCE + {yes, no, unknown}
one- and two-
and what we have done is that our predicates
but are definitionally
KB >( SENTENCE --c KB
symbols of the ABox
the first
and the second whether
from another.
Schematically,
this gives us
$3 Operations
Overall,
on the components
the structure
1: a TBox of roughly
TBox:
TELL:
KB X SYMBOL X TERM + KB
an
ASKI:
KB x TERM X TERM + {yes, no}
whose predicates come from the
the names of the TBox terms so
ASK:!:
KB x TERM x TERM -+ {yes, no}
of KRYPTON can be visualized
KL-ONGish
terms organized
ABox of roughly first-order sentences
TBox, and a symbol table maintaining
taxonomically,
that a user can refer to them. However, this is a somewhat
picture
since it suggests
directly.
that
users can manipulate
By symbol, I mean
as in Figure
Doea term1
Is terrnl
misleading
In fact, a user does not get access to either a network
is a fixed set of operations
All interactions
mediated
subsume
disjoint
term27
term27
Jrom
these structures
in the
The TBox ASK operations
TBox or to a collection of sentences in the ABox. What a user does get
instead
term.
the domain-dependent
over the TBox and ABox languages.
between a user and a KRYPTON knowledge
allow a user to inquire about the meaning of
terms being used (without
is known about the world).
base are
to understand
In addition,
the non-logical
also folding in what
the ABox uses these operations
terms in the sentences
it processes.
by these operations.
Of course there have to be additional
edge base. For instance,
no way of getting
ASK operations
the ones that we have mentioned
other than a yes/no
answer.
In the case of the ABox,
we have to be able to find out what individuals
have a given property;
in the TBox, there has to be some way of getting
TI!OX
the definitions
(e.g., the fact that
necessarily
3).
It is important
knowledge
taxonomy
1. KRYPTON
overview.
of angles of a triangle
system is completely
and ASK
operations.
or a set of first-order
the interface
Figure
the number
from
and disJointness
is
to stress that the service provided by KRYPTON as a
representation
of the TELL
the information
that is not provided by the subsumption
operations
on a knowlso far provide
provided
the notions
of a
clauses in normal form are not part of
by the system 4 The actual symbolic
to realize the TELL
used by KRYPTON
specified by a definition
In particular,
structures
and ASK operations
are not
available to the user. While it might be useful to think of a knowledge
base as structured in a certain way, this structure can only be inferred
base can be divided into
from the system’s
two groups: the TELL operations, used to augment a knowledge base,
and the ASK operations, used to extract information.
In either case,
The operations
on a KRYPTON knowledge
allow finer-grained
the operation
the operations
can be definitional
and asserts
that it is true.
the knowledge
operation
speaking,
is to change
defined in the TBox.
3The
status
of function
base and the vocabulary
Schematically,
symbols
and predicate
can be told (involving
to TELL)
to other terms
in the
of this approach
that
bases,5
but again it will be
used to implement
expressions
to knowledge
conceptually
language).
representa-
between what a system
in the language
and what it has to actually
tures in the implementation
remember
used as arguments
(involving
data struc-
This allows us to consider
an
these operations
41n [s], we present a definition of TELL and ASK that is completely independent
of how the knowledge is represented in a knowledge base and is based instead on
symbols with more than two argu-
the set of worlds that are compatible
ments is unclear at present. There is no problem incorporating
them as primitive8
into the ABox language; the issue is what facilities there should be for relating
them definitionally
property
tion is that there is a difference
used in the sentence, as
we can describe
to be deduced,
that count, not the data structures
One interesting
of the world implies that
sentence. The corresponding
ASK operation takes a sentence and asks
if it is true. The result is determined on the basis of the current theory
held by the knowledge
new operations
to be made among knowledge
them.
takes an ABox sentence
The effect, roughly
base into one whose theory
One might consider
distinctions
allowing even more of its structure
or assertional.
In terms of the ABox, the TELL
behavior.
with what is known.
