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The paper Functional Discourse Grammar by Kees Hengeveld and J. Lachlan Mackenzie describes objects in FDG using notation like the formulae below.

  1. (π v1: [head (v1)Φ]: [σ (v1)Φ])
  2. (π M1: [(A1) ... (A1+N)] (M1): Σ (M1)), where N ≥ 0

Much of the notation is described in the paper, e.g. square brackets describe non-hierarchical associations, but some such as circular brackets and colons are not. I am trying to read the paper without any linguistic background, I presume the notation would be obvious to students of linguistics.

What is the basis of this notation, and is there somewhere I can read up on it? Alternately is the paper intended to describe and define the notation from scratch?

I will try and clarify my current understanding. At a high level FDG is organised into a hierarchy of four levels, each of which consists of a number of layers. The first formula above describes the general structure of a layer, presumably as an algebraic function. Basically there are three components to each layer; an operator, a head, and a modifier. v1 is "a variable of the layer in question" - I'm not sure what this means, does the value of v1 identify which layer is being processed, or does it somehow represent some aspect of the actual language being generated?

The second formula is an instance of a particular layer, in this case the "Move" layer. This is a topmost layer of analysis within a discourse - it either "calls for a response or is itself a response". I understand the formula says that the Move layer contains a number of Discourse Acts [(A1) ... (A1+N)]. I don't know what Σ(M1) means - instinctively I read "sum of M1", but expect that doesn't fit here. I also don't know how Φ fits in, it is described as "a function ... a grammatical strategy which applies to the entire layer" but I'm not quite sure what this means.

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    Welcome to SE Linguistics! I'm not familiar with this notation and chances are many others aren't either. If you expand your question, tell us which symbols are defined in the article in what way, and what your guesses about the remaining symbols are this would greatly increase your chances of getting a useful answer. – robert Aug 31 '13 at 16:53
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    It's not at all obvious to students of linguistics. It's obvious to its authors, like all notations. But if they don't explain each term, and give lots of examples, it's useless because only they know what they mean. And only they know why they want that kind of notation. – jlawler Aug 31 '13 at 22:40
  • Sounds like the paper is defining the notation from scratch then. The trouble with reading a paper from an unfamiliar field is that you don't know what you don't know. I'm trying to understand the notation as if it was a mathematical definition of an algebraic function, instead I shouldn't attempt to read any more into it than is described in the text. – Rattle Aug 31 '13 at 23:37

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