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
67 (3) a. Max fell. • Complex Penguin Principle b. John pushed him. o(¢ ¢),¢ > x,¢ > ¢, o(x 0), [] (¢ ¢ As we mentioned before, Causal Law 3 will pro- but not: [] (¢ --* ¢), ¢ > X, ¢ > (, vide the basis for the distinct interpretations of o (x 0), n (¢ -. ¢ x (1) and (3). The clauses in (3) must be related by a discourse relation for the text to be coherent, Therefore there is a defeasible inference that the and therefore given the meanings of the discourse pushing caused the falling from the premises, as relations, the events described must be connected required. somehow. Therefore when considering the do- The use of the discourse relation Explanation main of interpreting text, one can re-state the is characterised by the following rule: above causal law as follows:7 • Explanation Causal Law 3 (a, A > Clauses a and/3 that are discourse-related Explanation(a, jr) where a describes an event el of x falling and/3 describes an event e~ of y pushing x In words, if a and f~ are discourse-related and the are normally such that e2 causes el. event described in/3 caused the event described in a, then Explanation(a, ~) normally holds. Fur- The representation of this in MASH is: thermore, Explanation imposes a certain tempo- ral structure on the events described so that if Causal Law 3 is a causal explanation of a then fPs event doesn't (a,/3)^f.n(x, me(a))^push(y, x, me(/3)) > precede a's: ca~se(m~(~), me(a)) • Axiom on Explanation This represents a mixture of WK and linguistic [] (Explanation(a,/3) -~ -~me(a ) -~ rne(/3) ) knowledge (LK), for it asserts that given the sen- tences are discourse-related somehow, and given The antecedent to Narration is verified by the the kinds of events that are described by these reader's beliefs, and given the results of the Com- sentences, the second event described caused the plex Penguin Principle above, the antecedent to first, if things are normal. Explanation is also verified. Moreover, the an- The logical forms for (3a) and (3b) are the tecedent to Explanation entails that of Narration, same as (7) and (8), save that standup and greet and these laws conflict because of the above ax- are replaced respectively with fall and push. ioms. So there is another complex Penguin Prin- Upon interpreting (3), the reader believes all de- ciple, from which Explanation(3a, 3b) is inferred. feasible wK and LK together with (3a), (3b) and The second application of the Penguin Prin- (3a, 3b). Hence the antecedents to two defeasible ciple in the above used the results of the first, laws are satisfied: Narration and Causal Law 3. but in nonmonotonic reasoning one must be wary Moreover, the antecedent of Law 3 entails that of dividing theories into 'subtheories' in this way of Narration, and the laws conflict because of the because adding premises to nonmonotonic deduc- axiom on Narration and the axiom that causes tions does not always preserve conclusions, mak- precede effects: ing it necessary to look at the theory as a whole. (Lascarides & Asher, 1991) shows that the pred- • Causes Precede Effects icates involved in the above deduction are suffi- [] (Vele2)(cause(el, e2) ~ ~e2 -~ el) ciently independent that in MASH one can indeed divide the above into two applications of the Pen- The result is a 'Complex' Penguin Principle: it guin Principle to yield inferences from the theory is complex because the consequents of the two as a whole. Thus our intuitions about the kind of defeasible laws are not ~ and -~ff, but instead the reasoning used in analysing (3) are supported in laws conflict in virtue of the above axioms. MASH the logic. We call this double application of the supports the more complex Penguin Principle: Penguin Principle where the second application ;'This law may seem very 'specific'. It could potentially uses the results of the first the Cascaded Penguin be generalised, perhaps by re-stating el as x moving and Principle. s e2 as y applying a force to x. For the sake of brevity we ignore this generalisation. 8On a general level, MASH is designed so that the con-
58 Distinct Discourse Structures describe also have different causal structures. These distinctions have been characterised in terms of Certain constraints are imposed on discourse defeasible rules representing causal laws and prag- structure: Let R be Explanation or Elaboration; matic maxims. We now use this strategy to anal- then the current sentence can be discourse re- yse the other texts we mentioned above. lated only to the previous sentence a, to a sen- tence fl such that R(fl, a), or to a sentence 7 such Elaboration that R(7, fl) and R(~, a). This is a simpler ver- sion of the definition for possible attachment sites Consider text (2). in Asher (forthcoming). Pictorially, the possi- ble sites for discourse attachment in the example (2) a. The council built the bridge. structure below are those marked open: b. The architect drew up the plans.
