ZoĆ© Christoff edited section_BDPs_on_logically_interdependent__.tex  almost 8 years ago

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Fix an opinion profile $\O$, an influence profile $\G$, and a set of constraints $\C$. Consider the stream $\O^0, \O^1, \ldots, \O^n, \ldots$ of opinion profiles recursively defined as follows:  \begin{itemize}%[noitemsep]  \item Base: $\O_0 := \O$  \item Step: for all $i \in \N$, $p\in \Atoms$, $\O_i^{n+1}(p) $O_i^{n+1}(p)  := \left\{  \begin{array}{ll}  \O^{n}_{R_p(i)}(p) O^{n}_{R_p(i)}(p)  & \mbox{if } \bigwedge_{p \in \Atoms} \O^{n}_{R_p(i)}(p) O^{n}_{R_p(i)}(p)  \wedge \bigwedge_{\varphi \in \C} \mbox{ is consistent} \\ \O_i^{n}(p) O_i^{n}(p)  & \mbox{otherwise} \end{array}  \right.  $.