Информационная система "Конференции"

Abstracts

Applications of logic in computer science

In the early 20th century, the Polish logician Stanislaw Leśniewski has developed three systems of logic as formal languages. These systems are Protothetics, Ontology and Mereology.

Leśniewski’s work deserves much more attention than it has received. The first quality of his work is that it is purely nominalistic. There is no explicit semantics in his systems: they are pure calculus. The second quality is that they are absolutely constructivistic. Apart from the primitive symbols, all terms are introduced by an explicit definition. For these reasons, Protothetics and Ontology are ideal candidates as universal programming languages.

In this paper, I provide a more general version of these systems by adding a lambda-abstractor. I introduce two new special functors and provide algebra of individuals. I then show that a canonical name for any functor can be provided through a recursive definition. Roughly, the procedure is a generalization of Post technique of normal form in propositional calculus but based on the algebra of individual rather then on the Boolean algebra.

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