Open We conclude Elaboration(2a, 2b) in a very sim- ilar way to example (3), save that we replace Explana~ lanati°n cause(me(~), me(a)) in the appropriate defensi- ble rules with prep(me(~), me(a)), which means that rne(~) is part of the preparatory phase of Closed Open me(a). In Law 2 below, Info(a,~) is a gloss for Narration "the event described in a is the council build- ing the bridge, and the event described in fl is Explanation/// ~xplanation the architect drawing up the plans", and the law represents the knowledge that drawing plans and Closed ~ Open building the bridge, if connected, are normally Narration such that the former is in the preparatory phase of the latter:
There are structural similarities between our • Elaboration notion of openness and Polanyi's (1985). The (a, ^ prep( e( ), me(a)) > above constraints on attachment explain the awk- Elaboration(a, fl ) wardness of text (9a-f) because (9c) is not avail- able to (gf) for discourse attachment. • Axiom on Elaboratio~ n (Elaboration(a, -* ne(a) (9) a. Guy experienced a lovely evening last night. • Law 2 b. He had a fantastic meal. (a,/3) ^ Info(a, > prep(me(Z), ) c. He ate salmon. The inference pattern is a Cascaded Penguin Prin- d. He devoured lots of cheese. ciple again. The two resolvable conflicts are Law e. He won a dancing competition. 2 and Narration and Elaboration and Narration. f. ?He boned the salmon with great ex- pertise. Background
According to the constraint on attachment, the Intuitively, the clauses in (4) are related by Back- only available sentence for attachment if one were ground. to add a sentence to (1) is John greeted him, whereas in (3), both sentences are available. Thus (4) Max opened the door. The room was pitch although the sentences in (1) and (3) were as- dark. signed similar structural semantics, they have very different discourse structures. The events they The appropriate reader's belief state verifies the antecedent of Narration. In addition, we claim flict between defeasible laws whose antecedents axe such that one of them entails the other is resolvable. Thus un- that the following laws hold: wanted irresolvable conflicts can be avoided.
59 • States Overlap Let Info(a,fl) be a gloss for "me(a) is Max (a, A state(me( )) > switching off the light and me(fl) is the room be- overlap(me(a), me( ) ) ing dark". So by the stative classification of dark, Info(a, fl) entails state(me(~)). Then Law 5 re- • Background flects the knowledge that the room being dark and (a, Z> ^ overlap(me(a), me(Z)) > switching off the light, if connected, are normally Background(a, fl ) such that the event causes the state: 9 • Axiom on Background [] (Background(a, • Causal Law 5 overlap(me(a), me(~) ) ) (a,/7) A Info(a,~) > cause(me(a), me(/7))
States Overlap ensures that when attached clauses The use of the discourse relation of Result is char- describe an event and state and we have no knowl- acterised by the following: edge about how the event and state are connected, gained from WK or syntactic markers like because • Result and therefore, we assume that they temporally (a, )^eause(me( ), > overlap. This law can be seen as a manifesta- • Axiom on Result tion of Grice's Maxim of Relevance as suggested D(Result(a,~) --. me(a) ~ me(fl)) in (Lascarides, 1990): if the start of the state is not indicated by stating what caused it or by in- The reader's beliefs in analysing (5) verify the an- troducing an appropriate syntactic marker, then tecedents of Narration, States Overlap and Law by Grice's Maxim of Relevance the starting point, 5. Narration conflicts with States Overlap, which and is irrelevant to the situation being described. in turn conflicts with Law 5. Moreover, the an- So the start of the state must have occurred be- tecedent of Law 5 entails that of States Overlap, fore the situation that the text is concerned with which entails that of Narration. So there is a occurs. As before, we assume that unless there is 