Towards a principled logic of anaphora

Patrick D. Elliott

Abstract. In the absence of alternatives with comparable empirical coverage, the dynamic approach to anaphora has shown an impressive longevity, having been refined and extended in the decades since Heim (1982) and Kamp’s (1981) foundational work. Like the dynamic approach to presupposition projection, the dynamic approach to anaphora can be criticized on the grounds of explanatory adequacy — dynamic semantics tailors the entry of each of the logical operators in order to derive the desired accessibility generalizations. Furthermore, dynamic semantics can be criticized on empirical grounds — it fails to account for, e.g., double negation and bathroom sentences. There has long been an intuition that a more explanatory account of anaphora is possible, using the same tools that have been developed for presupposition projection (George 2007, 2008, Schlenker 2008, 2009, a.o.). In this paper, I develop a simple, predictive logic of anaphora — Dynamic Alternative Semantics — framed as an extension of Groenendijk & Stokhof’s (1991) Dynamic Predicate Logic, using a strong Kleene trivalent semantics as the logical substrate. I argue that the resulting theory provides a much more principled treatment of the dynamics of the logical connectives, and furthermore captures data that is problematic for previous theories. I’ll also demonstrate that some of the accessibility generalizations in Groenendijk & Stokhof 1991, assumed in much subsequent work, are confounded by pragmatic factors such as ignorance inferences.

Keywords: dynamic semantics, anaphora, binding, partiality, trivalence, strong Kleene, logic, donkey anaphora

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