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''Donkey sentences'' are sentences that contain a ''donkey pronoun'' or ''donkey anaphora''. Such pronouns or anaphoric expressions may also be called ''d-type'' or ''e-type pronoun'', depending on theoretical approach to [[interpretation (logic)|interpretation]].

A donkey pronoun is a [[pronoun]] that is [[Bound variable pronoun|bound]] in [[semantics]] but not [[syntax]].<ref>
Emar Maier describes donkey pronouns as "bound but not [[c-command]]ed" in a [[Linguist List]] [http://www.linguistlist.org/issues/17/17-3393.html review] of Paul D. Elbourne's ''Situations and Individuals'' (MIT Press, 2006).</ref><ref>Barker and Shan define a donkey pronoun as
"a pronoun that lies outside the restrictor of a [[Quantification (linguistics)|quantifier]] or the [[Antecedent (grammar)|antecedent]] of a [[Conditional clause|conditional]], yet [[covariance|covaries]] with some [[Quantification (linguistics)|quantification]]al element inside it, usually an [[indefinite]]." Chris Barker and Chung-chieh Shan, [http://www.semanticsarchive.net/Archive/2Y2ODI4Z/barker-shan-donkeys.pdf 'Donkey Anaphora is Simply Binding'], colloquium presentation, Frankfurt, 2007.</ref> Some writers prefer the term "donkey anaphora", since it is the [[Reference|referential]] aspects and [[discourse]] or [[syntax|syntactic]] context that are of interest to researchers (see [[anaphora (linguistics)|anaphora]]).

The following sentences are examples of donkey sentences.
*Every farmer who owns a donkey beats it. — [[Peter Geach]] (1962), ''Reference and Generality''
* Every police officer who arrested a murderer insulted him.

Such sentences are significant because they represent a class of well-formed natural-language sentences that defy straightforward attempts to generate their [[formal language]] equivalents. The difficulty is with understanding how English speakers [[parsing|parse]] the scope of quantification in such sentences.<ref>David Lewis describes this as his motivation for considering the issue in the introduction to ''Papers in Philosophical Logic'', a collection of reprints of his articles. "There was no satisfactory way to assign relative scopes to quantifier phrases." ([[Cambridge University Press|CUP]], 1998: 2.)</ref>

Peter Geach's original donkey sentence was a [[counterexample]] to [[Richard Montague]]'s proposal for a generalized formal representation of [[Quantification (linguistics)|quantification]] in [[natural language]]. The example was reused by [[David Kellogg Lewis|David Lewis]] (1975), [[Gareth Evans (philosopher)|Gareth Evans]] (1977) and many others, and is still quoted in recent publications.

==Features==
Features of the sentence, "Every farmer who owns a donkey beats it," require careful consideration for adequate description (though reading "each" in place of "every" does simplify the formal analysis). The donkey pronoun in this case is the word ''it''. The [[indefinite article]] 'a' is normally understood as an [[existential quantifier]], but the most natural reading of the donkey sentence requires it to be understood as a nested [[universal quantifier]].

There is nothing wrong with donkey sentences: they are grammatically correct, they are well-formed, their syntax is regular. They are also logically meaningful, they have well-defined [[truth conditions]], and their semantics are unambiguous. However, it is difficult to explain how donkey sentences produce their semantic results, and how those results generalize consistently with all other language use. If such an analysis were successful, it might allow a computer program to accurately translate natural language forms into [[logical form]].<ref>Alistair Knott, [http://www.cs.otago.ac.nz/staffpriv/alik/papers/cirevision.pdf 'An Algorithmic Framework for Specifying the Semantics of Discourse Relations',] ''Computational Intelligence'' '''16''' (2000).</ref> The question is, how are natural language users, apparently effortlessly, agreeing on the meaning of sentences like these?

There may be several equivalent ways of describing this process. In fact, [[Hans Kamp]] (1981) and [[Irene Heim]] (1982) independently proposed very similar accounts in different terminology, which they called [[discourse representation theory]] (DRT) and [[file change semantics]] (FCS) respectively.

In 2007, Adrian Brasoveanu published studies of donkey pronoun analogs in [[Hindi]], and analysis of complex and [[modal logic|modal]] versions of donkey pronouns in English.

==Discourse representation theory==
Donkey sentences became a major force in advancing [[semantics|semantic]] research in the 1980s, with the introduction of [[discourse representation theory]] (DRT). During that time, an effort was made to settle the inconsistencies which arose from the attempts to translate donkey sentences into [[first-order logic]]. 

