Notes on a situation-free fragment for donkey anaphora Chris Barker, NYU, homepages.nyu.edu/ cb125 Introduction. These notes were produced at the

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1 Notes on a situation-free fragment for donke anaphora Chris Barker, NYU, homepages.nu.edu/ cb125 Introduction. These notes were produced at the request of Chris Kenned, for the purpose of providing something to look at in advance of a visit to Chicago on 25 Ma. M remarks will have two main goals: a critique the D-tpe approach to donke anaphora, as championed b Elbourne in his ecellent 2005 book; and a presentation of an alternative analsis based on continuations, as developed b me and m collaborator Chung-chieh han (Rutgers). These notes will epire at the end of Ma If ou want a more up-to-date version, please contact me at chris.barker@nu.edu. Feel free to ask questions in advance of the visit M comments on Elbourne will not be difficult to follow, especiall if ou are familiar with the literature on donke anaphora. Elbourne s first chapter provides a superb general discussion that introduces most of the issues and much of the data I will be evaluating. The presentation of the Barker-han fragment, however, will be more challenging to follow, since it will be unfamiliar to most people in the audience. Therefore this note will concentrate on presenting the fragment, up to the traditional donke sentence. The main competitors to the D-tpe analsis considered b Elbourne are Dnamic Predicate Logic (L), and Jacobson s variable-free framework. One of the more telling objections to the L approach involves disjustion (e.g., If a farmer owns a donke or a goat, he beats nit), and I will discuss disjunctive eamples in some detail. I will suggest that although Elbourne s criticisms of L are telling, the involve aspects of the L sstem that are not essential to a dnamic approach. Therefore Elbourne does not argue that dnamic accounts of anaphora are misguided, and in fact, I will suggest that anaphora is clearl dnamic. The fragment I will present is dnamic in the relevant sense. There is a presentation of the current fragment in a more developed paper available on the semantics archive ( Reconstruction as delaed evaluation ). For the conceptual motivation for continuations, see m 2002 Natural Language emantics paper ( Continuations and the nature of quantification ). For a discussion of the fragment presented below to binding and weak crossover, see han and Barker s 2006 paper in Linguistics and Philosoph ( Eplaining crossover and superiorit as -to-right evaluation ). 1

2 2 imple combination. We ll stack information about each epression like this: John j sntactic categor epression semantic value In the simplest case, sntactic combination reduces to standard combinator categorial grammar: John j \ = John j As usual, the categor under the slash (here, ) cancels with the categor of the argument epression; the semantics is functional application. Quantification: Quantificational epressions have an etra laer on top of their sntactic categor (likewise on top of their semantic value): everone Read the sntactic categor counterclockwise: For eample: means everone In the general case, we have: C D A/B g f...to form an. and takes scope over an... Replaces a, \ D E B right h = = everone C E A right g[h] f()

3 Below the horizontal line, combination is simple combinator categorial grammar (i.e., below the line, we have A/B combining with B to form an A; in the semantics, f combines with to form f()). Above the line is likewise a cancellation operation: here, the D on the cancels with the D on the right. emanticall, we insert the rightmost meaning element inside the brackets of the most meaning element (i.e., g combines with h to form g[h]). The fact that the meaning of the most element surrounds the meaning of the rightmost element epresses the generalization that the default order of semantic evaluation is -to-right. Tpe shifter 1 of 3: Lift: Comparing the analsis above of John with Everone reveals two distinct analses of. The simpler one is the basic leical entr, and the more comple one that participates in a quantificational sentence is derived through a standard tpe-shifter called Lift. 13 \ Lift \ In general: A epression Lift α α A epression ntacticall, Lift adds a laer with arbitrar (but matching!) sntactic categories. emanticall, it adds empt brackets, which amount to a null semantic operation (i.e., application of the identit function); we often will omit writing in the semantic values. Tpe shifter 2 of 3: : The final semantic value given above for. Everone was. In order to arrive at a traditional representation (i.e., one that is not split across two levels), we introduce the tpe-shifter :

4 4 α epression f α epression f[] It is sntacticall important that is more specific than Lift: applies onl when the two matching categories are. Appling to the analsis above for Everone gives everone everone. collapses at two-level meaning into a single level b inserting the semantic material below the line into the brackets above the line. Note that this substitution is variable-capturing! Further technical details are given in m manuscript Reconstruction as delaed evaluation (available at semanticsarchive.net). Pop quiz: Compute the sntactic categor and the semantic value of the following sentence: someone (\)/ everone =.o. e.o. how our cancellations. What is the relative scoping of the two quantifiers? Hint: proceed stepwise, following the snta (do the VP first). Pronouns: Pronouns create functional dependendies in the wa argued for b Jacobson in recent work..o. e.o. α α he λ

5 15 For instance, we have he λ \ = He λ He λ. Tpe shifter 3 of 3: Binding: Binding allows an arbitrar to control the value of a pronoun provided (onl ver roughl!) that the precedes the pronoun. α β epression f Bind α β epression f() ntacticall, the binding rule annotates the top right sntactic categor with, announcing the presence of a binder for an downstream pronouns. emanticall, it makes a cop of the value of the and makes it available to the downstream pronoun. For instance, appling Bind to everone, we have everone. Bind everone.() This gives us everone.() (\)/ his λ \ mother mom

6 6 = his mom lhm.([λ.]).([λ.[(mom ) ]]) (mom ) This lowered value reduces to.(mom ). Binding out of : everone s \ mother (\)/ him Interpretation:. (mom ). Nothing special need be said. Thus in this sstem, c-command is not required for binding. Weak crossover: his \ mother (\)/ everone = The problem with this final categor is that it cannot be lowered into a single-level analsis. The reason is that the trigger for the rule isn t met, since lowering requires the top right categor to be. The pronoun is looking ward for an antecedent, the binder is looking rightward for a pronoun to bind, and the never find each other. Hml

7 =.(far ) [.(don ) [if(owns )(beats )]] Bishop sentences work eactl the same wa (If a bishop meets a bishop, he blesses him). If a farmer owns a donke he beats it.(far ) ([λz.[.(don ) [if(owns )(beats z)]]]) If a farmer owns a donke he beats it.(far ) ([λz.]).(don ) ([λw.[if(owns )(beats w z)]]) = If a farmer owns a donke he beats it.(far ) ([λz.]).(don ) [if(owns )(beats z)] = If a farmer owns a donke he beats it.(far ) ([λz.]).(don ) ([λw.]) if(owns )(beats w z) if owns.(don ) () z beats λw. w (/)/ if 17 a farmer.(far ) () (\)/ owns a donke he λz. (\)/ beats it Donke Conditionals:

8 8 What is missing: inverse scope (inner application of Lift). cope bounding and scope islands. Binding of multiple pronouns. Generalized disjunction, eistential disjunction.