Type-logical Anaphora

We present a type-logical account of anaphora. The principal means is the introduction of type-constructors for`secondary wrap': wrap around the second of two split points in a discontinuous string. We illustrate in terms of preevaluated proof nets, proof nets in which lexico-syntactic interaction is computed in a lexical compilation rather than at the stage of derivation. We suggest that the account ooers an explanation of the delay of principle B eeect in the child acquisition of anaphora. Chomsky (1981) proposes Principles A, B and C governing anaphoric relations. Roughly speaking, Principle A states that a reeexive or reciprocal pronoun must be bound by a local c-commanding antecedent, Principle B states that a personal pronoun must not be bound by a local c-commanding antecedent, and Principle C states that a lexical noun phrase cannot be bound to a c-commanding antecedent. Thèdelay of Principle B eeect' is the term given to the phenomenon whereby in acquisition there seems to be non-complience with principle B. Jacobson (1999) discusses the combinatorics of categorial anaphora largely from the point of view of combinatory categorial grammar (Steedman 2000). She takes a step in the type-logical direction by introducing what is essentially a new binary type-constructor (notated as a superrx), however Principle B is not accommodated. Anaphora receives a related type-logical rendering in JJ ager (1998). Although JJ ager presents a sequent calculus enjoying Cut-elimination for his system, it is not especially elegant, invoking as it does an arbitrary atom in the right inference rule. More importantly, it is not clear how to present the system in natural deduction, perhaps the most transparent format for linguistic purposes, or in terms of proof nets, probably the best basis for computational concerns. Like the proposal of Jacobson, it does not take into account Principle B. In this paper we present a type-logical account of anaphora taking into account Principle B. The account rests on a generalisation of`discontinuity calculus' in which wrap is admitted around the second of two split points in a discontinuous string. We illustrate in terms of natural deduction and in terms of proof nets, and we suggest that delay of Principle B can be correlated to memory load in incremental construction of proof nets.