‘One possibility, for example, is an ABox ASK operator
form of limited inference over what is known.
TBox.
33
that only performs
some
interface
notation
plementation
that is, in some sense, more expressive
the translation.
supply
In [S], a modal
arguments
represented
‘auto-epistemic’
to TELL and yet the resulting
in first-order
than the im-
that the diflerence can be accounted
one, provided
for in
language
is used to
knowledge
is always
in efficiency over simply asserting
To this end, we are developing
that take into account
the meaning
extensions
dependencies
postulates
as aMoms~T
of standard
inference
rules
among predicates
derivable
from
TBox definitions.
terms.
For example, the reasoning
of a standard
resolution
theorem
prover
depends
$4 Building
KRYPTON
Having discussed
the desired functionality
edge representation
building
on noticing that an occurrence of @(z) in one clause is inconsistent with 1 $(z) in another. Given that realization, the two clauses
can be used to infer a resolvent clause. The scope of this inference
of the
KRYPTON
knowl-
system, we now sketch in general terms how we are
a system with these capabilitites.
rule can be expanded
The first thing
tency of two literals.8 That is, since triangle and rectangle
are disjoint,
and rectangle(z)
situation
is that
because
of the expressive
very general
reasoning
Specifically,
we cannot
typical
strategies
of the ABox
power of the assertional
language,
will be needed to answer questions.
representation
to the special-purpose
methods
to locate
a representational
object
of the cow-in-the-field
an instantiation
standing
Concept),
cows and that at least one of his animals
The second
predicate
point worth
ally inconsistent
the ABox is that
but
4.2
literals can still be resolved provided
polygon
of those
once told that Elsie is a cow, the ABox should
steps in a deduction,
to compute
of the first one since they depend on how the
the issue here is that
the ABox predicates are not simply unconnected primitives (as in firstorder logic), so that if we want to use standard first-order reasoning
we have to somehow make the connections
implied by the
TBox.
the simplest way to make the TBox-ABox
connection
strategy
performed
reasonably
cow we could automatically
first-order
reasoning
after defining
assert sentences
over the
the Concept
saying that every cow is
an animal and that cows are not bulls, as if these were observed
about
the world.
As far as the ABox is concerned,
term would be no more than the assertion
the definition
of a ‘meaning
In some sense, this would yield a ‘hybrid’ system
discussed
facts
stating
the
Absolutely
most important
by our TBox language
l), we stand
gain
%deed,
by far the most common rendering of definitions in systems based on firstorder logic is as assertions of a certain form (universally quantilied bi-conditionals),
a treatment
which fails to distinguish them from the more arbitrary
facts that
happen to have the same logical form.
route.
can be
limit on the TBox operations
One can imagine
wanting
a
providing
a set of term-forming
of getting
facilities
a usable
our
predicates
like those we have already discussed-see
at least a chance
algorithm
Table
while
that have been found useful
in AI applications.
The situation
of term-forming
language
is far from resolved,
of term subsumption
operators.
without
however.
The computational
seems to be very sensitive to the choice
For example, it appears that given our TBox
the VRDifITtole
I?
a significant
postulate
much less an efficient one. By restricting
initional
and provides
are as hard as theorem
to what might be called the ‘frame-definable’
algorithm will be O(n”) at worst;
however, the problem is as difficult
information,
nothing will be gained by our
itself.
same set of facts. Our goal, however, is to develop an ABox reasoner
that avoids such redundancies,
maintains the distinction between defand assertional
between
quickly with respect to the ABox.
would then be possible,
complexity
like the kind
in [3] and 1121, since we would have two notations
has to be
information
language that would allow arbitrary ‘lambda-definable’ predicates to be
specified. The trouble is that no complete algorithm for subsumption
of a
postulate’.6
an ABox reasoner
and disjointness
if the TBox operations
The first and perhaps
is provided
(in terms of operators
standard
if the TBox is
it should answer, in
three steps to ensure that the TBox operations
the ABox, and then to perform
For example,
Thus,
we could just as well have gone the meaning
TBox language
theory.
the conditionthat we include
we have to be very careful about how long it takes
is to cause the act of defining a term in the TBox to assert a sentence in
expanded
in the resolvent.
is disjoint from -rectangle,
that information.
implementation
We are taking
resultant
only when all the angles of
In such cases, the clauses containing
able to access TBox subsumption
not logical consequences
Conceptually,
with -rectangle(z)
has
The literal
Making a TBox
know that Elsie is an animal and is not a bull. However, these facts are
techniques,
assume that rectangle
angle right-angle).
