From predication to programming
Minds and Machines 11 (2):257-265 (2001)
| 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. | |||||||||
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Similar books and articlesEdward N. Zalta (1985). Lambert, Mally, and the Principle of Independence. Grazer Philosophische Studien 25:447-459.
G. Aldo Antonelli (2000). Proto-Semantics for Positive Free Logic. Journal of Philosophical Logic 29 (3):277-294.
Carlos Viegas Damásio & Luís Moniz Pereira (2002). Hybrid Probabilistic Logic Programs as Residuated Logic Programs. Studia Logica 72 (1):113 - 138.
Karel Lambert (ed.) (1991). Philosophical Applications of Free Logic. Oxford University Press.
Raymond D. Gumb (2002). The Lazy Logic of Partial Terms. Journal of Symbolic Logic 67 (3):1065-1077.
Karel Lambert (2003). Free Logic: Selected Essays. New Yorkcambridge University Press.
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