'Penguin-type' conflict where Law 5 has the most information to the contrary, the descriptive order specific antecedent. In MASH Law 5's consequent, of eventualities marks the order of their discovery. i.e. cause(me(ha), me(hb)), is inferred from these This together with the above assumption about premises. The antecedent of Result is thus sat- where the state starts entail that unless there's isfied, but the antecedent to Background is not. information to the contrary, the state temporally Result does not conflict with Narration, and so overlaps events or states that were described pre- by Defeasible Modus Ponens, both Result(ha, 5b) viously, as asserted in States Overlap. and Narration(ha, hb) are inferred. We assume that the logical form of the sec- Note that thanks to the axioms on Background ond clause in (4) entails state(me(~)) by the and Result and the inconsistency of overlap(el, e~) classification of the predicate dark as stative. and el -~ e2, these discourse relations are in- So Background is derived from the Cascaded consistent. This captures the intuition that if Penguin Principle: the two resolvable conflicts a causes b, then b could not have been the case are States Overlap and Narration and Back- when a happened. In particular, if Max switching ground and Narration. States Overlap and Nar- off the light caused the darkness, then the room ration conflict because of the inconsistency of could not have been dark when Max switched off overlap(el,e~) and el -~ e~; Background and the light. Narration conflict because of the axioms for Back- ground and Narration. Discourse Popping Result Consider text (9a-e): (5) has similar syntax to (4), and yet unlike (4) (9) a. Guy experienced a lovely evening last the event causes the state and the discourse rela- night. tion is Result. b. He had a fantastic meal. (5) a. Max switched off the light. 9For the sake of simplicity, we ignore the problem of b. The room was pitch dark. inferring that the light is in the room.
60 c. He ate salmon. • Defeaslbly Necessary Test for d. lie devoured lots of cheese. Elaboration (a, ^ > e. He won a dancing competition. -~Elaboration( a, fl) The discourse structure for (9a-d) involves Cas- • Constraint on Narration caded Penguin Principles and Defeasible Modus Elaboration((~, fll )A-~Eiaboration( a, f12) > Ponens as before. Use is made of the defeasible -~N arration(~t , ~2 ) knowledge that having a meal is normally part of experiencing a lovely evening, and eating salmon The result is a 'Nixon Polygon'. There is irre- and devouring cheese are normally part of having solvable conflict between Narration and the Con- a meal if these events are connected: straint on Narration because their antecedents are not logically related: Guy experienced a lovely evening last night Elaboration Narration(9d, 9e)
He had a fantastic meal -~Elaboration(9b, 9e) Elaboration(9b, 9e)
Elabora~-~f~~boration l (9d,De)
lie ate salmon He devoured (9d, 9e) Narration lots Of cheese -~prep(me(9b, 9e)) Elaboration(~
We study the attachment of (9e) to the preced- (9d, 9e) ing text in detail. Given the concept of openness Info(9b, 9e) introduced above, the open clauses are (9d), (95) Elaboration(9b, 9d) and (9a). So by the assumptions on text pro- cessing, the reader believes (9d, 9e), (9b, 9e) and (9a, 9e). (9d, 9e) verifies the antecedent to Narra- The above in MASH yields ]i~Narration(9d, 9e) tion, but intuitively, (9d) is not related to (9e) at and ~-~Narration(9d, 9e). We assume that be- all. The reason for this can be explained in words lieving (9d, 9e) and failing to support any dis- as follows: course relation between (9d) and (9e) is inco- herent. So (9d,9e) cannot be believed. Thus • (9d) and (9e) don't form a narrative be- the Nixon Diamond provides the key to discourse cause: 'popping', for (9e) must be related to one of the remaining open clauses; i.e. (95) or (9a). In fact - Winning a dance competition is nor- by making use of the knowledge