Mathematical Structures for Rational Discourse


Desmond Fearnley-Sander
Department of Mathematics
University of Tasmania


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.

Some extensions are outlined, and the relationship is considered of the work reported here to automatic theorem-proving.

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