The notion of problem, intuitionism and partiality
Keywordsabstract procedures, constructions, effective procedures, concepts, partiality
AbstractProblems are defined as abstract procedures. An explication of procedures as used in Transparent Intensional Logic (TIL) and called constructions is presented and the subclass of constructions called concepts is defined. Concepts as closed constructions modulo α- and η-conversion can be associated with meaningful expressions of a natural or professional language in harmony with Church’s conception. Thus every meaningful expression expresses a concept. Since every problem can be unambiguously determined by a concept we can state that every problem is a concept and every concept can be viewed as a problem.Kolmogorov’s idea of a connection between problems and Heyting’s calculus is examined and the non-classical features of the latter are shown to be compatible with realistic logic using partial functions.
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