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Discourse Relations and Defeasible Knowledge`

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Discourse Relations and Defeasible Knowledge` DISCOURSE RELATIONS AND DEFEASIBLE KNOWLEDGE* Alex Lascarides t Nicholas Asher Human Communication Research Centre Center for Cognitive Science University of Edinburgh University of Texas 2 Buccleuch Place, Edinburgh, EH8 9LW Austin, Texas 78712 Scotland USA alex@uk, ac. ed. cogsc£ asher@sygmund, cgs. utexas, edu Abstract of the event described in a, i.e. fl's event is part of the preparatory phase of a's: 2 This paper presents a formal account of the temporal interpretation of text. The distinct nat- (2) The council built the bridge. The architect ural interpretations of texts with similar syntax drew up the plans. are explained in terms of defeasible rules charac- terising causal laws and Gricean-style pragmatic Explanation(a, fl): For example the event de- maxims. Intuitively compelling patterns of defea,- scribed in clause fl caused the event described in sible entailment that are supported by the logic clause a: in which the theory is expressed are shown to un- derly temporal interpretation. (3) Max fell. John pushed him. Background(a, fl): For example the state de- The Problem scribed in fl is the 'backdrop' or circumstances under which the event in a occurred (so the event and state temporally overlap): The temporal interpretation of text involves an account of how the events described are related (4) Max opened the door. The room was pitch to each other. These relations follow from the dark. discourse relations that are central to temporal import. 1 Some of these are listed below, where Result(a, fl): The event described in a caused the clause a appears in the text before fl: the event or state described in fl: Narration(a,fl): The event described in fl is a consequence of (but not necessarily caused by) (5) Max switched off the light. The room was tile event described in a: pitch dark. (1) Max stood up. John greeted him. We assume that more than one discourse re- Elaboration(a,~): The event described in /? lation can hold between two sentences; the sick- contributes to the occurrence of the culmination ness in (6) describes the circumstances when Max took the aspirin (hence the sentences are related *This paper is greatly influenced by work reported in by Background) and also explains why he took (Lascarides & Oberlander, 1991). We would llke to thank Hans Kamp, Michael Morreau and .Ion Oberlander for the aspirin (hence the sentences are related by their significant contributions to the content of this pa- Explanation as well). per. All mistakes are solely our responsibility. t The support of the Science and Engineering Research (6) Max took an aspirin. He was sick. Council through project number GR/G22077 is gratefully acknowledged. HCRC is supported by the Economic and Social Research Council. The sentences in texts (1) and (3) and in (4) 1Extensive classifications of discourse relations are of- and (5) have similar syntax, and therefore similar fered in (Polanyi, 1985), (Scha & Polanyi, 1988) and (Thompson & Mann, 1987). 2We assume Moens and Steedman's (1988) tripartite structure of events, where an event consists of a prepara- tory phase, a culmination and a consequent phase. 55 logical forms. They indicate, therefore, that the eludes a causal 'law' gained from perception and constraints on the use of the above discourse re- experience that relates falling and pushing: 3 lations cannot rely solely on the logical forms of • Causal Law 3 the sentences concerned. Connected events el where x falls and e2 No theory at present is able to explain the dis- where y pushes z are normally such that e2 tinct temporal structures of all the above texts. causes el. Webber (1988) observes that Kamp & Rohrer (1983), Partee (1984), Hinrichs (1986) and Dowty There is no similar law for standing up and greet- (1986) don't account for the backwards movement ing. The above law is a defeasible law. Our claim of time in (2) and (3). Webber (1988) can account is that it forms the basis for the distinction be- for the backwards movement of time in (2), but tween (1) and (3), and that defeasible reasoning her theory is unable to predict that mismatching underlies the temporal interpretation of text. the descriptive order of events and their temporal First consider text (1). Intuitively, if there order is allowed in some cases (e.g. (2) and (3)) is no temporM information at all gained from but not in others (e.g. (1), which would be mis- WK or syntactic markers (apart from the simple leading if the situation being described were one past tense which is the only temporal 'expres- where the greeting happened before Max stood sion' we consider here), then the descriptive order up). of events provides the only vital clue as to their Our aim is to characterise the circumstances temporal