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The proponents of Centering Theory integrated Givón’s (1983) findings in a more formal model on topicality to account for referent tracking in discourse. This theory has its staring point in the work on attention focus in discourse and was developed at the beginning of the 1980’s within the framework of artificial intelligence. Firstly formulated by Grosz, Joshi and Weinstein (1995), Centering Theory was constantly adjusted and extended, most prominently by Walker and Prince (1996), Grosz and Sidner (1986) and was experimentally validated in the works of Brennan (1995) and Gordon and Chan (1995), among others. Assuming that within a discourse attention is focused or centred, the independent notion of “center” was introduced1. The “center of attention” of a discourse segment is accounted for in terms of focus of attention, choice of referring expressions and the perceived coherence between two adjacent sentences (Walker et al. 1998: 1). This relationship mirrors the formulations presented in Givón (1981, 1983) as that between the “set of potential antecedents” and the “anaphor” and integrates both referential distance and topic continuity as measure methods for topicality. Except for few works (Passoneau 1994, Grosz et al. 1995, Walker, Joshi and Prince 1998), the main concern of Centering Theory is the local or sentence-level relation that holds between the centers of attention in a given discourse segment. In other words, Centering Theory has a predictive power on the relations that hold locally, between two adjacent sentences.

Proponents of this model suggest that speakers form referential predictions on a clause-by-clause level, in the same vain as Givón (1983). The model introduces two sets of focused discourse referents (i.e. ‘centers’): the backward-looking center and the forward-looking center. The backward-looking center (Cb) is the most prominent discourse referent in both the current and the previous utterance. In English, the Cb position is generally associated with the subject of the current utterance. Intuitively, the Cb is the discourse entity that is the center of attention of the current utterance, being psychologically the most salient discourse referent for both speaker and hearer. The Cb is the local discourse topic and is identical to the preferred center of the immediately following sentence in an ideal discourse. In order to achieve a coherent discourse, the identity of the Cb has to be determined for each utterance. The only exception is the first sentence of a discourse segment, which does not contain a Cb, as discourse-initial utterances are interpreted as context-creating devices and not context elaborating ones (see Lambrecht 1994: 129 for a similar argumentation).

The second type of center is the forward-looking center (Cf), which is a list of competing discourse referents in the current utterance that are ranked according to several factors. In classical Centering Theory, referents on the Cf list are ranked according to their syntactic position. According to this ranking, in German and English, for example, the referent in subject position is ranked higher than the referent in direct object position, which, in turn, is ranked higher than the referent in indirect object position. Thus, a referent mentioned in subject position enters the list of Cfs as the highest ranked, preferred center (Cp), which is the most expected Cb for the next utterance. Thus, the theory predicts that a referent encoded in subject position is more prone to be mentioned in the immediately following sentence by virtue of its preferential syntactic position. Different instantiations of Centering Theory propose various other factors (e.g. animacy, clausal subordination and the lexical semantics of the verb) for the ranking of centers on the Cf list. Walker et al. (1998) note that the complete set of factors influencing the ranking of Cfs has yet to be determined. The interplay between the centers of two adjacent utterances is illustrated in example (9) for two sentences, U_i and U_i+1.

(9)	Relationship between the Cf and the Cb
	Utterance Ui: Mary gave Diana a cat.
	Utterance Ui+1: She told her that…

The first sentence, U_i, introduces two human female referents, Mary and Diana and one animate referent, a cat. These three referents compete for being rementioned in the next utterance and are thus represented on the list of forward-looking centers. The referent encoded in the highest syntactic position, the subject, is the most prone to be mentioned next and is thus the Cp for the next sentence, U_i+1. Accordingly, the first pronoun in the second sentence is preferentially interpreted as referring back to the Cp, Mary, than to the second ranked referent on the Cf list, Diana.

In Centering Theory, transitions from an initial utterance U_i to a second utterance U_i+1 are categorized according to the established relations between the centers. If the backward-looking center remains the same across utterances, the model outputs continue for the transition from U_i to U_i+1. If the backward-looking center remains the same but is no longer the preferred center in U_i+1, the model outputs the transition relation retain. Finally, if a new backward-looking center is introduced in U_i+1, which is different from the old one in U_i, the model outputs a smooth or rough shift, depending on whether the Cp remains the same or not. Center continuations, or transitions between utterances in which the backward-looking center is continued, are preferred in a coherent discourse. In contrast, a shift of the backward-looking center is dispreferred.

It is important to note that one of the differences between Ariel’s (1990) Accessibility Marking Scale and Centering Theory is that the two approaches make different predictions. For example, while Ariel’s model predicts, on the basis of four textual factors (i.e. distance, unity, competition and saliency), the type of referring expression that will be used for a particular referent, Centering Theory is primarily concerned with the referent that is most likely to be mentioned next as the most important or topical constituent. In other words, Centering Theory is more interested in the factors that contribute to the likelihood of subsequent mention of a referent. The type of referring expression used to pick up a referent in the subsequent discourse is considered a by-product of a referent’s expectancy to be mentioned next. The theory predicts that a Cb must be realized as a pronoun if any member of the Cf is realized as a pronoun, or if the Cb in the previous clause is realized as the present Cb as well.

