Cognitive Computing 2012 The computer and the mind 3. NEWELL & SIMON PHYSICAL SYMBOL HYPOTHESIS Professor Mark Bishop.

Cognitive Computing 2012

The computer and the mind

3. NEWELL & SIMON

PHYSICAL SYMBOL HYPOTHESIS

Professor Mark Bishop

10/04/23 (c) Bishop: The computer and the mind 2

Background The computing machine is not just hardware or software but

specifies the execution of software by hardware.

Computer Science is an empirical (derived from experience) discipline.

Each machine is an experiment - development of knowledge through empirical enquiry.

Newell and Simon’s paper focuses on two important examples: the symbolic system; heuristic search.


Symbols and physical symbol systems

All sciences are concerned with the essential nature of the systems they study.

Such characterisations are usually qualitative. E.g.

In biology the building block of all living things is the cell; In geology the surface of earth a collection of huge plates etc.

Laws of ‘qualitative structure’ are everywhere in science, usually defining the terms on which a science operates.

On a fundamental level computer science can be considered an attempt to (empirically) explain what symbols really are.


Ernst Cassirer: on signals and symbols

“Man has, as it were, discovered a new method of adapting himself to his environment. Between the

receptor system and the effector system, which are to be found in all animal species, we find in man a third link which we may describe as the symbolic

system. This new acquisition transforms the whole of human life. As compared with the other animals man lives not merely in a broader reality; he lives,

so to speak, in a new dimension of reality.”

Cassirer, An Essay on Man, (1944)


Cassirer: the philosophy of symbolic forms

A symbol has no actual existence as part of the physical world; it has a ‘meaning’.

Symbols - in the proper sense of this term - cannot be reduced to mere signals.

Symbols and signals belong to two different universes of discourse:

‘Signals’ are operators - a signal is part of the physical world of being and has a physical or substantial being.

‘Symbols’ are designators - a symbol is part of the human world of meaning.


Physical Symbol Systems, (PSS)

In a physical symbol system the term ‘physical’ denotes that the system is realizable in [machine] hardware and not restricted to human symbols systems.

A PSS defines ‘symbol’ as a set of ‘physical patterns’ Such patterns are components of a ‘symbol structure’, (or

expression).

A ‘symbol structure’ is composed of tokens related in a ‘physical way’, (e.g. by adjacency), plus processes capable of operating on such expressions to produce further expressions.

Thus a ‘physical symbol system’ is a set of ‘symbol structures’ mechanically evolving over time.


The physical symbol systems hypothesis

<http://aaai.org/AITopics/AIVideos/2007-0072>

A PSS has the necessary and sufficient means for ‘general intelligent action’.

It is an empirical and qualitative law.

A PSS is an instance of a universal machine, hence intelligent action will be realizable by universal computer.

The physical symbol system hypothesis asserts that the intelligent machine IS a PSS.


Steps towards the ‘physical symbol system’

Formal logic (cf. Russell & Whitehead)

An attempt to purge ‘meaning’ from symbols.

Turing Machines and Digital Computers

Universal computing machines.

Stored Program as data: The UTM: Turing Machine data can equally specify a program.

NB. Albeit Newell and Simon observe that in the early days no attempt was made to investigate machines with ‘self modifying code’.


The ‘designating’ symbol

List processing (LISP):

Data can now designate (indirection)

Indirection gives us ‘pointers’ and ‘dynamic memory’

Conclusion:

We needed emergence of all of the above to facilitate the emergence of the concepts of: (i) ‘symbol manipulation’; (ii) ‘the designating symbol’; and (iii) the ‘physical symbol system’.


Artificial intelligence (A.I.) and psychology

A.I. is concerned with constructing ‘intelligent computer systems’. Over its history lots of programs have been developed to

investigate specific small [toy] aspects of intelligent action. A common principle is heuristic (short-cut; non-exhaustive) search.

In Psychology, investigation of human problem solving entails the observation and modelling of human symbolic behaviour.

AI programs such as GPS (the ‘General Problem Solver’) were developed to simulate human problem solving behaviour. GPS: an attempt at generality in problem solving. The core concepts of GPS derived observation of human problem

solving in action.


Principle evidence for PSS At the time of Newell & Simon’s paper there appeared to be NO serious

competing hypothesis.

Contrast currently with the emergence of: connectionism; embodied cognitive science; Brooks: A.I. and the subsumption architecture. Radical embodied cognitive science & dynamical system theory; enactivism etc.

Newell and Simon claim that ‘gestalt theory’ (on ‘wholeness’) and behaviourism are inadequate as they lack the explanatory power of the PSS.

However, although the PSS hypothesis demonstrates that computer science can be construed as an empirical/experimental scientific enterprise, it does not specify how to use a PSS for intelligent action…


Heuristic search hypothesis Problem solutions represented as symbol structures.

A PSS exercises intelligence by search.

i.e. A PSS progressively modifies the symbol structure until it produces a possible problem solution.

