Dynamic semantics
framework in logic and natural language semantics
Dynamic semantics is a framework in logic and natural language semantics that treats the meaning of a sentence as its potential to update a context. In static semantics, knowing the meaning of a sentence amounts to knowing when it is true; in dynamic semantics, knowing the meaning of a sentence means knowing "the change it brings about in the information state of anyone who accepts the news conveyed by it." In dynamic semantics, sentences are mapped to functions called context change potentials, which take an input context and return an output context. Dynamic semantics was originally developed by Irene Heim and Hans Kamp in 1981 to model anaphora, but has since been applied widely to phenomena including presupposition, plurals, questions, discourse relations, and modality.
Dynamics of anaphora
The first systems of dynamic semantics were the closely related File Change Semantics and discourse representation theory, developed simultaneously and independently by Irene Heim and Hans Kamp. These systems were intended to capture donkey anaphora, which resists an elegant compositional treatment in classic approaches to semantics such as Montague grammar. Donkey anaphora is exemplified by the infamous donkey sentences, first noticed by the medieval logician Walter Burley and brought to modern attention by Peter Geach.
Donkey sentence (relative clause): Every farmer who owns a donkey beats it.
Donkey sentence (conditional): If a farmer owns a donkey, he beats it.
To capture the empirically observed truth conditions of such sentences in first order logic, one would need to translate the indefinite noun phrase "a donkey" as a universal quantifier scoping over the variable corresponding to the pronoun "it".
FOL translation of donkey sentence: :
∀
x
∀
y
(
(
farmer
(
x
)
∧
donkey
(
y
)
∧
own
(
x
,
y
)
)
→
beat
(
x
,
y
)
)
{\displaystyle \forall x\forall y(\,({\text{farmer}}(x)\land {\text{donkey}}(y)\land {\text{own}}(x,y))\rightarrow {\text{beat}}(x,y)\,)}
While this translation captures (or approximates) the truth conditions of the natural language sentences, its relationship to the syntactic form of the sentence is puzzling in two ways.
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