DEFAULTS IN UPDATE SEMANTICS

DEFAULTS IN UPDATE SEMANTICS

1996 | FRANK VELTMAN
This paper aims to introduce the framework of update semantics and analyze default reasoning within it. The traditional definition of logical validity is based on truth conditions, but update semantics defines meaning dynamically, as the change in information states caused by a sentence. An update system is defined by a language L, a set of information states Σ, and a function [] that assigns operations to sentences. The resulting triple ⟨L, Σ, []⟩ is called an update system. The meaning of a sentence is an operation on information states, and acceptance is defined as when a sentence does not change the information state. Update semantics allows for the analysis of dynamic phenomena, such as default reasoning. However, not all phenomena can be captured by additive update systems, which assume that information is added to existing states. Additive systems require that σ[φ] is defined for every state σ, and that the operation + has properties of a join operation. If σ[φ] is undefined, then the system is not additive. Presupposition is an example of a phenomenon that can be naturally explained within update semantics. A sentence φ presupposes ψ if, for every state σ, σ[φ] is defined only if σ ⊨ ψ. This definition is only applicable in systems where σ[φ] may be undefined. Another necessary condition for additivity is idempotence: for every state σ and sentence φ, σ[φ] ⊢ φ. This paper highlights the importance of update semantics in analyzing dynamic linguistic phenomena, particularly default reasoning, and shows how it differs from traditional static approaches.This paper aims to introduce the framework of update semantics and analyze default reasoning within it. The traditional definition of logical validity is based on truth conditions, but update semantics defines meaning dynamically, as the change in information states caused by a sentence. An update system is defined by a language L, a set of information states Σ, and a function [] that assigns operations to sentences. The resulting triple ⟨L, Σ, []⟩ is called an update system. The meaning of a sentence is an operation on information states, and acceptance is defined as when a sentence does not change the information state. Update semantics allows for the analysis of dynamic phenomena, such as default reasoning. However, not all phenomena can be captured by additive update systems, which assume that information is added to existing states. Additive systems require that σ[φ] is defined for every state σ, and that the operation + has properties of a join operation. If σ[φ] is undefined, then the system is not additive. Presupposition is an example of a phenomenon that can be naturally explained within update semantics. A sentence φ presupposes ψ if, for every state σ, σ[φ] is defined only if σ ⊨ ψ. This definition is only applicable in systems where σ[φ] may be undefined. Another necessary condition for additivity is idempotence: for every state σ and sentence φ, σ[φ] ⊢ φ. This paper highlights the importance of update semantics in analyzing dynamic linguistic phenomena, particularly default reasoning, and shows how it differs from traditional static approaches.
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[slides and audio] Defaults in update semantics