A Situation Semantics for Binding out of DP

In this paper I follow a suggestion in Bach and Partee ( 1980) to analyze the bound pronoun him in sentences like every boy 's mother likes him and some person from every city likes it as paycheck pronouns (here: her son and his city, respectively). I demonstrate how such an ap­ proach affords an elegant treatment of weak cross-over. I then show that a direct implementation of this idea yields incorrect truth conditions . A refined implementation using quantification over minimal situations along the lines of Heim ( 1 990) is proposed, which can handle the problematic cases and captures the cross-over facts . 1. A Reinhartian Account of Pronoun Binding and Cross-Over Tanya Reinhart, in Reinhart ( 1 983) and other works, has presented what I take to be one of the most elegant characterizations of the Weak Cross-Over (WCO) generalization: ( 1 ) Reinhart's Generalization: Pronoun binding can only take place from a c-commanding A-position. The crucial qualification here is ' from an A-position' , which excludes binding from a position derived by wh-movement or quantifier raising. In the following, I will refer to this generalization as the a-command requirement on pronoun binding (where a-command = c-command from an A-position) . For the purpose of the discussion, I will implement this generalization in the following way: We introduce a binding operator f3n , which can be optionally adjoined at LF. This operator signals that the DP immediately c-commanding it binds any free occurrence of a pronoun indexed n within its c-command domain: (2) a. pronoun binding (optional) : D� where n is an index, and DP occupies an A-position b. [f3n XP]W,g = AX . [ [Xp]w,g (pronn-tx] (x ) ] I Given the (fairly standard) interpretation of the binding operator (essentially Sag ( 1 976) , s de­ rived VP rule) and the explicit stipulation that it can only be adjoined next to an A-position we derive Reinhart's a-command requirement ( 1 ) . Almost, that is, for we need to ensure that no other mechanism can bind a pronoun from an A­ position, the most obvious candidate for that other mechanism being the rule that interprets operator­ trace dependencies. For the sake of concreteness I will do this by formally distinguishing a trace binding operator pn (mnemonic for 'movement' ) : (3) a. trace binding (obligatory) : D0p =} LF � Jl:'XP where n is a movement index b. [Pn XP]W,g = Ax . [XP]W,g [tn-tx] © 2001 by Daniel Btiring R. Hastings , B. Jackson and Z. Zvolenszky (eds) , SALT XI 56-75, Ithaca, NY: Cornell University. A SITUATION SEMANTICS FOR BINDING OUT OF DP 57 Note that crucially, the assignment function 9 has a sorted domain: pronouns versus traces ; that way it is possible that g(tn) =J g(pronn ) for a given integer n . The standard WCO contrast between, say, (4a) and (b) is thus captured via the full LFs given below: (4) a. Wh02 does his2 mother like t2 ? b. Wh02 t2 likes his2 mother? lik�P his2 mother (4a) , despite the coindexing, does not yield a bound interpretation for the pronoun his2 , because /-12 binds traces only; his2 is interpreted as a free variable. For his2 in (4a) to be bound, a {32 operator would have to be inserted; but adjunction of (32 to C is not permitted, since SpecC is an A.-position. In contrast to that, (4b) has his2 semantically dependent on who, because the trace of who binds it via the adjoined {32 . This adjunction is licit, since the trace occupies an A-position (if you believe that who in (4b) hasn ' t moved at all , the analysis gets even simpler; I just wanted to illustrate how a moved item can bind via its trace position in general) . To put the gist of this treatment a s a slogan: A.-dependencies and pronoun-binding dependencies are strictly distinct. This is diametrically opposed to treatments like in Heim and Kratzer ( 1 998) :ch.5 , in which pronoun binding is taken as a side effect of A.-trace binding. It is similar in spirit to treatments such as Jacobson ( 1 999), where pronoun binding is a semantic operation on predicates . Maybe there is a more principled reason why binding from an A.-position cannot bind pronouns, namely that the traces of A.-movement are of a semantic type other than (e) , so that no binding of an individual variable can occur as a ' side effect' of A.-trace binding (as has been suggested recently in Ruys (2000)) . This would avoid the stipulated restriction on {3-adjunction to A-positions. I will not speculate on this further, but everything that follows is compatible with such a refinement. It bears mentioning that the implementation of WCO made here is extremely local . In particular, no reference to the potential bindee and its configuration relative to the binder is made; in fact no reference to chains or indices is made at all , which resonates well with the idea endorsed in Categorial Grammar and more recently certain versions of the Principles & Parameters Theory that the internal structure of constituents, once they have been constructed, is opaque to further grammatical operations . 2. Embedded Quantifier Binding Both parts of Reinhart' s generalization are challenged by data like the following, much discussed in the literature cited here and elsewhere, which I will refer to as embedded quantifier binding (EQB) (here and henceforth, italics mark referential dependencies) :