Games and the Problem of Relevance

April 27, 2008

Hubert Dreyfus wrote his book What Computers Can’t Do long before Luciano Floridi came onto the scene. Yet the following point seems specifically constructed to shed light on the problem of relevance (mentioned in this post):

“As long as the domain in question can be treated as a game, i.e., as long as what is relevant is fixed, and the possibly relevant factors can be defined in terms of context-free primitives, then computers can do well in the domain” (Dreyfus, 27).

Dreyfus doesn’t expound upon exactly what kinds of games he has in mind; but I think it’s safe to say that he isn’t talking about all games. After all, there are certainly games like soccer (which is analogue) and nomic (which is unstable) that would foil a computer readily.

But there are certain games with qualities that make them ideal domains for attack by projects in artificial intelligence. Chess is one of these games. Let us try to itemize the qualities that make such games so conducive to formalization:

1) Such games consist of states.

2) Such games have rules that govern changes in state.

3) Such games are stable, i.e., the rules either stay constant or change only in correspondence with other rules that do stay constant.

4) Such games are transparent, i.e., the rules can be known because they are simple enough to understand.

5) Such games have a bounded set of rules, i.e., the rules can be itemized because they are finite in number.

6) Such games have a bounded set of states, i.e., the number of possible game states is finite, even if astronomical.

7) Such games have winning conditions that can be assessed from within the system itself, i.e., there are rules that can designate some states as won and others as lost. (Note: we can weaken this condition to include games that cannot be won or lost; but there must still exist rules that designate some states as better than others or worse than others, in order for such games to be conducive to productive computational analysis.)

To wrap all of this into a tidy package: such games (considered to be a collection of states, transition rules, and evaluation rules) must be representable as a finite state machine. If so, then they can be represented syntactically. And algorithms can be written for their governance.

Bear in mind, however, that this is a necessary condition, not a sufficient one. The above criteria merely distinguish games that can be formalized from ones that can’t. But within the set of games that can be formalized, there can (and most likely do) exists games with such complex states or such complex transition rules that they are computationally intractable. So we must add another necessary condition:

8) Such games must be tractable, i.e., not only must they have a finite number of states, transition rules, and evaluation rules; these states and rules must be few enough and simple enough to effectively compute the state-to-state transitions required for playing the game.

But even this addition doesn’t guarantee that the game will be a domain in which artificial intelligence projects can thrive. Formalization and tractability don’t imply that an artificially intelligent system (or its creators) will be capable of applying heuristics and/or strategic rules necessary for a high level of play.

Nonetheless, considering Deep Blue’s success in the face of so much skepticism, a little optimism might be in order if the above conditions happen to be met.

In closing, my food-for-thought question of the day is, “Can linguistic domains be transformed into games that meet the above criteria?” I think we’ll visit Wittgenstein soon. He has quite a bit to say about language games.


Dreyfus, Hubert L. What Computers Can’t Do. New York : Harper and Row, 1979.

3 Responses to “Games and the Problem of Relevance”

  1. […] the kind of language games mentioned at the end of my previous post, and which we’ll talk about later, need not be games that human beings play and need not be […]

  2. […] May 1, 2008 Simply put, heuristics are rules for governing how a formal system ought to move (where “move” is understood to mean “transition from one state to another according to valid transition rules.”)  But for our purposes, we should understand heuristics to have a quality of being definable fully within the system itself. In other words, the heuristic “Control the center” would have been useless to Deep Blue if the idea of “control” and the idea of “center” were impossible to define syntactically.  (Note: This should be reminiscent of our similar stipulation that winning conditions be definable within the system itself — an idea mentioned here.) […]

  3. […] I mention this because linguistic systems are known to possess potentially unbridled (and largely uncharted) recursive structures.  And also, linguistic systems happen to be an important frontier in AI research.  So my question is, can a computer be taught enough heuristics (of various orders) to function at an apparently high level of linguistic competence?  If the answer is yes (which is a huge “if”), then perhaps one way to effect such a break through would be to first begin with very simple languages games with clearly defined winning conditions and clearly defined transition rules (as mentioned in this post.) […]

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