Intensions as Such: An Outline

Abstract

The formal expression of pro positional attitudes, especially when nested (iterated), is an important problem for AI. An interesting first-order extensional logical system for such expression has been proposed by Creary. In this system concepts (and concepts of concepts, etc.) are made explicit. The system includes concept functions, which are special functions which act on and deliver concepts. We point out a difficulty with these functions. A alternative system is proposed, in which there is a concept-forming function corresponding roughly to complex-concept formers (especially phrase the proposition that) implicit in English sentences. The resulting system has a more primitive and natural notional base than Creary's has. We avoid problems with quantification inside propositions which are objects of propositional attitudes by recasting quantified expressions into variable-free form by means of certain functions (combinators).