Mathematical Structures for Rational Discourse
Department of Mathematics
University of
Tasmania
Australia
This paper reports the implementation of a
system for the creation of rational automata: automata that communicate
with one another, display curiosity, learn and are creative. The author calls
the implemented automata narrow minds. The formal mathematical structure
of a rational automaton is defined, a sketch is given of how they work and how
they interact, and a sample dialogue between narrow minds is presented.
Equation processing plays a central role. It is argued that basic everyday
thinking and basic mathematical thinking, though very different in some ways,
can be implemented using the same mechanisms.
The narrow minds system takes a step toward
the productive social interaction of rational and, in particular,
mathematically capable autonomous computer entities. Its implementation rests
upon two fundamental computational paradigms: equational programming and
object-oriented programming, the one for implementation of simple intelligence,
the other for implementation of simple social interaction.The system user can
control the level of intelligence of the narrow minds that are created, how
they interact in dialogue, how they speak, and, to some extent, how they think.
Parallelism is intrinsic to the system, as it is to human communities.
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