Time is a constraint in any real PSS.

Newell & Simon do not consider fully parallel search etc.

Limited resource PSS and the serial PSS are synonymous.


Problem solving: Plato and Meno

“How do you enquire Socrates into that which you know not?”

“What will you put forth as the subject of enquiry?”

“And if you find what you want, how will you ever know that this is what you did not know?”

Theory of Recollection (Plato)

‘Knowledge is the recollection of timeless forms from before our immortal souls were imprisoned inside our bodies’.


Problem solving: heuristic search Establish a test for a class of symbol structures and a generator of

possible solution PSSs.

Repeatedly generate and test until the PSS satisfies the test.

NB. This process is not like dreams; we can't immediately just generate a solution as we don’t know how good a solution is until we test it.

Consider chess: We can't immediately generate best positions (‘as if in a dream’). We must painstakingly search thru all available solutions and somehow

evaluate them to find 'best' (cf. Meno). Even Deep Blue can't solve perfectly for chess (and so must approximate).

A PSS must use ‘limited processing’ to search the space of possible solutions; an intelligent PSS makes wise choices of what to evaluate next (e.g. alpha-beta pruning)


Extracting information from the problem space

If solutions are randomly distributed we can do no better than random search.

But in tasks which require ‘intelligence’:

The expectation is that solution distributions are not random;

the pattern of solutions is detectable; the ‘generator’ is capable of ‘adaptive behaviour’ as it

discovers this pattern.


Intelligence by incremental application of knowledge

Consider the algebraic expression: AX + B = CX + D.

We could generate solutions for X by repeated ‘trial and error’.

This would be extremely unintelligent.

The problem is best solved by ‘incremental application of knowledge’.

Thus rearranging the above algebraic expression demonstrates intelligent problem solving. I.e. X = (D – B) / (A – C)

This methodology demonstrates ‘intelligence’ to find a solution without the need for either reincarnation or access to Plato’s ‘perfect forms’ !


Search trees

Combinatorial explosion in search

If the generator forms ‘B’ branches then we get a tree of ‘BD’ tests where ‘D’ is depth of search.

Chess involves very broad trees which rapidly form very large search spaces.

Although we note that human players only evaluate a few moves by being very selective in what branches to evaluate.


Measuring intelligence

The raw amount of search involved in solving a problem is not a measure of intelligence..

A problem’s difficulty is more accurately approximated by the amount of search that would be required without application of intelligence.

“The hope is periodically ignited that a chess playing program will be developed to win by brute force”. As it happened IBM’s ‘Deep Blue’ [effectively] did just this!

The need to avoid combinatorial explosion

Only rarely can breadth be reduced to unity - as in the algebraic manipulation example - so typically we must deploy heuristics to guide the search and narrow the search tree.


Simple heuristic search

Attempts to answer the question, “What is to be done next in the search process?” E.g. From what node in tree do we (re) start next search?

Best-fit search: examine the relative distance of each node from final solution.

Means-end analysis: the search process over the problem space combines aspects of both forward and backward reasoning in that both the condition and action portions of rules are looked at when considering which rule to apply.

Differences between the current and goal states are used to propose operations which reduce the differences.


Weak and strong search ‘Best Fit’ search evolved from Logic Theorist and ‘Means-End Analysis’

evolved with GPS. For reasons related to the size of their memory, early chess programs used

‘Depth First’ search as they couldn't store large search trees in memory. It is suggested that the poor performance of A.I. systems against humans is

due to humans using more SEMANTIC knowledge on very parallel hardware;

Deep Blue??

Newell and Simon observe that there has been little mathematical investigation into search algorithms.

This is not so true now…

The above ‘weak search’ methods seek to control combinatorial explosion when it cant be avoided (e.g. TSP).

‘Strong search’ methods aim to eliminate it by utilizing structure in the solution domain.


Intelligence without much search The use of ‘non-local information’

When playing chess usually only use knowledge locally - should try to combine it to produce a global picture.

eg. HEARSAY speech understanding project uses various types of search on phonemes; lexical; syntatic & semantic and combines it globally onto a blackboard.

‘Semantic Recognition Systems’ Store lots of problem specific knowledge.

eg. For chess might store upwards of 50K interesting patterns [Deep Blue].

‘Appropriate Representations’ Consider chess board with two diagonal corners removed. Can it be covered by exactly 31 tiles?

We could evaluate (massive) search tree or observe that opposite ends of a diagonal are same colour, so can‘t do it.


Conclusion

‘With the development of physical symbol systems and heuristic search Newell and Simon significantly moved the process of

intelligent problem solving away from Plato, at a time when intelligent thought was

deemed intangible’.

Cognitive Computing 2012 The computer and the mind 3. NEWELL & SIMON PHYSICAL SYMBOL HYPOTHESIS Professor Mark Bishop.

Documents

c bishop

mind6 physical symbol

symbol manipulation

physical world

universal computer

intelligent computer

term physical

physical way