Centering: A Framework for Modeling the Local Coherence of Discourse

3 Basic center definitions

1. What are the centers of an utterance?
   The entities that link the utterance to other utterances in its discourse segment. Utterances (not sentences in isolation) have centers, and centers are semantic objects, not words or phrases.
   • Grosz et al., 1995, Centering (Computational Linguistics), §3
2. Define the forward-looking and backward-looking centers.
   Each utterance \(U_n\) has a partially ordered set of forward-looking centers \(C_f(U_n)\), ranked by prominence. Each non-initial utterance has a single backward-looking center \(C_b(U_{n+1})\): the highest-ranked element of \(C_f(U_n)\) that is realized in \(U_{n+1}\).
   • Grosz et al., 1995, Centering (Computational Linguistics), §3
3. What do “realizes” and “directly realizes” mean in centering?
   A phrase directly realizes a center \(c\) if \(c\) is its semantic interpretation; “realizes” generalizes this (e.g. \(c\) is an element of the situation described). Realization combines syntactic, semantic, discourse and intentional factors.
   • Grosz et al., 1995, Centering (Computational Linguistics), §3
4. Define the three centering transitions.

   transition	\(C_b(U_{n+1}) = C_b(U_n)\)?	\(C_b(U_{n+1})\) highest in \(C_f(U_{n+1})\)?
   continuation	yes	yes
   retaining	yes	no
   shifting	no	—

   (Later work split shifting into smooth and rough shifts.)
   • Grosz et al., 1995, Centering (Computational Linguistics), §3