Topical Referents for Individuals and Possibilities

In a classic paper Partee (1973) noted detailed referential and anaphoric parallels between tenses and pronouns in English. Since then these parallels have been successfully analyzed in terms of domain-neutral principles of discourse reference and anaphora — most fully developed in Kamp & Reyle (1993) — which apply uniformly to referents of various logical types. These include ordinary individuals (the kings and cabbages sort) as well as times, events and states. The referential parallel has long been known to extend even further, to the modal domain — a discovery due to Kaplan (1978). More recently, the anaphoric parallel has likewise been extended. At the intuitive level, there is now consensus that individuals and possibilities are on a par for the purposes of reference and anaphora. But it remains an open question whether the formal analogue of an individual in the modal domain — in intuitive terms, a possibility — is a possible world (as in Kaplan 1978, Schlenker 1999), a class of possible worlds (Stone 1997) or a dynamic update (e.g., Frank & Kamp 1997). Orthogonal to this issue, it has also been observed that in all semantic domains some referents are more central than others, in the sense of the centering theory of Grosz et al (1995). For example, Stone & Hardt (1997) show that ‘sloppy’ ellipsis in English generalizes across all semantic domains, and that it can be uniformly analyzed as strict discourse anaphora to center-sensitive referents, with the illusion of sloppiness due to center shift. In this paper I first present crosslinguistic evidence that the parallels between individuals and possibilities are indeed pervasive. Moreover, the centering parallels are even more detailed than has so far been recognized. These parallels favor the view that a possibility — the modal analogue of an individual — is best analyzed as a class of possible worlds, as in Stone (1997). Adopting this view, I then develop a semantic representation language, which I call Logic of Change with Centered Worlds, in which the observed cross-domain parallels can be formally explicated. This logic combines theoretical insights drawn from three sources: the Logic of Change of Muskens (1995), the extension to modal anaphora due to Stone (1997), and the related Logic of Change with Centering presented in Bittner (2001).