Donkey sentences present the following problem, when represented in first-order logic: The systematic translation of every existential expression in the sentence into existential quantifiers produces an incorrect representation of the sentence, since it leaves a free occurrence of the variable y in BEAT(''x''.''y''):

: <math>  \forall x\, (\text{FARMER} (x) \and \exists y \,( \text{DONKEY}(y) \and \text{OWNS}(x,y)) \rightarrow \text{BEAT}(x,y)) </math>

Trying to extend the scope of existential quantifier also does not solve the problem:

: <math>  \forall x \,\exists y\, (\text{FARMER} (x) \and \text{DONKEY}(y) \and \text{OWNS}(x,y) \rightarrow \text{BEAT}(x,y)) </math>

In this case, the logical translation fails to give correct truth conditions to donkey sentences:  Imagine a situation where there is a farmer owning a donkey and a pig, and not beating any of them. The formula will be true in that situation, because for each farmer we need to find at least one object that either is not a donkey owned by this farmer, or is beaten by the farmer. Hence, if this object denotes the pig, the sentence will be true in that situation.

A correct translation into first-order logic for the donkey sentence seems to be:

: <math>  \forall x\, \forall y\, (\text{FARMER} (x) \and \text{DONKEY}(y) \and \text{OWNS}(x,y) \rightarrow \text{BEAT}(x,y)) </math>

Unfortunately, this translation leads to a serious problem of inconsistency. One possible interpretation, for example, might be that every farmer that owns any donkeys beats every donkey. Clearly this is rarely the intentional meaning. Indefinites must sometimes be interpreted as existential quantifiers, and other times as universal quantifiers, without any apparent regularity. 

The solution that [[Discourse representation theory|DRT]] provides for the donkey sentence problem can be roughly outlined as follows: The common semantic function of non-anaphoric [[noun phrase]]s is the introduction of a new [[discourse referent]], which is in turn available for the binding of anaphoric expressions. No quantifiers are introduced into the representation, thus overcoming the scope problem that the logical translations had. 
==In Lojban==
The normal donkey sentence can be translated as
{{mu|ro da poi te cange cu darxi ro xasli poi da ponse ke'a}}
There are some more difficult variations of donkey sentences, however.

Other versions:
{{mu|ro da poi te cange gi'e ponse su'o xasli zo'u da darxi de}}

==See also==
*[[Epsilon calculus]]
*[[Generic antecedent]]
*[[Lambda calculus]]
*[[Montague grammar]]
*[[Singular they]]

==Notes==
{{Reflist}}

==References==
* Kamp, H. and Reyle, U. 1993. From Discourse to Logic. Kluwer, Dordrecht.
* Kadmon, N. 2001. Formal Pragmatics: Semantics, Pragmatics, Presupposition, and Focus. Oxford: Blackwell Publishers. 

