Embodied Construction Grammar

Embodied Construction Grammar (ECG) is a representational formalism designed to support embodied models of language use and learning. It is:

embodied, in that ECG structures parameterize active simulations based on motor and perceptual schemas (Lakoff, Langacker, Talmy, Narayanan)
construction-based, in that the basic linguistic unit is a construction, or form-meaning pairing (Fillmore and Kay, Goldberg, Langacker, Croft);
constraint-based, in that constraints of all kinds (phonological, syntactic, semantic, etc.) are expressed using a unification-based grammar;
and formal(ized), in that it has been both formally defined and computationally implemented.

ECG is intended to serve multiple functions spanning several domains.

ECG is a tool for linguistic analysis: it provides formal notations with which specific analyses of linguistic phenomena can be precisely expressed (and compared).
ECG supports models of language comprehension: it is the representational substrate for a simulation-based model of language understanding.
ECG is the target for models of language learning: it is learnable by statistically based, cognitively motivated models of early language acquisition.

Introductory papers (along with a brief history)

Although the theoretical core of ideas underlying ECG are relatively stable, the precise details of its formalization have undergone several phases of development.

The foundational chapter introducing ECG was published in 2005 (though it had circulated since 2001). It contains a general overview of the formalism and its application to language understanding.
Bergen and Chang, 2005. Embodied Construction Grammar in simulation-based language understanding. [ref]
A subsequent workshop paper extended the ECG formalism to include four primitives (schemas, constructions, maps and spaces) that together capture essential ideas from cognitive linguistics.
Chang, Feldman, Porzel and Sanders, 2002. Scaling cognitive linguistics: Formalisms for language understanding. [ref]
An alternate introductory chapter from my dissertation describes a version of ECG employed in modeling language acquisition. (Note that Section 3.1 functions as a standalone short overview, and 3.1.4 provides an even more bare-bones synopsis of (one version of) the ECG notation.)
Chang 2008. Embodied Construction Grammar. Chapter 3, Constructing grammar: A computational model of the emergence of early constructions.

Subsequent and continuing work has extended the reach of ECG to a broader range of phenomena at varying degrees of linguistic analysis.

The 8th Meeting of the International Cognitive Linguistics Association (ICLC) included a theme session on Embodied Construction Grammar; topics spanned a range of languages (English, Spanish, Georgian, Spanish, Afrikaans) and construction types (discourse-based, reference, aspect, verbal morphology).
Additional notations have been added to handle probabilistic omission of arguments, a rampant phenomenon in Mandarin Chinese. See work by Eva Mok and John Bryant.
Ellen Dodge's dissertation has applied ECG to account for English verbal alternations.

An ever-shifting cadre of conspirators continues the ECG crusade; see here for the latest developments.