Abstract
This paper is an extension of the first-order logic for partial functions [GL 89a] [GL 89b] to a logic of programs in the framework of a first order λμ-calculus. We define a typed functional language coupled to a logic with a definedness operator and a three-boolean valued semantics with an associated consequence relation. We study the proof theory of our logic through a tableaux method and show how to obtain complete sequent calculi for reasoning about partial recursive functions.
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Gavilanes-Franco, A. (1990). A first-order logic for partial recursive functions. In: Rovan, B. (eds) Mathematical Foundations of Computer Science 1990. MFCS 1990. Lecture Notes in Computer Science, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029619
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DOI: https://doi.org/10.1007/BFb0029619
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