The goal of this chapter is demonstrate one particular use of abduction in the processing of natural language discourse. DICE (Discourse In Commonsense Entailment) can be used to model both interpretation and generation. For interpretation, it uses defeasible deduction to determine the discourse structures and event structures underlying multisentential texts. For generation, it uses abduction to build up specifications of texts from underlying event structures. Thus, abduction is the primary

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... chanism of generation, and has a smaller role to play in interpretation. To demonstrate how the approach works in generation and interpretation, we introduce two exemplary problems, which involve brevity and accommodation respectively. We then outline a formal model of implicature, and indicate how it is recruited for interpretation by deduction and generation by abduction. We show how brief but accurate discourses can be generated under this model, and then turn to a possible role for abduction in changing the context of interpretation. Finally, we mention one of the differences between this approach, and weighted abduction in Hobbs, Edwards (1988) and Hobbs, Stickel, Appelt, and Martin (1990) . 1 2 Laconic discourses and total eclipses 1.2 Two exemplary problems The problem of laconic discourse It is a commonplace that brevity is the soul of wit. Natural language generation systems have, on occasion, striven for it. In developing the approach to discourse structuring in DICE, our primary focus has been on domains where temporal and causal relations between eventualities have to be communicated briefly but accurately. That is to say, we have been investigating methods whereby temporal information can be left unstated but inferrable. We call the texts which possess this putatively desirable property laconic discourses. Let's consider in turn three questions. First, are laconic discourses desirable? If they are, do they introduce any risks? And finally, what basic mechanism do we need if we are to deal with the risk effectively? Are laconic discourses a good thing? Contrast (1) and (2) , which are supposed to describe the same course of events. (1) Max entered the office. Then, John greeted him with a smile. After that, he showed Max to the seat in front of his desk. He then offered Max a cup of coffee. (2) Max entered the office. John greeted him with a smile. He showed Max to the seat in front of his desk and offered him a cup of coffee. (2) seems somewhat more direct than the relatively verbose (1), and is perhaps preferable as a result. Part of the difference is that (1) makes all the temporal relations explicit; there is, for example, no doubt as to the temporal relation between Max's entry and John's greeting. (2), by contrast, leaves this temporal relation implicit. The entry is mentioned first, and the greeting mentioned second, but no explicit ordering is mentioned. In the current genre, the order of mention generally correlates with the order of events, and we would take the ordering of these events to be implicitly conveyed by text (2), and explicitly by (1). It is tempting to generalise from such cases, and suggest that brevity is invariably preferable to verbosity. However, brevity has its risks, as we can see when we consider (3). (3) Jon switched off the heating. Judy came in and said the room was too hot. What does this mean? On the one hand, knowledge of the correlation between order of mention and order of events would lead a hearer/reader to believe that the switching off preceded Judy's statement. On the other hand, general world knowledge about heating mechanisms and cooperative behaviour might well lead to believe that the switching off was a consequence of Judy's statement. Thus, the knowledge exploits in interpretation will have a crucial effect on whether (3) is taken to be a simple narrative, or a causal explanation. The problem is clear: if a speaker/writer ¡ wishes to exploit brevity, she runs the risk of misleading , unless she is sure what knowledge will bring to bear. We may conclude, then, that leaving temporal progression unmarked is natural but risky. Two exemplary problems 3 What mechanism does ¡ require if she is to avoid risky utterances like (3) while still generating desirable realizations such as (2) ? We assume that one way for ¡ to test for misleading utterances is for her to reason about the implicatures the hearer will infer, given the discourse context and likely background knowledge. We conclude that we therefore require a formal model of implicature to inform a speaker or writer's generation process. The problem of total eclipses It has been observed in the literature (Harkness 1985; Hamann 1989 ) that some discourses set up an expectation of a contingent link between two eventualities, and that there are differing ways of responding to utterances which frustrate that expectation. In particular, Hamann has observed that temporal connectives, such as before, after and when appear to have this effect: The [temporal clause] event not only informs of time location but has a narrative relevance in its own right . . . only some of [the many possible colocating events] make sense in context . . . total unconnectedness . . . leads to a purely temporal reading, or to some profound statement about the way of the world -brought about by the interpreter's willingness to see a narrative connection (Hamann 1989, 43) On her account, (4a) and (4b) can be taken to describe the same pair of events, but (4b), by yoking the events together with an after-clause, carries an additional implicature that the leaving was contingent upon the homecoming -perhaps by being caused by it. The fact that after leads to such an expectation is involved in the explanation of the oddness of (5). 