## Semiotic Theory Of Information : 6

2014 Oct 14

Through the 1970s I gradually recovered from my early traumas with Fortran, and with the aid of more symbol-friendly programming languages like Lisp and Pascal began to play around again with implementing simple forms of graphical calculi inspired by Peirce and Spencer-Brown in the form of programs that carried out the requisite transformations in automatic or guided interactive fashions.

Experiments like these, moving from scribblings on paper to algorithms and data structures in electronic media, brought about a transformation in my perspective on symbolic logic and other semiotic processes.  The shift was very gradual over the decade that followed, but I think it began with thinking of computer memory as very like a sheet of paper, a tabula rasa, or a Sheet of Assertion as Peirce dubbed the unmarked state in his systems of logical graphs.

Thinking this way naturally brings out the system-theoretic aspects of semiosis in general and logic in particular.  One begins with sign relations as subsets of cartesian products ${O \times S \times I},$ where ${O, S, I}$ are sets of objects, signs, and interpretant signs, respectively, and over time one begins to see dynamic systems in place of those sets.  Then one day in the mid 1980s I distinctly remember flashing on the fact that the graph-theoretic data structures I and my programs were manipulating in memory were actually diagrams in Peirce’s sense.

With that pre-ramble, here is a bit of background from (Awbrey & Awbrey, 1990) that describes our system-theoretic approach to agents with a capacity for learning and reasoning.

### The State Space Approach to Intelligent Systems

The common definition of a system as a list of variables is useful but not absolute.  It characterizes the system only as measured from a particular frame of observation.  The property of a system that we really care about is its state space, or a representation showing the possible states of a system.  When considering systems that exhibit complex sets of properties, such as being able to transform information and to act with intelligent purpose, it becomes more difficult to specify in advance the exact nature of the state space, or even whether a space exists that satisfies a given set of specifications.  Therefore we do not consider the state space of intelligent systems to be given absolutely, as the subset of some predefined space (like ${\mathbb{R}^{n}}$), but defined provisionally, subject to a list of constraints and subject to revision.

When considering intelligent behavior, we are most interested in the state of information that an interpreter system has about an object system, and this information has its expression in a system of signs.  The characterizations sign, object, interpreter are not so much exclusive categories of entities as roles that systems may play within the so-called sign relation.  Although interested in the nature and relations of these systems in themselves, whatever we can say about them takes place within the domain of signs.  As we use the words, sign is the general category, while symbol is a particular type of sign.  From the pragmatic point of view, almost all the actual work of computation is involved with transformations between expressions in the symbolic domain.

To be continued …