Symbolic paradigmSymbolic paradigm

Heavily influenced by the architecture of Heavily influenced by the architecture of the von Neumann computer, both in terms the von Neumann computer, both in terms of:of:

style of algorithmic representation, andstyle of algorithmic representation, and data storagedata storage

Pylyshyn's "classical view"Pylyshyn's "classical view"

Computers and minds have 3 distinct levels of Computers and minds have 3 distinct levels of representation:representation:

1. Semantic (knowledge) level: this level 1. Semantic (knowledge) level: this level explains why things happen; we speak of explains why things happen; we speak of goals.goals.

2. Symbol level: the important one.2. Symbol level: the important one.

3. physical/biological level.3. physical/biological level.

Symbol levelSymbol level

Content of knowledge is encoded by symbolic Content of knowledge is encoded by symbolic expressions, which have parts, and each expressions, which have parts, and each part encodes some semantic content.part encodes some semantic content.

Syntax and semanticsSyntax and semantics

Remember: syntax refers to the principles Remember: syntax refers to the principles that determine what and how symbols may that determine what and how symbols may be combined into well-formed structures as be combined into well-formed structures as a given level; and usually, to principles a given level; and usually, to principles determining permissible cross-determining permissible cross-representation relationships. representation relationships.

Sometimes this latter is called Sometimes this latter is called semanticssemantics

SemanticsSemantics

Semantics is generally understood to refer Semantics is generally understood to refer to the principles determining the correctness to the principles determining the correctness of claims of truth and reference assigned to of claims of truth and reference assigned to representations.representations.

automatic formal system (Haugeland):automatic formal system (Haugeland):

a physical device such that:a physical device such that:

1. some configuration of its parts can be 1. some configuration of its parts can be regarded as the tokens and positions of regarded as the tokens and positions of some formal system; andsome formal system; and

2. it automatically manipulates those tokens in 2. it automatically manipulates those tokens in accord with the rules of that systemaccord with the rules of that system

A classical model is an...A classical model is an...

A formal system consists A formal system consists of:of:

a finite set of a finite set of types of formal tokens or types of formal tokens or pieces; pieces;

a set of rules for how tokens may be a set of rules for how tokens may be combined to form a permissible initial combined to form a permissible initial representation; all such rules are based on representation; all such rules are based on the type of the tokens;the type of the tokens;

a set of rules for how one representation a set of rules for how one representation may be changed to another;may be changed to another;

The type of a token can be always be The type of a token can be always be determined to any degree of accuracy, i.e., determined to any degree of accuracy, i.e., perfectly.perfectly.

The system is medium-independent;The system is medium-independent;

Time?Time?

...plays no explicit role in a world of formal ...plays no explicit role in a world of formal representations. Implicit is the assumption representations. Implicit is the assumption that neither user's time nor internal time has that neither user's time nor internal time has any effect on representations, except insofar any effect on representations, except insofar as the rules of the system as the rules of the system change change the the representation.representation.

In a classical symbolic In a classical symbolic model, in addition:model, in addition:

all representations are representations of all representations are representations of external states of affairs (true semantics); or external states of affairs (true semantics); or of other representations [pointers]; or of of other representations [pointers]; or of procedures [pointers to functions]; or they procedures [pointers to functions]; or they are (syntactically permissible) combinations are (syntactically permissible) combinations of these.of these.

Issue of Issue of controlcontrol

The system can be viewed as passing through The system can be viewed as passing through a sequence of states; the overwhelming largest a sequence of states; the overwhelming largest part of the system undergoes no change part of the system undergoes no change (memory). The system includes specifications (memory). The system includes specifications of what changes are permissible under what of what changes are permissible under what conditions = operations. Principles of conditions = operations. Principles of controlcontrol determine which operations are relevant at determine which operations are relevant at which stages.which stages.

One can speak of One can speak of controlcontrol residing at residing at different places in a system; it is at one different places in a system; it is at one place at any given time. Time is discrete; place at any given time. Time is discrete; one can thus speak of the state of the system one can thus speak of the state of the system at moment at moment nn; and of the transition from ; and of the transition from state state nn to state to state n+1 n+1. .