1 (4) a. John came home. Mary left. b. Mary left after John came home. (5) ? The moon eclipsed the sun after John came home. The explanation goes along the following lines. Sentences of the form A after B usually link eventualities which can cause one another, where is a clause, but not when it is an adverb. However, we also have a strong prior intuition that eclipses are not contingent on human activities. When a conflict like this arises, we either (i) derive a purely temporal reading; or (ii) derive a 'profound' reading. Following strategy (i), we would read (5) as simply locating the solar eclipse at a time after the time of the homecoming; here, the clause after John came home is functioning just as after 7pm would function. Following strategy (ii), we would read (5) as pointing out a new and 1 Hamann's original example involved the event of Jupiter's completing its orbit, and the version of this chapter delivered at the Alghero meeting used this same example. It was pointed out there, however, that the Jupiter event is somewhat spurious, there being no begin-and end-points to an elliptical orbit. We have therefore varied the example to involve an eclipse, a real (and dateable) event. 4 Laconic discourses and total eclipses surprising fact about the world; there is a human whose movements influence planetary motion. Is there an assumption of connection in after-sentences? Is Hamann's account the correct one? Even if it is not, an account which seeks to explain implicit assumptions about temporal structure ought to be able to specify what is going on in a case such as (5). We therefore conclude that we require a formal model of implicature to inform a hearer or reader's interpretation process. The formal model of implicature In recent work, we have developed DICE as a formal model of some of the implicatures relating to discourse and temporal structure (In this section, we first define more precisely the concept of laconic discourse, before introducing our representation of discourse structure. We then exemplify the varieties of knowledge which, encoded as defeasible rules, influence discourse processing in this model; these include Gricean pragmatic maxims (cf. Grice 1975), causal knowledge, and discourse contextual effects. We then indicate how the processes of interpretation and generation are logically modelled; in the former, an underlying logic uses the rules to construct discourse structures and temporal structures from NL text; in the latter, the same rules are used under a different inference regime, to construct discourse structures and NL text from temporal structures. Temporal constraints and laconic discourse First, then, let us be more precise about what makes a text laconic. We consider a set of relations between eventualities (events and states), and say that it includes the following: a causal relation, a part-whole relation, an overlap relation, and an immediate precedence relation. Since all of these except overlap are asymmetric, the set actually specifies seven possible relationships between a pair of eventualities . Three points about this set should be noted. First, causal and part-whole relations are -in some sense -more ontologically committed than the overlap and precedence relations; the former require eventualities in a way that the latter need not. Secondly, the relation of immediate precedence is taken to be a temporal precedence compatible with a causal or part-whole or whole-part relation. Finally, the bias towards relations between events distinguishes the current approach from those, such as Allen's theory (Allen 1984), which are based on relations between time intervals; one effect of taking eventualities to be basic is that we need a relatively small set of possible relations between them. Now, let us specify the notions of temporal coherence and reliability, which we first discussed in Lascarides and Oberlander (1992b): 2 2 There we also introduced the notion of temporal precision, which we do not touch upon here. Note that these clauses should be read as full definitions. Discourse structure 5 Temporal Coherence A text is temporally coherent if its reader can infer that at least one of the relations in holds between the eventualities described in the sentences. Temporal Reliability A text is temporally reliable if one of the relations in which its reader infers to hold does in fact hold between the eventualities described in the sentences. Although we have characterised reliability in terms of what actually holds, what matters is, of course, what the text's speaker/writer ¡ believes to hold -or what ¡ intends to come to believe holds. We don't here distinguish these possibilities, because we are naively assuming that a writer sets out to transfer information. This is, of course, a simplification, but it is one which is tenable in the simple cases we examine. We are now in a position to say that discourse is laconic when it is: (i) temporally reliable; (ii) temporally coherent; and (iii) not fully explicit with respect to the set . Full explicitness is only comparative, of course. For current purposes, we will say that a text is not fully explicit with respect to when an expression specifying one of the relations could be added to the text without affecting the text's reliability or coherence. Hence, we can say that (1) could result from adding expressions in this way to (2). For this reason, (2), but not (1) , is laconic. (1) Max entered the office. Then, John greeted him with a smile. After that, he showed Max to the seat in front of his desk. He then offered Max a cup of coffee. (2) Max entered the office. John greeted him with a smile. He showed Max to the seat in front of his desk and offered him a cup of coffee. Discourse structure Here we introduce three key elements of our approach to discourse structure: coherence relations combined with DRT; structural openness, and the concept of key events. Our basic approach is to follow (Asher 1992), and augment Kamp's discourse representation theory with a number of Hobbsian discourse coherence relations (Kamp 1981; Hobbs 1979; Hobbs 1985; Polanyi 1985; Mann and Thompson 1987) . The coherence relations we have examined in most detail are Narration, Explanation, Elaboration, Result and Background; these are the discourse relations most relevant to temporal structure, and the only ones we discuss below. On this representation, discourse representation structures DRSs are segmented, so that they include both traditional DRSs, and a set of discourse relations between DRSs. (6-9) provide intuitive examples of four of the relations, here (as in all the examples we discuss) holding between DRSs corresponding to simple clauses. Max stood up. John greeted him.