Natural language is often criticised, e.g., by advocates of formal methods, for its informality, ambiguity, and lack of explicit structure1. But who would deny the value of talking, listening, reading, and writing? Clearly natural language is a very useful and powerful way to communicate, and it is obviously far more widely used than any formal alternative. Nobody tells stories in first order logic or in Java.
There is also growing evidence that natural language is far more structured than most people realize, and in particular, that discourse structure (i.e., the structure of multi sentence units) carries a great deal of important information. For example, work by Abbott  and others shows that the nouns and verbs used in stating requirements can provide important clues to an object oriented design for computer based systems. In particular, the nouns give clues about classes and their attributes, and the verbs give clues about methods. Syntactic structure can also indicate relationships of inheritance and clustering. However, one cannot expect to find mechanical algorithms that will do such analyses with consistent reliability, in part because of the enormous importance of context for determining meaning.
One of the most powerful types of discourse in natural language is story telling, i.e., narrative. The most careful structural analyses of narrative have been done by William Labov , and refined by Charlotte Linde , within the tradition called socio-linguistics; this research is based on an enormous amount of empirical data, and is far more precise than alternative traditions such as literary theory and post-structuralism. The data is taken from recordings of oral narratives of personal experience; these are naturally occurring stories with a live audience, typically of friends or relatives, where the narrator is an agent in the story. It can be argued that such narratives are the most basic, since it is likely that they have been used by humans for tens of thousands of years, well before humans invented writing, wrote novels, or made movies.
We now look at some details of this research. According to the principle of accountability, a member of some group who tells an informal story must establish to the audience the relevance of the actions reported. The most typical way to accomplish accountability is to include specific evaluative material within the body of the story that relates the narrative material to shared social values. We can briefly summarize the discourse structure of narratives of personal experience as follows:
It may be surprising that values are an integral part of the internal structure of stories, rather than being confined to the optional summary "moral" at the end. But in fact, naturally occurring stories embody evaluative material in many ways. Values in narrative may appear relatively explicitly, as justifications for the narrator's choice of what to tell, or a character's choice of what to do; they may also appear in a more implicit way, in certain patterns, such as repetition, unusual or strong lexical items, and unusual syntax. Evaluative material plays the crucial role of connecting the events reported to the values shared by the social group within which the story is being told. Note that the narrative presupposition, that the order of narrative clauses is the order of the events that they report, unless some trouble is taken to indicate otherwise, is a convention, and not a necessity; for example, Becker  shows that in Balinese narratives, if no special care is taken then the events reported in a sequence of narrative clauses are taken as occurring simultaneously rather than sequentially (a computer scientist might say that the default connective for a narrative sequence in English is sequential composition, ";", whereas in Balinese it is parallel composition, "||").
To better explain and illustrate these ideas, let us analyse a simple story. The nursery rhyme given below is strictly speaking not a naturally occurring spontaneous story, nor a narrative of personal experience, in the sense of Labov . However, it is often read, or repeated from memory with minor variations, to children in natural social settings, and thus an analysis of the values in it should tell us something about what our society teaches its children. The analysis will be somewhat sketchy, omitting many details of argument, because to include them all would be very tedious2. Here is the text:
Jack and Jill went up the hill to fetch a pail of water; Jack fell down and broke his crown, and Jill came tumbling after. Up Jack got, and home did trot, as fast as he could caper, Jill put him to bed and plastered his head with vinegar and brown paper.(The second verse is one among several variations; see Opie  for this and other background information.) The first line of the first verse can be seen as both an abbreviated orientation section, and as an initial narrative clause, since the characters, Jack and Jill, and the place, "the hill," are introduced, as well as an action, "went up," which is in the narrative past tense. The second line is an evaluative clause, giving a reason for the action of the first clause. The third and fourth lines give further narrative clauses (there are two in the third line). The narrative presupposition gives the order of the events reported: first Jack and Jill went up the hill, then Jack fell down, then he broke his crown, and then Jill came tumbling after.