Centering Theory has been widely adopted in the fields of computational linguistics and psycholinguistics; however, various aspects still need to be integrated in the existing framework. One challenge for Centering Theory is to model the referential management within longer discourse segments, departing from local, sentence-to-sentence relations. Furthermore, Centering Theory could be extended to include a discussion about lower-situated entities on the Cf-list, which make good candidates for Cbs two or three sentences after being introduced in the discourse. Table 2.3 presents an example taken from the multi-sentence-continuation study on pe-marking in Romanian (see Chapter 5), which highlights important aspects, which cannot be accounted for by the current version of Centering Theory. Several observations can be made on the basis of the discourse segment presented in Table 2.3. In the first utterance (U₁) a referent is introduced in subject position, which becomes the Cb in the next sentence (U₂). As predicted by Centering Theory, the Cb is realized by means of a reduced type or referring expression in U₂. As Romanian is a pro-drop language, the re-mentioned Cb in subject position is realized by the least explicit type of referring expression in that language, a null pronoun. In U₂, a second referent (i.e. ‘PE a boy’) is introduced in a non-prominent position (i.e. as an indefinite noun phrase realized as a direct object, which is preceded by the optionally occurring differential object marker pe) and this referent becomes the second-ranked referent on the Cf list in U₂. The story continues with the already established Cb, Graur, mentioned in subject position in U₃ and ranked highest on the Cf list of U₃. Additionally, a new referent is added in U₃ (i.e. ‘PE a lady’) as the second-ranked referent, which was introduced as a pe-marked definite noun phrase in direct object position. The interesting observation is that the lower-ranked Cf pe a boy becomes the Cb in U₄ and is picked up by means of a null pronoun in the same sentence. The shift of the Cb between U₃ and U₄ is formally indicated by the proximal demonstrative this ('acest'). The third referent, which was initially introduced by a pe-marked definite noun phrase in direct object position, becomes the Cb in U₈.

Utterances	Cb	Cf list with preferred center	Sentence Transitions
U1 U2	Graur s-a hotărât să meargă în oraş. ‘Graur decided to go downtown.’	n.a.	[Graur]	n.a.
Pe drum l-a văzut pe un băiat intrând într-un magazin. ‘On the way, he saw pe a boy entering a store.’	[Graur]	[Graur, boy]	(CONTINUE)
U3	Graur o recunoscu imediat pe doamna de lânga acest băiat suspect. ‘Graur immediately recognized the lady next to this suspect boy.’	[Graur]	[Graur, lady, boy]	CONTINUE
U4	Purta o şapca Hello Kitty, ‘He was wearing a Hello Kitty cap’	[boy]	[boy]	SMOOTH SHIFT
U5	iar în mâna dreapta avea o geantă diplomat. ‘and in his right hand he had a suitcase.’	[boy]	[boy]	CONTINUE
U6	Tiptil, tiptil, s-a furişat dupa băiat în magazin. ‘Slowly, slowly, he followed the boy into the store.’	[Graur]	[Graur, boy]	SMOOTH SHIFT
U7	Graur se temea să nu fie observant de cineva. ‘Graur feared someone could see him.’	[Graur]	[Graur]	CONTINUE
U8	Femeia presimți ceva. ‘The woman suspected something.’	[lady]	[lady]	SMOOTH SHIFT

Table 2.3:

Sample continuation story from the experimental study on pe-marking in Romanian (Chapter 5)

The main observation from this example is that particular referents seem to have the potential to shift the topic with a certain delay. The relations and restrictions between utterances of a discourse segment are analysed in Centering Theory in a linear way, such that each utterance necessarily connects with the one immediately preceding it, although in a given context, the discourse relations are not always between adjacent utterances. As it will become more evident in the discussions from Chapters 3-5, certain referents are more prone to shift the topic (i.e. become Cbs in Centering Theory terms) two or three sentences after being introduced in the discourse. The example in Table 2.3 argues in favour of an adjustment of the ranking criteria of the Cfs in such a way as to encompass referents that have the potential to become Cbs as the discourse progresses. Several other studies showed that under certain conditions, other referents might outrank subjects in salience or accessibility. Smyth and Chambers (1996), for example, found out that repeated-name penalties arise for subject and object referents alike. Moreover, they showed that reading times for pronoun referents are faster when they refer back to a parallel object referent than to a non-parallel subject or indirect object referent. Thus, besides the grammatical roles of the referent, syntactic parallelism between Cp and Cb seems to play a role as well (Smyth 1994). In Section 2.3.3 we discuss other factors that impact the ranking of referents on the Cf list.

The review presented so far focused on approaches to language processing concerned with the online-tracking of referents. This includes questions about what referents of a sentence speakers (re-)use in the subsequent discourse and what type of referring expression they choose for this referent. The majority of studies presented so far have adopted a backward-looking perspective, focusing on the relation between an anaphoric expression and its antecedent and the different factors that determine the use of a particular anaphoric expression at a particular point in the discourse (Givón 1983, Gernsbacher 1989, Arnold 1998, Ariel 2001, Chiriacescu 2011a, Kehler et al., 2008 Kaiser 2011). It is generally assumed that each anaphoric expression is linked to one referent in the immediately preceding discourse that is selected from a list of discourse referents that are ranked with respect to their accessibility. The general assumption is that there is an inverse relation between the explicitness (in terms of descriptive, lexical, and phonological material) of the anaphoric expression and the accessibility of its antecedent expression. In other words, a less explicit type of referring expression of the anaphor often correlates with an accessible referent; the opposite holds for more explicit types of referring expressions (e.g. definite noun phrases), which correspond to less-accessible referents. In English, pronouns have been associated with highly accessible referents and most studies to date have investigated the factors that correspond to such referents. By adopting a backward-looking perspective, most studies have investigated the characteristics of the anaphor that license the use of a pronoun in discourse. Most investigations are moreover local, as the accessibility of a referent was mainly computed between two adjacent sentences. In what follows, I will briefly discuss some of the more important factors that have been shown to contribute to the accessibility of referents in terms of subsequent pronominalization and next mention.