order, and one assumes that descriptive under which each of the above discourse relations order matches temporal order. This principle is hold, and to explain why texts can invoke dif- a re-statement of Grice's (1975) maxim of Man- ferent temporal relations in spite of their similar ner, where it is suggested that text should be or- syntax. derly, and it is also motivated by the fact that Dahlgren (1988) represents the difference be- the author typically describes events in the or- tween (1) and (3) in terms of probabilistic laws der in which the protagonist perceives them (cf. describing world knowledge (WK) and linguistic Dowty (1986)). This maxim of interpretation can knowledge (LK). Our approach to the problem be captured by the following two laws: is generally sympathetic to hers. But Dahlgren's account lacks an underlying theory of inference. • Narration Furthermore, it's not clear how a logical conse- Unless there's information to the contrary, quence relation could be defined upon Dahlgren's clauses a and j3 that are discourse-related representation scheme because the probabilistic are such that Narration(a, ~) holds. laws that need to interact in certain specific ways • Axiom for Narration are not logically related. Unlike Dahlgren (1988), If Narration(a, fl) holds, and a and fi de- we will supply an inference regime that drives the scribe the events el and e2 respectively, then interpretation of text. el occurs before e2. The properties required of an inference mech- anism for inferring the causal structure underly- Narration is defensible and the Axiom for Narra- ing text is discussed in (Lascarides & Oberlander, tion is indefeasible. The idea that Gricean-style 1991). The work presented here builds on this in pragmatic maxims should be represented as de- two ways; first by supplying the required notion of feasible rules is suggested in (Joshi, Webber & inference, and second by accounting for discourse Weischedel (1984)). structure as well as temporal structure. The above rules can be defined in MASH--a logic for defensible reasoning described in (Asher & Morrean, 1991). We will demonstrate shortly Temporal Relations and that an intuitively compelling pattern of defensi- Defeasible Reasoning ble inference can then underly the interpretation of (1). Let us consider texts (1) and (3) on an intu- MASH supplies a modal semantics for a lan- itive level. There is a difference in the relation guage with a default or generic quantifier, and a that typically holds between the events being de- 3The causal law's index corresponds to the index of the scribed. Intuitively, world knowledge (WK) in- text for which it is relevant. 56 dynamic partial semantics of belief states is built • Narration on top of this modal semantics to c~pture intu- (or, ~) > Narration(c~,~3) itively compelling patterns of non-monotonic tea- soning. We use a propositional version of MASH • Axiom on Narration here. Defaults are represented as ¢ > ¢ (read r~ (Na,','atio,~(~, ~) --, me(~) ~ me(Z)) as "¢ then ¢, unless there is information to the We assume that in interpreting text the reader contrary"). The monotonic component of the the- believes all LK and WK (and therefore believes ory defines a notion of validity ~ that supports Narration and its axiom), the laws of logic, and axioms such as ~ [:3(¢ --* ¢) ~ ((X > ¢) --~ the sentences in the text. The sentences in (1) are (X > ¢)). The dynamic belief theory supplies the represented in a DnT-type framework as follows:6 nonmonotonic component, and the corresponding nonmonotonic validity, ~, describes what reason- able entailments follow from the agent's beliefs. (7) [e1,~1][~1 <now, hold(el,Q),s~andup(rn, el)] supports (at least) the following patterns of common sense reasoning: (8) [~, t~][t2 < now, hold(~2, t2),gr~t(j, m, ~2)] Defensible Modus Ponens ¢>¢,¢ ~ ¢ In words, (7) invokes two discourse referents el and ~1 (which behave like deictic expressions), but not ¢>¢,¢,-~¢ ~ ¢ where el is an event of Max standing up, tl is e.g. Birds fly, Tweety is a bird ~ Tweety flies, a point of time earlier than now and et occurs at but not: Birds fly, Tweety is a bird that doesn't it. (8) is similar save that the event e2 describes fly ~ Tweety flies. John greeting Max. (7) and (8) place no condi- Penguin Principle tions on the relative temporal order between et ¢ >¢,¢>C¢>-~,¢ ~-~i and e2. These are derived at a higher level of anal- but not: ¢ > ¢,¢ :> (,¢ > -,(,¢ ~ ( ysis than sentential semantics by using defensible e.g. Penguins are birds, Birds fly, Penguins don't reasoning. fly, Tweety is a Penguin ~ Tweety doesn't fly, Suppose that the reader also believes that the and does not ~ Tweety flies. clauses in text (1) are related by some discourse Nixon Diamond relation, as they must be for the text to be coher- not (¢ > ¢,I > "¢,¢,( ~ ¢ (or --¢)) ent. Then the reader's beliefs also include (7, 8). e.g.
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