By Samuel Moy

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Stiazhkin] [1964] Становление идей математической логики , Москва, Наука. [1969] History of mathematical logic from Leibniz to Peano,, Cambridge, Mass. / Lon don, MIT Press. ). Thiel, C. [1987] Scrutinizing an alleged dichotomy in the history of mathematical logic, V. L. Rabinovich, editor; Abstracts, LM PS ’87, (Moscow, Acad. Sci. USSR), vol. 3, §13, 254-255. , et al. [1987] Bericht iiber das Projekt “Sozialgeschichte der Logik”, preprint, 37pp. van der Waerden, B. L. [1985] A history of algebra, from Al-Khwarizmi to Em my Noether, Springer-Verlag, Berlin / Heidelberg / New York / Tokyo.

Wells, editor and translator, North-Holland, Amsterdam / London. Mautner, F. I. [19461 An extension of Klein’s Erlanqer program: loqic as invariant-theory, Amer. J. Math. 68, 345-384. Mitchell, О. H. [1883] On a new algebra of logic, in C. S. Peirce [1883a], 22-106. Monk, J. D. [1986] The contributions of Alfred Tarski to algebraic logic, J. Symbolic Logic 51 6, 899-906. Monk, J. D. , North-Holland, Amsterdam / NY / Lon don / Oxford / Tokyo. N IN E T EEN T H C E N T U R Y ROOTS OF A L G E B R A IC LO G IC 29 Peacock, G.

Again, we deal only with the case of a while-loop. 9 E xam ple. Consider the loop construct while -ife do В od. In Figure 2 the control flow graph and the relations Z , e, and a of the corresponding program, a say, are shown. Assume a postcondition q and let t E (BSxS)VxV be a vector such that t C Z t y a q y ZL. , predicates on states. Using the concrete forms of the relations Z , e and a as given in Figure 2, the inclusion t C Z t y a q y Z L is equivalent to the following three conditions: (у V b) A (z V b) C x Bx A BL С у q C z.