## Dynamic Logic (1984)

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Venue: | Handbook of Philosophical Logic |

Citations: | 899 - 7 self |

### BibTeX

@INPROCEEDINGS{Harel84dynamiclogic,

author = {David Harel and Dexter Kozen and Jerzy Tiuryn},

title = {Dynamic Logic},

booktitle = {Handbook of Philosophical Logic},

year = {1984},

pages = {497--604},

publisher = {MIT Press}

}

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### Abstract

ed to be true under the valuation u iff there exists an a 2 N such that the formula x = y is true under the valuation u[x=a], where u[x=a] agrees with u everywhere except x, on which it takes the value a. This definition involves a metalogical operation that produces u[x=a] from u for all possible values a 2 N. This operation becomes explicit in DL in the form of the program x := ?, called a nondeterministic or wildcard assignment. This is a rather unconventional program, since it is not effective; however, it is quite useful as a descriptive tool. A more conventional way to obtain a square root of y, if it exists, would be the program x := 0 ; while x < y do x := x + 1: (1) In DL, such programs are first-class objects on a par with formulas, complete with a collection of operators for forming compound programs inductively from a basis of primitive programs. To discuss the effect of the execution of a program on the truth of a formula ', DL uses a modal construct <>', which