.ASEC(Glossary of Technical Terms)

<<Go through thesis, dumping terms into the glossary>

The "jargon" of a field facilitates communication among practitioners
of  that field, but  it too often  excludes novices. I  have tried to
soften the impact of each "buzz-word" when it was first used, but the
reader may need  to frequently refresh his memory  about the meanings
of certain terms.

This  glossary  is  divided into  two  sections.  The  first contains
primarily Mathematics terms, strangely biassed because it just covers
what is  referenced in this thesis. The  second glossary, of Computer
Science and  Artificial Intelligence  terms,  suffers from  the  same
tunnel vision. They may  suffice for reading this document,  but they
are certainly ⊗4not⊗* meant to be used for more general purposes.


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. ASSEC(Glossary of Math Terms)

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.BEGIN TURN ON "↑↓_" TURN OFF "{⎇" SELECT 1

Abduction: In logic, a syllogism of the form "from A, conclude that
B is probably true". If your mental frame for an automobile contains
a hundred necessary features, and you see something satisfying only 90 of them, 
you
can ⊗4abductively⊗* conclude it is probably an automobile.

Cardinality:  the concept  of "number".    Two sets  are of  the same
cardinality iff they have the same number of elements.

Composition of two relations R and S: This is a new  relation denoted
R⊗7o⊗*S,  and  defined  as  R⊗7o⊗*S(x) =  R(S(x)).  So  R⊗7o⊗*S  maps
elements of  the domain of S into elements of the range of R.  Notice
that if R and S are both functions, then so is R⊗7o⊗*S. The intuitive
picture of this  process is to operate on x  with the relation S, and
⊗4then⊗* apply R to the results.

Function: an operation f which associates, to each element x of  some
set D,  an element f(x)  of some set  R. D and  R are the  domain and
range of f.  Notice that a function may be considered a special kind
of relation.
For a ⊗4relation⊗* f (on DxR) to be called a ⊗4function⊗*, f must satisfy two
important constraints: (i) it must be always-defined on its domain; that is,
for all domain elements x⊗6ε⊗*D, f(x) must exist. (ii) f must be single-valued;
that is, f(x) must be a singleton.

Iff: if and only if; implies and is implied by; is equivalent to; ⊗8<==>⊗*.

Integers: positive and negative whole numbers; i.e. ...,-2, -1, 0, 1,
2,...

Map: used  as a verb,  this word indicates  the action of  applying a
function  or a relation; e.g.,  we say that  ⊗4squaring⊗* maps 7 into
49.  Used as a noun, it is a synonym for function.

Mathematical concept: this  is taken to  mean all the  constructions,
definitions,  conjectures,  operations,  structures,  etc.    that  a
mathematician deals with. Some examples: Set-intersection, Sets,  The
unique factorization theorem, every entry listed in this glossary.

Mathematical  intuition: this  is  the mental  imagery  which can  be
brought  to  bear.   Typically,  we  transform  the  situation to  an
abstract, simplified one, manipulate  it there, and re-translate  the
results into the original notation.  For example, our intuition about
"ordering" may involve the image of marks on a yardstick. We can then
answer   questions   involving    ordering   rapidly,   using    this
representation.   Three  features of  the intuitive  image  should be
noted: (i) it is  typically fast and simple,  (ii) it is opaque,  one
cannot introspect  too  easily on  "why it  works", and  (iii) it  is
fallible, occasionally leading to wrong results.

Mathematical research:  The fundamental idea here is that mathematics
is an ⊗4empirical⊗*  science, just as much  as chemistry or  physics.
In  doing  research,  the  ultimate  goal is  the  creation  of  new,
interesting  theories, but  the techniques  used include  looking for
patterns in empirical data, inducing new  conjectures, modelling some
aspects of the real world, etc. Although the final product looks like
a smooth, formal  development, magically flowing  from postulates  to
lemmas to theorems, the actual research process involved untold blind
alleys,  rough guesses,  and  hard work.   (Analogy:  The  process of
painting is rarely itself artistic.)

Mathematical theory: to qualify as a theory, we must have (i) a basis
of undefined primitive terms, (ii) definitions involving these, (iii)
axioms   involving  all   the  primitives  and   defined  terms  (iv)
conjectures  and  theorems relating  these  terms.    To  be  at  all
worthwhile, however, the theory must also meet the fuzzy requirements
that (v) there is some correspondence between the primitives and some
"real-world"   concepts,  between   the   axioms  and   some   "real"
relationships, and (vi)  some of the theorems are unexpected, hard to
prove, elegant, interesting, etc.

