Sentence examples for some additional notations from inspiring English sources

Exact(5)

We next introduce some additional notations.

To encode the result included in Proposition 4.1, we introduce some additional notations.

Combined with Table 1, Table 2 shows some additional notations, which we will use in the proposed two methods afterwards.

Before presenting necessary conditions so that (hbox {ARS}_{supseteq {L}_0, supseteq {R}_0} ({s}_0,{s}_1,{c}_0,{c}_1)) and ({AR}_{{L}_0,{R}_0} ({L}, {S})) are not empty, let us use some additional notations as follows.

Before presenting the formal algorithm, we need to introduce some additional notations and results about "dividing maps".

Similar(55)

For this, we need some additional notation.

For that, we need to introduce some additional notation.

To formally describe the first game, some additional notation is required.

To provide the formal definition of farsighted stability, we need some additional notation.

We first need some additional notation: the plausibility relation \ \preceq_i\) can be lifted to subsets of \(W\) as follows[10] Belief: \(B_i(E =\{w \mid Min_{\preceq_i}(\Pi_i(w))\subseteq E\}\) This is the usual notion of belief which satisfies the standard properties discussed above (e.g., consistency, positive and negative introspection).

In order to describe how is refined using { c1, c2,…, c n } we need some additional notation.

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