Donkey sentence
Encyclopedia
Donkey sentences are sentences that contain a certain type of anaphora
, such as:
Donkey sentences became a major force in advancing 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):
Trying to extend the scope of existential quantifier also does not solve the problem:
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:
Unfortunately, this translation leads to a serious problem of inconsistency. Indefinites must sometimes be interpreted as existential quantifiers, and other times as universal quantifiers, without any apparent regularity.
The solution that 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.
Anaphora (linguistics)
In linguistics, anaphora is an instance of an expression referring to another. Usually, an anaphoric expression is represented by a pro-form or some other kind of deictic--for instance, a pronoun referring to its antecedent...
, such as:
- Every farmer who owns a donkey beats it.
- Every police officer who arrested a murderer insulted him.
Donkey sentences became a major force in advancing semantic
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
research in the 1980s, with the introduction of discourse representation theory
Discourse representation theory
Discourse Representation Theory is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT-style approaches include a level of abstract mental representations within its...
(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
First-order logic
First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate 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):
Trying to extend the scope of existential quantifier also does not solve the problem:
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:
Unfortunately, this translation leads to a serious problem of inconsistency. Indefinites must sometimes be interpreted as existential quantifiers, and other times as universal quantifiers, without any apparent regularity.
The solution that DRT
Discourse representation theory
Discourse Representation Theory is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT-style approaches include a level of abstract mental representations within its...
provides for the donkey sentence problem can be roughly outlined as follows: The common semantic function of non-anaphoric noun phrase
Noun phrase
In grammar, a noun phrase, nominal phrase, or nominal group is a phrase based on a noun, pronoun, or other noun-like word optionally accompanied by modifiers such as adjectives....
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.