From Predication to Programming

Author: Lambert K.¹

Source: Minds and Machines, Volume 11, Number 2, May 2001 , pp. 257-265(9)

Publisher: Springer

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Abstract:

A free logic is one in which a singular term can fail to refer to an existent object, for example, `Vulcan' or `5/0'. This essay demonstrates the fruitfulness of a version of this non-classical logic of terms (negative free logic) by showing (1) how it can be used not only to repair a looming inconsistency in Quine's theory of predication, the most influential semantical theory in contemporary philosophical logic, but also (2) how Beeson, Farmer and Feferman, among others, use it to provide a natural foundation for partial functions in programming languages. Vis à vis (2), the question is raised whether the Beeson-Farmer-Feferman approach is adequate to the treatment of partial functions in all programming languages. Gumb and the author say ``No'', and suggest a way of handling the refractory cases by means of positive free logic. Finally, Antonelli's solution of a problem associated with the Gumb-Lambert proposal is mentioned.

Keywords: extensional; negative free logic; partial functions; positive free logic; predication; programming; proto-semantics; proof of unsoundness

Language: English

Document Type: Regular paper

Affiliations: 1: Universities of California at Irvine, and Salzburg

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