Mersenne prime: a prime number which happens to be of the form 2↑p-1,
where p is prime.

Natural numbers: non-negative integers; i.e., 0, 1, 2, 3,...

No.: an abbreviation for "Number".

Number: in the typical loose fashion of computer scientists, I intend
this to mean a non-negative integer: i.e., a ⊗4natural⊗* number.

Ordering: the  concept of "before" and "after".  This distinguishes a
list from a bag  (multiset).  The formal  axioms for ordering  simply
state the obvious properties of the intuitive image of a list.

Prime numbers: natural  numbers which have  no divisors other  than 1
and themself; e.g., 17, but ⊗4not⊗* 15 (=3x5). Primes are interesting
because of the myriad times they crop up in diverse theorems  -- from
the Chinese  Remainder Theorem (solving systems  of linear congruence
equations), to  the Law of Quadratic Reciprocity, to Fermat's Theorem
(for all integers  n, for all  primes p, n↑p  is congruent to n  (mod
p)).  The "secret" of  their value lies in the fact that all integers
can be factored  ⊗4uniquely⊗* into  a set  of prime  divisors.   This
"Unique  Factorization  Theorem"  lets  us   reduce  questions  about
integers to questions about primes.

Prime pairs: two prime numbers whose difference is two; e.g., 17 and 19.

Relation: an operation which associates, for each element of some set
D, a set of elements  E = {e↓1, e↓2,...⎇ of  some set R. D and R  are
the  domain and  range of  the  relation. For  example, the  relation
"⊗6≤⊗*" associates  to 5 the set of numbers {5, 6, 7, 8,...⎇ -- i.e.,
all integers which 5 is less than or equal to.   The domain and range
of this relation are the integers.

Set-theoretic: having to do (in the context of this thesis) with
elementary finite set theory, and the primitive notions of mathematics
(e.g., union, insert, predicate, conjecture).

Unity: a fancy way of referring to the natural number "1".

⊗6|⊗*: The relation "divides-evenly-into". Thus we say 2|6.

⊗6α¬⊗*: The operation of negation. "⊗6α¬⊗*X" is read as "not X".

⊗6∨⊗*: Disjunction. "A⊗6∨⊗*B" is read as "A or B".

⊗6∧⊗*: Conjunction. "A∧B" is read as "A and B".

⊗6α⊗⊗*: Exclusive or. "Aα⊗B" is read as "A or B, but not both".

.SELECT 1;

⊗6α→⊗*: Implication. "Aα→B" is read as "If A then B".

⊗6α↔⊗*: Logical equivalence. "Aα↔B" is read as "A if and only if B".

⊗6α∀⊗*: Universal quantification. "⊗6α∀⊗*X" is read as "For all X".

⊗6α∃⊗*: Existential quantification. "α∃X" is read as "For some X".

. ASSECP(Glossary of AI Terms)

ACTORs: A modular form of representation,  useful for distributing of
the  task  of  ⊗4control⊗* among  several  components  in a  computer
program. Each ACTOR is a black box, with no parts or slots, but which
does have  some assertions (a  "contract") which  he must honor.   It
merely  responds to a fixed  set of messages,  by sending out certain
messages of his  own.  These  are delivered via  a bureaucracy.   See
[Hewitt 76].

AI: an abbreviation for Artificial Intelligence.

Bag: A bag is a kind of  list structure, a  bunch of elements which
are unordered, but one in  which multiple copies of the  same element
are permitted.  One may visualize  a paper bag  filled with cardboard
letters. Technically, we shall say  that a set is ⊗4not⊗*  considered
to be a bag.  A bag is denoted  by enclosure within parentheses, just
as sets are within braces. So the bag containing X and four Y's might
be written (X  Y Y Y  Y), and  would be considered  indistinguishable
from the bag (Y Y Y X Y).

BEINGs: A modular form of representation of knowledge, conceived as a
collection of cooperating experts.   Each expert  is modelled by  one
module, which consists of a list of Question/Answering-program pairs.
The set of questions  is fixed for all the Beings in the system. When
any Being has a question, he broadcasts it to the entire  system, and
some Being who recognizes it will take over control and try to answer
it  by running ⊗4his⊗* appropriate  Answering-program. In the process
of running  this, some new  questions may  arise. Notice that  Beings
distribute responsibility for control  and for static knowledge.  See
[Lenat 75b].

