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Foundations for calculational logic. (English) Zbl 0929.03037
Broy, Manfred (ed.) et al., Mathematical methods in program development. Proceedings of the NATO ASI, Marktoberdorf, Germany, July 30–August 11, 1996. Berlin: Springer. NATO ASI Ser., Ser. F, Comput. Syst. Sci. 158, 83-126 (1997).
Summary: For the past 20 years, researchers in the formal development of algorithms – programming methodology – have been developing a calculational approach to logic, in which a calculational format using substitution of equals for equals, weakening, and strengthening are the major tools. This work is giving us a perspective on logic that is different from that of others: for us, logic is a tool instead of just an area of academic study. These lectures summarize our present understanding of this calculational logic. Covered are: propositional logic, predicate logic, treating undefined terms, the use of weakening or strengthening steps, a useful theorem on monotonicity, metatheorem Witness, and the everywhere operator. Some interesting proofs are developed.
For the entire collection see [Zbl 0874.00040].

MSC:
03B70 Logic in computer science
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