==Further reading==
{{Refbegin|colwidth=30em}}
*Abbott, Barbara. [http://www.springerlink.com/content/h341505636560743/ 'Donkey Demonstratives'.] ''[[Natural Language Semantics]]'' '''10''' (2002): 285–298.
*Barker, Chris. 'Individuation and Quantification'. ''[[Linguistic Inquiry]]'' '''30''' (1999): 683–691.
*Barker, Chris. 'Presuppositions for Proportional Quantifiers'. ''[[Natural Language Semantics]]'' '''4''' (1996): 237–259.
*Brasoveanu, Adrian. ''Structured Nominal and Modal Reference''. [[Rutgers University]] PhD [[dissertation]], 2007.
*Burgess, John P. '''E Pluribus Unum'': Plural Logic and Set Theory', ''Philosophia Mathematica'' '''12''' (2004): 193–221.
*Cheng, Lisa LS and C-T James Huang. [http://www.springerlink.com/content/gh791025x82x6766/ 'Two Types of Donkey Sentences'.] ''[[Natural Language Semantics]]'' '''4''' (1996): 121–163.
*Cohen, Ariel. ''Think Generic!'' Stanford, California: [[Center for the Study of Language and Information|CSLI Publications]], 1999.
*Conway, L. and S. Crain. 'Donkey Anaphora in Child Grammar'. In ''Proceedings of the North East Linguistics Society'' (NELS) '''25'''. [[University of Massachusetts Amherst]], 1995.
*[[Gareth Evans (philosopher)|Evans, Gareth]]. 'Pronouns'. ''[[Linguistic Inquiry]]'' '''11''' (1980): 337–362.
*[[Peter Geach|Geach Peter]]. ''Reference and Generality: An Examination of Some Medieval and Modern Theories''. Ithaca, New York: [[Cornell University Press]], 1962.
*Geurts, Bart. ''Presuppositions and Pronouns''. Oxford: [[Elsevier]], 1999.
*Harman, Gilbert. 'Anaphoric Pronouns as Bound Variables: Syntax or Semantics?' ''[[Language (journal)|Language]]'' '''52''' (1976): 78–81.
*[[Irene Heim|Heim, Irene]]. [http://www.springerlink.com/content/u533354617l67818/ 'E-Type Pronouns and Donkey Anaphora'.] ''[http://www.springer.com/linguistics/semantics/journal/10988 Linguistics and Philosophy]'' '''13''' (1990): 137–177.
*[[Irene Heim|Heim, Irene]]. ''The Semantics of Definite and Indefinite Noun Phrases''. [[University of Massachusetts Amherst]] PhD [[dissertation]], 1982.
*Just, MA. 'Comprehending Quantified Sentences: The Relation between Sentencepicture and Semantic Memory Verification'. ''[[Cognitive Psychology]]'' '''6''' (1974): 216–236.
*Just, MA and PA Carpenter. 'Comprehension of Negation with Quantification'. ''Journal of Verbal Learning and Verbal Behavior'' '''10''' (1971): 244–253.
*Kanazawa, Makoto. [http://www.springerlink.com/content/h1145h642pr81r5r/ 'Singular Donkey Pronouns Are Semantically Singular'.] ''[http://www.springer.com/linguistics/semantics/journal/10988 Linguistics and Philosophy]'' '''24''' (2001): 383–403.
*Kanazawa, Makoto. 'Weak vs. Strong Readings of Donkey Sentences and Monotonicity Inference in a Dynamic Setting'. ''[http://www.springer.com/linguistics/semantics/journal/10988 Linguistics and Philosophy]'' '''17''' (1994): 109–158.
*[[Manfred Krifka|Krifka, Manfred]]. 'Pragmatic Strengthening in Plural Predications and Donkey Sentences'. In ''Proceedings from Semantics and Linguistic Theory'' (SALT) '''6'''. Ithaca, New York: [[Cornell University]], 1996. Pages 136–153.
*Lappin, Shalom. 'An Intensional Parametric Semantics for Vague Quantifiers'. ''[http://www.springer.com/linguistics/semantics/journal/10988 Linguistics and Philosophy]'' '''23''' (2000): 599–620.
*Lappin, Shalom Lappin and Nissim Francez. 'E-type Pronouns, i-Sums, and Donkey Anaphora'. ''[http://www.springer.com/linguistics/semantics/journal/10988 Linguistics and Philosophy]'' '''17''' (1994): 391–428. 
*Lappin, Shalom. 'Donkey Pronouns Unbound'. ''[[Theoretical Linguistics (journal)|Theoretical Linguistics]]'' '''15''' (1989): 263–286.
*[[David Kellogg Lewis|Lewis, David]]. ''Parts of Classes'', Oxford: [[Blackwell Publishing]], 1991.
*[[David Kellogg Lewis|Lewis, David]]. 'General Semantics'. ''Synthese'' '''22''' (1970): 18–27.
*[[Barbara Partee|Partee, Barbara H]]. 'Opacity, Coreference, and Pronouns'. ''Synthese'' '''21''' (1970): 359–385.
*[[Richard Montague|Montague, Richard]]. 'Universal Grammar'. ''Theoria'' '''26''' (1970): 373–398.
*[[Stephen Neale|Neale, Stephen]]. ''Descriptions''. Cambridge: [[MIT Press]], 1990.
*[[Stephen Neale|Neale, Stephen]]. 'Descriptive Pronouns and Donkey Anaphora'. ''[[Journal of Philosophy]]'' '''87''' (1990): 113-150.
*[[Willard Van Orman Quine|Quine, Willard Van Orman]]. ''[[Word and Object]]''. Cambridge, Massachusetts: [[MIT Press]], 1970.
*Rooij, Robert van. [http://jos.oxfordjournals.org/cgi/content/abstract/23/4/383 'Free Choice Counterfactual Donkeys'.] ''[[Journal of Semantics]]'' '''23''' (2006): 383–402.
*Yoon, Y-E. ''Weak and Strong Interpretations of Quantifiers and Definite NPs in English and Korean''. [[University of Texas at Austin]] PhD [[dissertation]], 1994.
* Kamp, Hans. and Reyle, U. 1993. From Discourse to Logic. Kluwer, Dordrecht.
* Kadmon, N. 2001. Formal Pragmatics: Semantics, Pragmatics, Presupposition, and Focus. Oxford: Blackwell Publishers.
{{Refend}}

