Dynamic syntax

Dynamic Syntax is a grammar formalism that aims to represent the real-time nature of the parsing/production process. Under the Dynamic Syntax approach, linguistic knowledge is considered to be the ability to parse spoken language in context, whilst syntax is the constraint-based way in which representations of context can be built up from words encountered in a string. While it has similarities to Combinatory categorial grammar in terms of the representations it generates, it is unique amongst grammar formalisms in that it puts word-by-word left-to-right incremental build-up of representations at the heart of the formalism, rather than incrementality only being used in external parsing algorithms.

Parts of the formalism

Dynamic Syntax constitutes several core components: semantic formulae and composition calculus (epsilon calculus within typed lambda calculus), trees (lambda application ordering), and tree building actions (lexical and computational actions).

Semantic formulae and compositional calculus

The semantic formulae which classical Dynamic Syntax generates are a combination of Epsilon calculus formulae and Lambda calculus terms (in recent years Record Types from the formalism Type Theory with Records (TTR)) have been used such as in Purver et al. (2011)).

The formulae are either simple first order logic constants such as $john'$, predicate terms such as $run'(john')$ or functions such as $\lambda x.run'(x)$. Normal lambda calculus substitution ($\beta$-reduction) means a function can be applied to a simple term to return a predicate such that $(\lambda x.run'(x))~john'=run'(john')$. The Epsilon calculus extension to first order logic is implemented in quantifiers, where $(\exists x)A(x)\ \equiv \ A(\epsilon x\ A)$, e.g. the string "a boy" may result in the formula $boy'(\epsilon x\ boy')$ being generated.

References

• Cann R, R Kempson, L Marten (2005) The dynamics of language. Oxford: Elsevier.
• Kempson R, W Meyer-Viol, D Gabbay (2001) Dynamic syntax. Oxford: Blackwell.