Dynamic 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.

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. Intersective update: Let [\![\varphi]\!] be the proposition denoted by \varphi . Then \varphi is intersective if and only if for any C , we have that C[\varphi] = C \cap [\![\varphi]\!] Intersective update was proposed by Robert Stalnaker in 1978 as a way of formalizing the speech act of assertion. In Stalnaker's original system, a context (or context set) is defined as a set of possible worlds representing the information in the common ground of a conversation. For instance, if C = \{w,v,u\} this represents a scenario where the information agreed upon by all participants in the conversation indicates that the actual world must be either w , v , or u . If [\![\varphi]\!] = \{w,v\} , then updating C with \varphi would return a new context C[\varphi] = \{w,v\} . Thus, an assertion of \varphi would be understood as an attempt to rule out the possibility that the actual world is u . From a formal perspective, intersective update can be taken as a recipe for lifting one's preferred static semantics to dynamic semantics. For instance, if we take classical propositional semantics as our starting point, this recipe delivers the following intersective update semantics. Intersective update semantics based on classical propositional logic: C[P] = \{w \in C \mid w(P) = 1 \} C[\neg \varphi] = C - C[\varphi] C[\varphi \land \psi] = C[\varphi] \cap C[\psi] C[\varphi \lor \psi] = C[\varphi] \cup C[\psi] The notion of intersectivity can be decomposed into the two properties known as eliminativity and distributivity. Eliminativity says that an update can only ever remove worlds from the context—it can't add them. Distributivity says that updating C with \varphi is equivalent to updating each singleton subset of C with \varphi and then pooling the results. Eliminativity: \varphi is eliminative iff C[\varphi] \subseteq C for all contexts C Distributivity: \varphi is distributive iff C[\varphi] = \bigcup\{ \{w\}[\varphi] \mid w \in C\} Intersectivity amounts to the conjunction of these two properties, as proven by Johan van Benthem. These sentences cannot be analysed as logical contradictions within purely intersective frameworks such as the relational semantics for modal logic. The Epistemic Contradiction Principle only holds on the class of relational frames such that Rwv \Rightarrow (w=v) . However, such frames also validate an entailment from \Diamond \varphi to \varphi . Thus, accounting for the infelicity of epistemic contradictions within a classical semantics for modals would bring along the unwelcome prediction that "It might be raining" entails "It is raining". Update Semantics skirts this problem by providing a nonintersective denotation for modals. When given such a denotation, the formula \Diamond \neg \varphi can update input contexts differently depending on whether they already contain the information that \varphi provides. The most widely adopted semantic entry for modals in update semantics is the test semantics proposed by Frank Veltman. The test semantics for modals: C[\Diamond \varphi ] = \begin{cases} C & \text{if } C[\varphi] \neq \varnothing \\ \varnothing & \text{otherwise} \end{cases} On this semantics, \Diamond \varphi tests whether the input context could be updated with \varphi 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 \varphi will always output a context that fails the test imposed by \Diamond \neg \varphi . ==Notes== ==External links== Dynamic Semantics, Stanford Encyclopedia of Philosophy Dynamic Semantics Notes, Daniel Rothschild Dynamic Semantics and Pragmatic Alternatives, ESSLLI 2017 Course Notes

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