Bug: a flaw in a computer program. As Corey Sacerdoti put it, a bug refers to
something which is broken but not badly.

Concept: within the context of this document, the word "concept" typically
refers to a precise frame-like data structure, a BEING. Semantically, each concept
is meant to correspond to one abstract entity that we would intuitively
call a concept: an object, an operator, a conjecture, etc. See "facet".

Cooperating Knowledge Sources: Very often, in tackling a problem, one
receives some hints and some constraints from very different sources,
phrased  in  very  different  languages,  often addressing  different
representations of the problem.  For example, in trying  understand a
human speaker, our memory of the previous discussion and knowledge of
the  speaker may narrow down the possible  ⊗4meanings⊗* of what he is
saying. Our ears, of course, register the precise acoustic wave-forms
he  is  uttering.   Our  English vocabulary  forces  us to  interpret
imperfect signals as real words.   Our eyes see his gestures and  his
lip movements,  and give us  more information.   All these  different
sources of information  must be used, and yet they all are talking in
different "languages" to us.   The most  trivial solution is to  keep
all the sources  independent, and keep working until one  of them can
solve  the  problem all  by itself.   A  much  better solution  is to
transform all their babblings into one  canonical representation, one
single language. This way, all the knowledge sources can cooperate.

Coupled:  two  functional  subsystems  are  causally  connected;  one
influences the other. See the entry for "Linear".

CPU time: Central-Processing-Unit runtime (cpu time) is the number of
execution cycles  of the computer  that the AM  program has  used up.
This is  conveniently measured in seconds,  minutes, and hours, where
one cpu minute is the amount of processing done in one minute of real
time, when  AM has 100% of  the machine, and is  runninng without any
input or output.

CS: an abbreviation for Computer Science.

Execution: a program is actually used by ⊗4running⊗* it on a particular
set of input data. This process is known as program ⊗4execution⊗*.

Facet: Within the context of this document, the word "facet" denotes a
slot of the kind of data-structure known as "concepts" (qv).
Thus "⊗4a facet of the Compose concept⊗*" really just means a slot of a
particular frame, a part of certain BEING,
one single attribute/value pair taken from the property list of the Lisp
atom named Compose.
Semantically, each facet holds information
pertaining to a single aspect of the concept it is a part of; hence the
suggestive name: "facet".

FRAMEs: A modular representation of knowledge.  Each module is a list
of Feature/Value pairs. The ⊗4value⊗* represents a default assumption
which can  be relied on  until/unless new information  comes in about
that feature.  Each frame has whatever ⊗4features⊗* (called  "slots")
seem  appropriate.    Whenever a  situation  S  is  encountered,  the
frame(s)  for  S are  activated.   As  new information  rolls  in, it
replaces the  default  information  in  various slots.    Notice  the
emphasis on distributing static knowledge (⊗4data⊗*), not necessarily
control, in such a system. See [Piaget 55] or [Minsky 75].

Function: a small, executable part of a program. When fed the proper kind of
argument(s), a function will "run" and ultimately produce some sort of value.
Unlike pure mathematical functions (see the previous glossary), a Lisp function
can have side effects (qv).

Garbage collection: As a Lisp program executes, various list structures (pointer
networks) are created. When the last pointer to a structure is removed, that
structure has essentially been irretrievably forgotten. If the operating
system knew which storage cells were thus "free", it could re-cycle them,
reuse them. The process of finding and liberating such discarded lists is called
garbage collection. This is performed automatically by the Lisp language,
whenever space is almost all filled up.

Hack: A quick job that produces what is needed, but
not well. Introducing a heuristic which was only used once, in a predetermined
way (e.g., to fix a particular bug), would be a real hack.

Hand-crafting:  the human programmer carefully  designs his system in
such a  way that the  pieces just  manage to  mesh. For instance:  he
provides just  the perfect set  of axioms so  that his theorem-prover
can solve a certain problem, or he modifies the program's  strategies
so that they efficiently  manipulate the axiom set in  just the right
way.

Heterarchy: A kind  of control structure for a computer program which
is distinct  from hierearchy.   Heterarchical  structuring views  the
whole program as a collection  of equal partners, an unstructured set
of  functions.  "Control" is  viewed  as  a spotlight,  which  can be
flicked from one  function to another.  The functions can affect  who
does or doesn't get control  next, but there is no guarantee who will
get control, or that control will revert back to some function  which
once had it.   Aside from  the lure of  its democratic flavor,  it is
clearly a natural way to represent cooperating knowledge modules.