Since we take the point of view that
if the
are indeed TBox terms, then
cow is defined in the TBox. In general,
polygon
also imply
effect, “only when all the angles are right angles”.
proving;
Concept
For example,
of the condition
asked whether
has escaped into the field.
needs to have access to the TBox definitions
For example,
is inconsistent
The
TBox definitions
since, among other
Smith owns nothing
about
symbols of the ABox language
the ABox reasoner
terms.
noticing
by the fact that
inconsistencies.
5 are right angles.
sub-
are inconsistent.
for it (i.e.,
we may not know all the cows or even how many there are.
Yet, we may very well have been told that
polygon(z)
and since polygon
and rectangle(z)
been defined as (VRGenerIc
the negation
systems.
to find out if there is a cow in the field, it will not
For example,
things,
an implementation
limit ourselves
of frame-based
be sufficient
about
are inconsistent;
‘polygon(z)
is complicated
‘conditional’
to notice
informa-
the inconsis-
triangle(z)
Making an ABox
and disjointness
means of recognizing
sumes rectangle,
4.1
by using subsumption
tion from the TBox as an additional
operator,
the term subsumption
with the VRDifIRole operator,
as propositional
theorem proving
‘There are already precedents in the theorem-proving
literature (see [8] and Ill])
for using special information
about subsumption
and disjointness of predicates as
a way of guiding a proof procedure.
8See [IS] for a similar
approach
to augmenting
resolution
by ‘building-in’ a theory.
As a second step towards
fulfilling
the TBox, we have adopted
sumption
relationships
data structure.
this efficiency
a caching
for symbols
an explicit
We are also developing
methods
cache to include both absolute and conditional
about TBox terms.
The key open question
is how to determine
conditional
a useful subset
relationships
regarding
determines
the new symbol
Because
incrementally
the taxonomy
reflects
R., and Hendrix,
IJCAI-77,
151
the no-
I61
relation-
Cambridge,
its correct position.
the relationship
Levesque, H. J., “A Formal Treatment
1981. Also available
3, Fairchild
The
Laboratory
Alto, CA, February,
that-an
implementation
and the definition
taxonomy
strategy.
is that
and
and
of Incomplete
Knowledge
Science, University
as FLAIR Technical
for Artificial
Intelligence
Report
of
No.
Research,
Palo
1982.
“Some Results on the Complexity
Levesque, H. J.,
Language,”
of Subsump-
in preparation,
1983.
stra-
it is precisely
181
The meaning of the TBox language
of the TBox operators
in Proc.
of a
PI
and classification
Knowledge
System,”
Hayes, P. J., “The Logic of Frames, n in Frame Conceptions
Text Understanding,
Metzing, D. (ed.), Walter de Gruyter
Toronto,
we can
thing to notice about this implementation
based on a taxonomy
Deduction
MA, 1977, 23.5-246.
tion in a Frame-based
One very important
“A Network-Based
G.,
and its Natural
Bases,” Ph. D. thesis, Dept. of Computer
symbol to all the other defined symbols.
tegy
ing
Intelli-
Co., Berlin, 1979, 46-61.
for which it is still
about
Fikes,
Representation
scheme is that the symbol taxonomy
more and more informed
Artificial
[14], wherein a
a partial-ordering,
move the symbol down towards
overall effect of this classification
slowly becomes
[4]
this
of possible
the subsumption
and each symbol
for ProbIem-Sola
Information,”
gence 16, 3 (1981), 225-255.
these extensions
KL-ONE
“A Common Representation
E.,
and Language-Comprehension
information
of the large number
Charniak,
of
for extending
an efficient TBox, we have adopted
process sequentially
unknown.
