Dynamic semantics is a framework in logic and natural language semantics which 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 systems , 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. FOL Translation of Donkey Sentence : : To explain these peculiarities, Heim and Kamp proposed that natural language indefinites are special in that they introduce a new discourse referent which remains available outside the syntactic scope of the operator that introduced it. To cash this idea out, they proposed their respective formal systems which capture donkey anaphora because they validate Egli's Theorem and its corollary. Egli's Theorem : Egli's Corolary : Update semantics is a framework within dynamic semantics which was developed by Frank Veltman. In Update Semantics , each formula is mapped to a function which takes and returns a discourse context. Thus, if is a context, then is the context one gets by updating with . Systems of Update Semantics vary both in how they define a context and in the semantic entries they assign to formulas. The simplest update systems are intersective ones, which simply lift static systems into the dynamic framework. However, Update Semantics includes systems more expressive than what can be defined in the static framework. In particular, it allows information sensitive semantic entries, in which the information contributed by updating with some formula can depend on the information already present in the context. This property of Update Semantics has led to its widespread application to presuppositions, modals, and conditionals. Intersective update: Let be the proposition denoted by . Then is intersective iff for any , we have that These sentences have been argued to be bona fide logical contradictions, unlike superficially similar examples such as Moore sentences  which can be given a pragmatic explanation. On this semantics, tests whether the input context could be updated with without getting trivialized, i.e. without returning the empty set. If the input context passes the test, it remains unchanged. If it fails the test, the update trivializes the context by returning the empty set. This semantics can handle epistemic contradictions because no matter the input context, updating with will always output a context which fails the test imposed by .For a complete derivation of the Epistemic Contradiction Principle within Update Semantics, see for instance Goldstein (2016), p. 13. This derivation crucially depends on a particular definition of entailment, as well as an intersective semantic entry for and a treatment of as updating consecutively with the conjuncts in their linear order.
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. FOL translation of donkey sentence : : To explain these peculiarities, Heim and Kamp proposed that natural language indefinites are special in that they introduce a new discourse referent that remains available outside the syntactic scope of the operator that introduced it. To cash this idea out, they proposed their respective formal systems that capture donkey anaphora because they validate Egli's theorem and its corollary. Egli's theorem : Egli's corollary : Update semantics is a framework within dynamic semantics that was developed by Frank Veltman. In update semantics , each formula is mapped to a function that takes and returns a discourse context. Thus, if is a context, then is the context one gets by updating with . Systems of update semantics vary both in how they define a context and in the semantic entries they assign to formulas. The simplest update systems are intersective ones, which simply lift static systems into the dynamic framework. However, update semantics includes systems more expressive than what can be defined in the static framework. In particular, it allows information sensitive semantic entries, in which the information contributed by updating with some formula can depend on the information already present in the context. This property of update semantics has led to its widespread application to presuppositions, modals, and conditionals. Intersective update: Let be the proposition denoted by . Then is intersective if and only if for any , we have that These sentences have been argued to be bona fide logical contradictions, unlike superficially similar examples such as Moore sentences , which can be given a pragmatic explanation. On this semantics, tests whether the input context could be updated with without getting trivialized, i.e. without returning the empty set. If the input context passes the test, it remains unchanged. If it fails the test, the update trivializes the context by returning the empty set. This semantics can handle epistemic contradictions because no matter the input context, updating with will always output a context that fails the test imposed by .For a complete derivation of the Epistemic Contradiction Principle within Update Semantics, see for instance Goldstein (2016), p. 13. This derivation crucially depends on a particular definition of entailment, as well as an intersective semantic entry for and a treatment of as updating consecutively with the conjuncts in their linear order.
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Translation of Donkey Sentence
translation of donkey sentence
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Theorem
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Update Semantics
update semantics
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Update Semantics
update semantics
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Update Semantics
update semantics
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update semantics
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if and only if
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