Hierarchy:  This term  refers to  a kind of  control structure  for a
computer program.  The typical hierarchical structure is one in which
a function  calls a  subroutine, which processes  and then  returns a
value  to that function.   A program  is viewed as  a tree structure,
with lines indicating "calling".

Interact: a dynamic mode of communication between a human and a computer
program. The human reacts to what the program is printing out on his terminal,
and the program in turn reacts to what the user types in. This may take the
form of questioning and answering, or interrupting and commenting.

Interestingness: Note that this is not a valid English word. In the context of
AM, it refers to a numeric value, computed by little Lisp programs stored in
the "Interest" facets of various concepts. Despite the danger of imbuing such
a humble scheme with all the mystique of what is and isn't interesting,
it is felt that a sufficient component of that evaluation has been captured
to warrant the name. Pragmatically, it is of much more use to the user to
see "Interestingness of Compose has just risen" than to see a message like
"G00034 incremented".

Kludge (or Kluge): This is a program feature which is an unfair shortcut
around a specific problem. One "kludgy" way of improving the
algorithm of a given concept is to ask the user for a better algorithm.

Linear:   a   system   whose   components,   inputs,    and   outputs
⊗4superimpose⊗* -- i.e., don't couple.

Lisp: a ↓_LIS_↓t-↓_P_↓rocessing programming language. Primitive operations exist for
manipulating nested list structures. Since Lisp functions are also merely lists,
it is easy to create and modify entities which are then executed (qv).

Modular  Representations of  Knowledge  in AI  Systems:  Knowledge is
partitioned into packets (called modules, frames, units, productions,
Beings, experts, Actors)  along lines of:  different applicabilities,
expertise,  purpose,  importance, generality,  etc.   Each  packet is
structurally similar  to all  the rest.   Advantages:  By having  the
knowledge discretized,  pieces can  be added  and/or removed  with no
trouble.    The  knowledge  of the  system  is  easily  inspected and
analyzed.   The structural  similarity yields  several advantages:  a
simple  control  system suffices  to  "run"  all  the knowledge,  the
modules can  intercommunicate easily,  new  modules can  be  inserted
without knowing precisely  "who else" is  already in the system.   In
general,  the less similarly-structured the  modules are, the simpler
the inter-communication media  must be.  Modular representation is  a
natural way to implement cooperating knowledge sources.

Number: in the typical loose fashion of computer scientists, I intend
this to mean a non-negative integer: i.e., a ⊗4natural⊗* number.

.OPENDP: PAGE;

Open research problem: a limitation of the AM system.

Recur: Often, part of a definition  will refer back to that very same
definition.   This may lead  to an infinite circular  loop, or it may
terminate. The following definition of "is larger than" is recursive,
because the last line recurs:
.WBOX(15,15)
MBOX	 set R ⊗4is larger than⊗* set S $
MBOX		if R={⎇ but S≠{⎇, or $
MBOX		if neither is empty and  $
MBOX			Remove-element(R) ⊗4is larger than⊗* Remove-element(S).  $
.EBOX


Recurse: a transitive verb  which means "to swear again."  It must be
distinguished from "recur", above.

Side effects: while a function is executing, it may cause changes in the state of
its environment which persist even after the function has returned a value. This is
like hysteresis effects. For example, a function may create or destroy some list
structure, define a new function, reset some variable, etc.
Such activities are called side effects of the function.

Space: The memory of a computer is quite finite. Though it may be supplemented
by slow auxilliary devices (tapes, discs, etc.), the actual number of storage
cells in the computer's fast "core" memory is a limiting factor in program
behavior. Storage space, or just "space", refers to these internal memory
cells. When space is exhausted, the only remedy is to perform a garbage
collection (qv).

System: this can mean a computer program, and occasionally is just an
another  way  of  referring  to  AM.  In  general,  a system  is  any
collection of entities related to form a meaningful whole.

Terminal: a communications device for passing information between a computer
system and a human. This could be a teletype, a TV screen and keyboard, etc.
The terminal is usually portable and remotely located from the computer.

User: the human being who sits at a computer terminal and watches AM run 
(occasionally, perhaps, interacting with AM).

.END