F. Neven, M. Otto, J. Tyszkiewicz and J. Van den Bussche, Adding for-loops to first-order logic, Lecture Notes in Computer Science Vol. 1540, Springer-Verlag (1999) 58--69.

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Program schemes, arrays, Lindström quantifiers and zero-one laws - Stewart (1999)   (Correct)

.... especially dynamic logic [9, 30] One might also view many query languages from database theory as classes of program schemes, although query languages tend to operate on relations as opposed to individual elements (for example, see the while language from [1, 4, 5] and the language BQL from [4, 33]) Supported by EPSRC Grants GR K 96564 and GR M 12933. One of the most basic classes of program schemes is that obtained by allowing assignments, while instructions with quantifier free tests and non determinism. In [6] the relative expressibilities of this class of program schemes, NPS(1) ....

F. Neven, M. Otto, J. Tyszkiewicz and J. Van den Bussche, Adding for-loops to first-order logic, Lecture Notes in Computer Science Vol. 1540, Springer-Verlag (1999) 58--69.

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