Since we know that ordering is significant in English narratives, it is interesting to notice that Jack always comes before Jill. As far as the semantics is concerned, this ordering would not matter in the first line, but because it is part of a general pattern, we can consider it to be an evaluative feature of the narrative. Note the delicacy, and not quite water-tight quality of this argument; this is entirely typical, since rigorous proofs are impossible in this area. It is not so much a matter of proving something, or extracting the truth, as it is of uncovering some resonance within the text. Any such analysis is contingent, local and open; moreover, it is best done in a group, so that the analyst is accountable to other analysts, in which case the analysis itself becomes emergent and embodied at that level. Nonetheless, any such interpretation can be considered to be some part of the meaning of the text; of course, each interpretation will seem more cogent to some analysts and groups than others, and some may seem dubious to most. This is consistent with Peirce's triadic relational notion of meaning.
What can we conclude about this story? I think we may conclude that water is important to this (somewhat mythical) culture, and that males are more important than females in it. This need not be the end of the analysis: one can get some further results by using the causal presupposition, which says that, other things being equal, given clauses in the order A, B we may assume that A causes B. (For example, "You touch that, you gonna die.") I encourage readers to follow up this remark as an exercise in further analysis of the nursery rhyme text.
Analyses like those sketched above can be useful in a wide variety of personal and business situations. For example, we may want to know what are the implicit values in a threatening document that we have received from a colleague, or we may want a deeper insight into what motivates our boss, or a friend. Similar analyses are also important in a wide variety of media studies, since it is narrative that gives many art works their power.
Research by Goguen and Linde ,  has shown that plans, explanations, directions, and other everyday types of discourse have a high level structure that relates directly to their social and semantic domains. These structures are called discourse types, and they can be described very precisely by grammars, in much the same way as is traditional in linguistics for structure at the sentential level. The structure of narrative sketched above is a good example, in fact, the original example that inspired the others. Just to give a taste, the default presupposition for clauses in the reasoning discourse type is logical consequence, in the direction indicated by the English word "because."
For a more precise (perhaps too precise) formal analysis, see The Structure of Narrative.
 Russell Abbott. Program design by informal English descriptions. Communications of the Association for Computing Machinery, 26(11):882-894, 1983.
 Alton L. Becker. Text-building, epistemology, and aesthetics in Javanese shadow theatre. In Alton L. Becker and A.Yengoyan, editors, The Imagination of Reality: Essays on Southeast Asian Symbolic Systems. Ablex, 1979.
 Joseph Goguen. Requirements Engineering as the Reconciliation of Social and Technical Issues. In Requirements Engineering: Social and Technical Issues, edited with Marina Jirotka, Academic Press, 1994, pages 165-199.
 Joseph Goguen, James Weiner, and Charlotte Linde. Reasoning and natural explanation. International Journal of Man-Machine Studies 19:521-559, 1983.
 William Labov. The transformation of experience in narrative syntax. In Language in the Inner City, pages 354-396. University of Pennsylvania, 1972.
 Charlotte Linde. Life Stories: the Creation of Coherence. Oxford, 1993.
 Charlotte Linde and Joseph Goguen. Structure of planning discourse. Journal of Social and Biological Structures, 1:219-251, 1978.
 Iona Opie and Peter Opie. The Oxford Dictionary of Nursery Rhymes. Oxford, 1951.
* Paragraphs 2 through 9 were extracted from  and then edited. The rest of this essay is new; it is aimed at computer scientists, rather than linguists or any kind of social scientist.
1. Ambiguity and informality can actually be advantagous features of natural language. For example, they can facilitate the gradual evolution of requirements for complex systems, without forcing too early a resolution of conflicts and ambiguities that are inherent in the initial situation; it is important not to prejudge the many tradeoffs that will have to be explored later on, such as cost versus almost everything else, including speed and functionality . Also, natural language can permit the resolution of conflicts through the careful construction of deliberate ambiguities; for example, this is rather common in large government financed projects, as well as in diplomacy. One current example is the proposal to proclaim Jerusalem to be under the sovereignty of God, rather than that of either Israel or the Palestinian Authority.
2. Some further details can be found in .