The most important type of control is The most important type of control is hierarchical; hierarchical; in such a system, one in such a system, one function or subroutine passes control function or subroutine passes control temporarilytemporarily to another subroutine, and it to another subroutine, and it expects control to return to it when the expects control to return to it when the "lower" subroutine exits."lower" subroutine exits.

Example: additionExample: addition

addition; arguments (2) a,b; return 1 addition; arguments (2) a,b; return 1 numbernumberi=0;i=0;

number Sum, Carry, Temp; Sum=0; number Sum, Carry, Temp; Sum=0; Carry = 0;Carry = 0;start: Temp = Carry + a[i] + b[i];start: Temp = Carry + a[i] + b[i];

if Temp > 9 then {Carry = 1 and if Temp > 9 then {Carry = 1 and Temp = Temp = Temp - 10} else {Carry = 0};Temp - 10} else {Carry = 0};Sum[i] = Temp;Sum[i] = Temp;if ( i < Length (a) or i<Length(b) or if ( i < Length (a) or i<Length(b) or Carry) Carry) thenthen{i= i+1; loop back}{i= i+1; loop back}else {quit loop}else {quit loop}return Sum;return Sum;

There is thus a Last-in-first-out stack of There is thus a Last-in-first-out stack of control-passers.control-passers.

Another type of control accepts calls to Another type of control accepts calls to subroutines triggered by exogenous events. subroutines triggered by exogenous events. Certain representations are designated as Certain representations are designated as designating external events, and they may designating external events, and they may have precedence in the control structure have precedence in the control structure (users or lower-level exceptions).(users or lower-level exceptions).

TOTE: test operate test TOTE: test operate test exitexit

The classical unit of operation is the The classical unit of operation is the subroutinesubroutine, or TOTE unit:, or TOTE unit:

a subroutine which has control a subroutine which has control teststests to to determine if condition T is met; if it is, it determine if condition T is met; if it is, it performs some operation; if not, it performs some operation; if not, it exits .exits .

When a subroutine When a subroutine exitsexits, control shifts, control shifts

passing control, or passing control, or messagesmessages

Message-passing is conceptually distinct from Message-passing is conceptually distinct from control-passing. A subroutine may not know control-passing. A subroutine may not know anything about how some state of affairs anything about how some state of affairs should be handled; it does not know who should be handled; it does not know who should get control to handle a state of affairs; should get control to handle a state of affairs; but it announces the state of affairs (in general, but it announces the state of affairs (in general, or to a limited audience), and other or to a limited audience), and other subroutines may elect to respond to the new subroutines may elect to respond to the new message. message.

memorymemory

In classical systems, memory is accessed by In classical systems, memory is accessed by the subroutine in control; it is accessed by the subroutine in control; it is accessed by knowing the knowing the addressaddress of the information; the of the information; the (hardware) system returns (hardware) system returns memory contentmemory content in response to being given in response to being given memory addressmemory address. .

Memory (2)Memory (2)

The issue of how to extract information The issue of how to extract information relevant to a representation when one does relevant to a representation when one does not know the address of that information is not know the address of that information is a tricky one in traditional computational a tricky one in traditional computational analysis. analysis.

How do you get to a lexical entry when you How do you get to a lexical entry when you have its phonetic form, say?have its phonetic form, say?

1 way: search through the entire lexicon for 1 way: search through the entire lexicon for a phonetic match.a phonetic match.

onoe of the dumbest: search in a random onoe of the dumbest: search in a random (but linear) order.(but linear) order.

better: order your list by frequency, and better: order your list by frequency, and trust in Zipf.trust in Zipf.

better: hash function....better: hash function....

hash functionhash function

assigns an address explicitly based on the assigns an address explicitly based on the content (e.g., the spelling, or the phonetic content (e.g., the spelling, or the phonetic form).form).

E.g., assign values to each letter, and add E.g., assign values to each letter, and add the sum of the values of the letters.the sum of the values of the letters.

Deal with "collisions":Deal with "collisions":

dogdog and and godgod map to the same value by the map to the same value by the simplest hash function. Various solutions...simplest hash function. Various solutions...

Levels of analysis: Marr's Levels of analysis: Marr's accountaccount

David Marr: work in England, MIT; early David Marr: work in England, MIT; early demise. Influential book demise. Influential book VisionVision. .

