Deterministic dynamic logic is strictly weaker than dynamic logic

A.P. Stolboushkin, M.A. Taitslin
1983 Information and Control  
There is a language L and structures A~ and A 2 for L such that, for each closed formula F of deterministic regular dynamic logic, the formula F is valid in A ~ if and only if F is valid in A 2. There is, however, a closed formula of nondeterministic regular dynamic logic is both valid in A t and not valid in A z. Thus, nondeterminism adds to the expressive power even in the presence of quantifiers. This answers Meyer's question. Moreover, the proof here, unlike that of Berman, Halpern, and
more » ... yn (1982, in "Automata, Language, and Programming," Springer, Berlin), holds in the presence of first-order tests as well as quantifier-free tests. 48
doi:10.1016/s0019-9958(83)80024-2 fatcat:idckkuwbjvfdzh2sjvxzrsfqpi