Algorithmic logic

Algorithmic logic is a calculus of programs which allows the expression of semantical properties of programs by appropriate logical formulas. It provides a framework that enables proving the formulas from the axioms of program constructs such as assignment, iteration and composition instructions and from the axioms of the data structures in question see Mirkowska & Salwicki (1987), Banachowski et al. (1977). $\qquad \left[{\begin{array}{l}\mathrm {Propositional\ calculus} \\or\\\mathrm {Sentential\ calculus} \end{array}}\right]\subset \left[{\begin{array}{l}\mathrm {Predicate\ calculus} \\or\\\mathrm {First\ order\ logic} \end{array}}\right]\subset \left[{\begin{array}{l}\mathrm {Calculus\ of\ programs} \\or\\{\mbox{Algorithmic logic}}\end{array}}\right]$
Algorithmic logic is one of many logics of programs. Another logic of programs is dynamic logic, see dynamic logic, Harel, Kozen & Tiuryn (2000).

Bibliography

1. [Mirkowska & Salwicki] |Mirkowska, Grażyna; Salwicki, Andrzej (1987). Algorithmic Logic. Warszawa & Boston: PWN & D. Reidel Publ. p. 372. ISBN 8301068590.
2. [Banachowski et al.] |Banachowski, Lech; Kreczmar, Antoni; Mirkowska, Grażyna; Rasiowa, Helena; Salwicki, Andrzej (1977). An introduction to Algorithmic Logic - Metamathematical Investigations of Theory of Programs. Banach Center Publications. Vol. 2. Warszawa: PWN. pp. 7–99.
3. Harel, David; Kozen, Dexter; Tiuryn, Jerzy (2000). Dynamic Logic. Cambridge Massachusetts: MIT Press. p. 459.