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| | This point draws the chase back through the briar patch of that earlier complexity theory, the prime decomposition or group complexity theory of finite automata and their associated formal languages or transformation semigroups (Lallement, ch. 4). This more general study requires the use of semi-direct products (Rotman, 1984) and their ultimate extension into wreath products or cascade products, along with the corresponding notions of divisibility, factorization, or decomposition (Barr & Wells, 1990, ch. 11). This theory seems to have reached a baroque stage of development, either too difficult to pursue with vigor, too lacking in applications, or falling short of some essential insight. It looks like another one of those problem areas that will need to be revisited on the way to integrating AI and systems theory. | | This point draws the chase back through the briar patch of that earlier complexity theory, the prime decomposition or group complexity theory of finite automata and their associated formal languages or transformation semigroups (Lallement, ch. 4). This more general study requires the use of semi-direct products (Rotman, 1984) and their ultimate extension into wreath products or cascade products, along with the corresponding notions of divisibility, factorization, or decomposition (Barr & Wells, 1990, ch. 11). This theory seems to have reached a baroque stage of development, either too difficult to pursue with vigor, too lacking in applications, or falling short of some essential insight. It looks like another one of those problem areas that will need to be revisited on the way to integrating AI and systems theory. |
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| − | =====1.2.2.2. Statements, Questions, Commands=====
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| − | <pre>
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| − | When signs are created that can be placed in reliable association with the
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| − | results of observations and the onsets of actions, these signs are said to
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| − | denote or evoke the corresponding events and actions. This is the beginning of
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| − | declarative, imperative, and interrogative uses of symbolic expressions. The
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| − | interrogative mode is associated with residual properties of the state occupied
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| − | by a system. The question marks a difference between states denoted by
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| − | declarative expressions, a divergence between expectation and actuality. The
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| − | inquisitive use of a sign notes a surprise to be explained, usually by adducing
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| − | the signs of less obvious facts to the account. A surprise incites the system
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| − | to an effort whose end is to bring the system's habits of expectation in line
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| − | with what actually happens on a recurring basis.
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| − |
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| − | The imperative mode is associated with convergent possibilities of the states in
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| − | which a system may come to reside. The command calls attention to a discrepancy
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| − | between actuality and intention, a difference between the states independently
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| − | declared to be observed and desired. The injunctive use of a sign sets a
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| − | problem to be resolved, usually by executing the actions enjoined by a series of
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| − | signs. A problem incites the system to an effort whose end is to bring what
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| − | actually happens on a recurring basis in line with the system's hopeful
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| − | anticipations. If this problem turns out to be intractable, then the
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| − | expectation that these intentions can be fulfilled may have to be changed. In
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| − | this way the different modes of inquiry are often embroiled in intricate
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| − | patterns of interaction.
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| − |
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| − | In proceeding from surprise and problem states to arrive at explanations and
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| − | plans of action that are suited to resolving these states, the system's aim is
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| − | expedited by certain resources, all of which involve massive and complex systems
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| − | of signs and symbolic expressions. It helps to have a library, an access to the
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| − | records of individual and collective past efforts and experiences. To be used
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| − | for clear and present indications this library must have a ready index of its
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| − | contents, a form of afterthought that is not too thoughtless in design. It
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| − | helps to a have laboratory, a workshop or a study, any facility where
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| − | imagination reigns for composing and testing improvised programs and theories,
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| − | for prototyping on-the-spot inventions. To be used for free and unbiased
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| − | evaluation this factory of imagination must be a mechanism of forethought
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| − | without malice, where symbolic expressions extempore are not confused with
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| − | actions and do not exact the same price in energy spent and pain risked.
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| − | But how can all this information and flexibility, constraint vying with freedom
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| − | of interpretation, be accorded a place in the present state of a system? Can
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| − | Epimetheus and Prometheus find a way to "get along" in the current state of
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| − | things? Is the phase space of a system really big enough for both of them?
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| − | If signs and symbols are to receive a place in systems theory it must be
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| − | possible to construct them from materials available on that site. But the only
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| − | thing a system has to work with is its own present state. How do states of a
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| − | system come to serve the role of signs? How can it make sense to say that
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| − | system regards one of its own states as a sign of something else? How do
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| − | certain states of a system come to be taken by that system, as evidenced by its
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| − | interpretive behavior, as signs of something else, some object or objective? A
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| − | good start toward answering these questions would be made by defining the words
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| − | used in asking them. In looking at the concepts that remain to be given
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| − | system-theoretic definitions it appears that all of these questions boil down to
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| − | one: What character in the dynamics of a system would cause it to be called a
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| − | sign-using system, one that acts as an interpreter in a non-trivial sense?
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| − | </pre>
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| | =====1.2.2.2. Statements, Questions, Commands===== | | =====1.2.2.2. Statements, Questions, Commands===== |