==External links==
* [http://www.ims.uni-stuttgart.de/~hans/hpl-drt.pdf The Handbook of Philosophical Logic]
* [http://homepages.cwi.nl/~jve/papers/05/drt/drt.pdf Discourse Representation Theory]
* [http://www.alta.asn.au/events/altss_w2003_proc/public_lectures/knott/knott.html Introduction to Discourse Representation Theory]
* [http://plato.stanford.edu/entries/discourse-representation-theory/ SEP Entry]
* [http://www.csi.uottawa.ca/~kbarker/teach/5386/donkey.html Archive of CSI 5386 Donkey Sentence Discussion]
*Barker, Chris. [http://books.google.com.au/books?id=ZIqGqn98OOMC&pg=PA303&lpg=PA303&dq=%22a+presuppositional+account+of+proportional+ambiguity%22&source=web&ots=0CAAK5sHZ8&sig=2DamB3jw3NRit9ebKBHXd7S2kwE&hl=en 'A Presuppositional Account of Proportional Ambiguity'.] In ''Proceedings of Semantic and Linguistic Theory'' (SALT) '''3'''. Ithaca, New York: [[Cornell University]], 1993. Pages 1–18.
*Brasoveanu, Adrian. [http://semanticsarchive.net/Archive/2FlYTZjO/donkey_pluralities_aug2007.html 'Donkey Pluralities: Plural Information States vs. Non-Atomic Individuals'.] In ''Proceedings of Sinn und Bedeutung'' '''11'''. Edited by E. Puig-Waldmüller. Barcelona: [[Pompeu Fabra University]], 2007. Pages 106–120.
*[[Gareth Evans (philosopher)|Evans, Gareth]]. 'Pronouns, Quantifiers, and Relative Clauses (I)'. ''Canadian Journal of Philosophy'' '''7''' (1977): 467–536.
*Geurts, Bart. [http://www.ru.nl/ncs/bart/papers/donkeys.pdf 'Donkey Business'.] ''[http://www.springer.com/linguistics/semantics/journal/10988 Linguistics and Philosophy]'' '''25''' (2002): 129–156.
*Huang, C-T James. [http://books.google.com.au/books?id=EHuiqtSwgv8C&pg=PR6&lpg=PR6&dq=logical+form+james+huang+university&source=web&ots=ApZYb_mjwz&sig=Y_HCVE4B51WqrsZkpPjXDKFTcOY&hl=en 'Logical Form'.] Chapter 3 in ''Government and Binding Theory and the Minimalist Program: Principles and Parameters in Syntactic Theory'' edited by Gert Webelhuth. Oxford and Cambridge: [[Blackwell Publishing]], 1995. Pages 127–177.
*[[Hans Kamp|Kamp, Hans]]. [http://books.google.com.au/books?hl=en&lr=&id=clYhtZ3RdTIC&oi=fnd&pg=PA1&dq=hans+kamp&ots=VpW0df39DM&sig=t_IQKL__NvUhJay3INoH7Bjdjlc 'A Theory of Truth and Semantic Representation'.] In J. Groenendijk and others (eds.). ''Formal Methods in the Study of Language''. Amsterdam: Mathematics Center, 1981.
*Kitagawa, Yoshihishi. [http://books.google.com.au/books?id=GA1Mr2xx5rUC&pg=PA54&lpg=PA54&dq=%22donkey+pronoun%22&source=web&ots=C19MpQ4-44&sig=o5tUkGAsG1pfOK6aRTZVKs28Z5s&hl=en 'Copying Variables'.] Chapter 2 in ''Functional Structure(s), Form and Interpretation: Perspectives from East Asian Languages''. Edited by Yen-hui Audrey Li and others. [[Routledge]], 2003. Pages 28–64.
*[[David Kellogg Lewis|Lewis, David]]. [http://books.google.com.au/books?id=Iqx80pAilKcC&pg=PA97&dq=%22adverbs+of+quantification%22+%22cast+of+characters%22&sig=XUVYIRzLEjd-nPAi_2wq-J1DcdA 'Adverbs of Quantification'.] In ''Formal Semantics of Natural Language''. Edited by Edward L Keenan. Cambridge: [[Cambridge University Press]], 1975. Pages 3–15.
*[[Richard Montague|Montague, Richard]]. [http://semantics.uchicago.edu/kennedy/classes/s08/semantics2/montague73.pdf 'The Proper Treatment of Quantification in Ordinary English'.] In KJJ Hintikka and others (eds). ''Proceedings of the 1970 Stanford Workshop on Grammar and Semantics''. Dordrecht: Reidel, 1973. Pages 212–242.

[[Category:Pronouns]]
[[Category:Quantification]]
[[Category:Semantics]]