Proposed 3 levels: Proposed 3 levels: computational theorycomputational theory representation and algorithmrepresentation and algorithm hardware implementationhardware implementation

Computational theoryComputational theory

the nature of the problem that the organism the nature of the problem that the organism we're studying must solve:we're studying must solve:

arithmetic, the inference of 3-d spatial arithmetic, the inference of 3-d spatial bodies from 2-d retinal projections, bodies from 2-d retinal projections, perception of sequences of words from perception of sequences of words from continuous sound, etc.continuous sound, etc.

Computational TheoryComputational Theory

"Although algorithms and mechanisms "Although algorithms and mechanisms are empirically more accessible, it is are empirically more accessible, it is the top level, the level of computational the top level, the level of computational theory, which is critically important theory, which is critically important from an information-processing point of from an information-processing point of view. The reason for this is that the view. The reason for this is that the nature of the computations that nature of the computations that underlie perception depends more upon underlie perception depends more upon the computational the computational

problems that have to be solved than upon the problems that have to be solved than upon the particular hardware in which their solutions particular hardware in which their solutions are implemented...an algorithm is likely to are implemented...an algorithm is likely to be understood more readily by be understood more readily by understanding the nature of the problem understanding the nature of the problem being solved than by examining the being solved than by examining the mechanism (and the hardware) in which it mechanism (and the hardware) in which it is embodied."(is embodied."(VisionVision, p. 27), p. 27)

"...trying to understand perception by "...trying to understand perception by studying neurons is like trying to studying neurons is like trying to understand bird flight by studying only understand bird flight by studying only feathers. It just cannot be done...."feathers. It just cannot be done...."

"It is surprising that this level of approach "It is surprising that this level of approach did not play a more forceful role in the early did not play a more forceful role in the early development of artificial intelligence. For development of artificial intelligence. For far too long, a heuristic program for far too long, a heuristic program for carrying out some task was held to be a carrying out some task was held to be a theory of that task, and the distinction theory of that task, and the distinction between what a program did and how it did between what a program did and how it did it was not taken seriously. "it was not taken seriously. "

As a result, (1) a style of explanation As a result, (1) a style of explanation evolved that invoke the use of special evolved that invoke the use of special mechanisms to solve particualr problems, mechanisms to solve particualr problems, (2) particular data structures, such as the (2) particular data structures, such as the lists of attribute-value pairs called property lists of attribute-value pairs called property lists in the LISP prgoramming language, lists in the LISP prgoramming language, were held to amount to theories of the were held to amount to theories of the representation of knowledge, and (3)representation of knowledge, and (3)

there was frequently no way to determine there was frequently no way to determine whether a program would deal with a particualr whether a program would deal with a particualr case other than by running the program.case other than by running the program.

Failure to recognize this theoretical distinction Failure to recognize this theoretical distinction between between whatwhat and and howhow also greatly hampered also greatly hampered communication between the fields of artificial communication between the fields of artificial intelligence and llinguistics. Chomsky's (1965) intelligence and llinguistics. Chomsky's (1965) theory of theory of

transformational grammar is a true transformational grammar is a true computational theory in the sense defined computational theory in the sense defined earlier. ...Chomsky himself was very clear earlier. ...Chomsky himself was very clear about htis -- it is roughly his distinction about htis -- it is roughly his distinction between competence and performance...but the between competence and performance...but the fact that his theory was defined by fact that his theory was defined by transformations, which look like transformations, which look like computaitonas, seems to have confused many computaitonas, seems to have confused many people....people....

...finding algorithms by which Chomsky's ...finding algorithms by which Chomsky's theory mayu be implemented is a completely theory mayu be implemented is a completely different endeavor from formulating the theory different endeavor from formulating the theory itself. In our terms, it is a study at a different itself. In our terms, it is a study at a different level, and both tasks have to be done....It even level, and both tasks have to be done....It even appears that the emerging "trace" theory of appears that the emerging "trace" theory of grammar (ref) may provide a way of grammar (ref) may provide a way of synthesizing the two approaches -- showing synthesizing the two approaches -- showing that, for example, that, for example,

some of the rather ad hoc restrictions that some of the rather ad hoc restrictions that form part of the computational theory may form part of the computational theory may be consequences of weaknesses in the be consequences of weaknesses in the computaional power that is available for computaional power that is available for impementing syntactical decoding."(29).impementing syntactical decoding."(29).