Symbolic paradigm

1. Symbolic paradigm

2. Heavily influenced by the architecture of the von Neumann computer, both in terms of: • style of algorithmic representation, and • data storage

3. Pylyshyn's "classical view" Computers and minds have 3 distinct levels of representation: 1. Semantic (knowledge) level: this level explains why things happen; we speak of goals. 2. Symbol level: the important one. 3. physical/biological level.

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

5. Syntax and semantics • Remember: syntax refers to the principles that determine what and how symbols may be combined into well-formed structures as a given level; and usually, to principles determining permissible cross-representation relationships. • Sometimes this latter is called semantics

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

7. A classical model is an... automatic formal system (Haugeland): a physical device such that: 1. some configuration of its parts can be regarded as the tokens and positions of some formal system; and 2. it automatically manipulates those tokens in accord with the rules of that system

8. A formal system consists of: • a finite set of types of formal tokens or pieces; • a set of rules for how tokens may be combined to form a permissible initial representation; all such rules are based on the type of the tokens; • a set of rules for how one representation may be changed to another;

9. The type of a token can be always be determined to any degree of accuracy, i.e., perfectly. • The system is medium-independent;

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

11. In a classical symbolic model, in addition: • all representations are representations of external states of affairs (true semantics); or of other representations [pointers]; or of procedures [pointers to functions]; or they are (syntactically permissible) combinations of these.

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

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

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

15. Example: addition addition; arguments (2) a,b; return 1 number i=0; number Sum, Carry, Temp; Sum=0; Carry = 0; start: Temp = Carry + a[i] + b[i]; if Temp > 9 then {Carry = 1 and Temp = Temp - 10} else {Carry = 0}; Sum[i] = Temp; if ( i < Length (a) or i<Length(b) or Carry) then {i= i+1; loop back} else {quit loop} return Sum;

16. There is thus a Last-in-first-out stack of control-passers. • Another type of control accepts calls to subroutines triggered by exogenous events. Certain representations are designated as designating external events, and they may have precedence in the control structure (users or lower-level exceptions).

17. TOTE: test operate test exit The classical unit of operation is the subroutine, or TOTE unit: a subroutine which has control tests to determine if condition T is met; if it is, it performs some operation; if not, it exits . When a subroutine exits, control shifts

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

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

20. Memory (2) • The issue of how to extract information relevant to a representation when one does not know the address of that information is a tricky one in traditional computational analysis. • How do you get to a lexical entry when you have its phonetic form, say?

21. 1 way: search through the entire lexicon for a phonetic match. • onoe of the dumbest: search in a random (but linear) order. • better: order your list by frequency, and trust in Zipf. • better: hash function....

22. hash function • assigns an address explicitly based on the content (e.g., the spelling, or the phonetic form). • E.g., assign values to each letter, and add the sum of the values of the letters. • Deal with "collisions":

23. dog and god map to the same value by the simplest hash function. Various solutions...

24. Levels of analysis: Marr's account David Marr: work in England, MIT; early demise. Influential book Vision. Proposed 3 levels: • computational theory • representation and algorithm • hardware implementation

25. Computational theory • the nature of the problem that the organism we're studying must solve: • arithmetic, the inference of 3-d spatial bodies from 2-d retinal projections, perception of sequences of words from continuous sound, etc.

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

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

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

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

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

31. there was frequently no way to determine whether a program would deal with a particualr case other than by running the program. • Failure to recognize this theoretical distinction between what and how also greatly hampered communication between the fields of artificial intelligence and llinguistics. Chomsky's (1965) theory of

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

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

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