PI
that could be defined between the symbols.
As a final step towards
background
taxonomy
disjointness
tion of a classifier, much like the one present in
ship between
ffor
defined by the user in a tree-like
We, in effect, are maintaining
the defined symbols.
requirement
scheme in which we store sub-
McSkimin,
J. R., and Minker, J.,
Semantic
Network
Networks:
do not depend at all on the
or on how well the classifier is doing at some point.
Representation
Findler,
PI
Calculus
Based
Searching,”
in Associative
and Use of Knowledge
by Computers,
N. V. (ed.), A ca d emit Press, New York, 1979, 205238.
Moore, R. C.,
“The Role of Logic in Knowledge
and Commonsense
g5 Conclusion
“A Predicate
for Deductive
in Proc.
Reasoning,”
Representation
AAAI-82,
Pittsburgh,
1982, 428433.
KRYPTON
The
based
system
vantages
of each.
tured descriptions
organized
supports
component
standard
logic for expressing
first-order
two components
interact
through
An implementation
of a
As of this writing,
terminological
operators,
knowledge.
1131
the
of the
[14]
JACM
with
in 1151.
IEEE
PI
Computer,
to Representation
September,
Brachman,
R. J.,
Knowledge
Representation,”
and
H. J.,
“KRYPTON:
PI
System,” to appear in
1983.
Levesque,
Closure
in First-Order
“Knowledge
Calculus:
How to Have Your Cake and Eat it Too,” in Proc.
AAAI-82,
Pittsburgh,
Schmolze,
Representation
and Predicate
1982, 193196.
J. G., and Brachmnn,
Laboratory
Languages
Workshop,”
R. J., eds.,
“Proceedings
FLAIR Technical
for Artificial
Intelligence
Report
Research,
of
No.
Palo
Schmolze,
J. G., and Lipkis, T. A.,
Stickel,
M. E.,
“A Nonclausal
Program,”
“Classification
System,”
in Proc.
Connection-Graph
in Proc.
AAAI-82,
in the
KL-
IJCAI-83,
Resolution
Pittsburgh,
1982, 229-233.
J., Fikes, R.E., andLevesque,
Approach
and Domain
Knowledge Representation
Karlsruhe, W. Germany, 1983.
References
A Functional
Tioga
Rich, C.,
Theorem-Proving
Brachman,R.
Intelligence,
27, 2 (1980), 235-249.
ONE
1151
[l]
of Artificial
Alto, CA, May, 1982.
methodol-
its interaction
“Equality
R.,
the Second KL-ONE
is under-
the operations
investigating
Reiter,
Principles
Co., Palo Alto, CA, 1980.
4, Fairchild
system in Interlisp-D
described
These
it.
using the taxonomy/classification
a version of the theorem-prover
[12]
each
interface;
used to implement
KRYPTON
ogy discussed above, and are currently
of
utilizes the power of
incomplete
N. J.,
Databases,”
Lomponent
some domain
term-forming
component
we have implemented
component
Ill1
of struc-
the assertional
Nilsson,
Publishing
and an assertional
the formation
a functionally-specified
user has no access to the structures
[lo]
is a distilled version of frames,
by a set of compositional
The assertional
frame-
the disad-
the representation
to be used to characterize
with clear import.
way.
separates
taxonomically;
The terminological
characterized
to integrate
a terminological
component
allows these descriptions
interest.
KRYPTON
components:
The terminological
an attempt
in such a way as to minimize
To do this,
task into two distinct
one.
represents
and logical facilities
H. J.,
in Proc.
“Competence
AAAI-82,
in
Pittsburgh,
1982, 189192.
35
Stickel, M. E., “Theory Resolution: Building-In Nonequational
Theories,” in Proc. AAAI-83, Washington. D. C., 1983.