that winning a mally not part Of a meal; dance competition is normally part of experienc- - So (9e) doesn't normally elaborate (9b); ing a lovely evening if these things are connected, - But since (9d) elaborates (95), (9e) can Elaboration(9a, 9e) and Narration(9b, 9e) follow normally form a narrative with (9d) as before, in agreement with intuitions. only if (9e) also elaborates (9b). Thcse intuitions can be formalised, where Info(a, fl) Conclusion is a. gloss for "me(a) is having a meal and me(fl) is winning a dance competition": We have proposed that distinct natural inter- * Law 9 pretations of texts with similar syntax can be ex- (a, ^ I fo( , Z) > prep(me( ), me(.)) plained in terms of defeasible rules that represent
61 causal laws and Gricean-style pragmatic maxims. ume 136, pp277-322. Amsterdam: Mathematical The distinct discourse relations and event rela- Centre Tracts. tions arose from intuitively compelling patterns Kamp, Hans & Rohrer, Christian [1983] Tense of defeasible entailment. The Penguin Principle in Texts. In Bauerle, R., Schwarze, C. and yon captures the intuition that a reader never ignores Stechow, A. (eds.) Meaning, Use and Interpreta- information salient in text that is relevant to cal- tion of Language, pp250-269. Berlin: de Gruyter. culating temporal and discourse structure. The Nixon Diamond provided the key to 'popping' Lascarides, Alex [1990] Knowledge, Causality from subordinate discourse structure. and Temporal Representation. Research Report No. HCRC/RP-8, Human Communication Re- We have investigated the analysis of texts in- search Centre, University of Edinburgh, Edin- volving only the simple past tense, with no other burgh, June, 1990. temporal markers present. Lascarides & Asher (1991) show that the strategy pursued here can Lascarides, Alex & Asher, Nicholas [1991] Dis- be applied to the pluperfect as well. Future work course Relations and Common Sense Entailment, will involve extending the theory to handle texts DYANA deliverable 2.5b, available from Centre for that feature temporal connectives and adverbials. Cognitive Science, University of Edinburgh. Lascarides, Alex & Oberlander, Jon [1991] Tem- poral Coherence and Defeasible Knowledge. In References Proceedings to the Workshop on Discourse Co- herence, Edinburgh, April 1991. Asher, Nicholas [forthcoming] Abstract Objects, Moens, Marc & Steedman, Mark [1988] Tem- Semantics and Anaphora. poral Ontology and Temporal Reference. Com- Asher, Nicholas & Morreau, Michael [1991] putational Linguistics, 14, 15-28. Common Sense Entailment: A Modal Theory of Partee, Barbara [1984] Nominal and Temporal Nonmonotonic Reasoning, in Carlson, Greg & Anaphora. Linguistics and Philosophy, 7, 243- Pelletier, Jeff (eds.) The Generic Book, Proceed- 286. ings to JELIA90, University of Chicago Press. Polanyi, Livia [1985] A Theory of Discourse Dahlgren, Kathleen [1988] Naive Semantics for Structure and Discourse Coherence. In Eilfort, Natural Language Understanding, Kluwer Aca- W. H., Kroeber, P. D. and Peterson, K. L. (eds.) demic Publishers; Boston, USA. Papers from the General Session at the Twenty- Dowty, David [1986] The Effects of Aspeetual First Regional Meeting of the Chicago Linguistics Class on the Temporal Structure of Discourse: Se- Society, Chicago, April 25-27, 1985. mantics or Pragmatics? Linguistics and Philoso- Scha, Remko & Polanyi, Livia [1988] An Aug- phy, 9, 37-61. mented Context Free Grammar. In Proceedings Grice, H. Paul [1975] Logic and Conversation. of the 121h International Conference on Compu- In Cole, P. and Morgan, J. L. (eds.) Syntaz and tational Linguistics and the 24th Annual Meeting Semantics, Volume 3: Speech Acts, pp41-58. New of the Association for Computalional Linguistics, York: Academic Press. Budapest, Hungary, 22-27 August, 1988, 573-577. Itinrichs, Erhard [1986] Temporal Anaphora in Thompson, Sandra A. & Mann, William C. Discourses of English. Linguistics and Philoso- [1987] Rhetorical Structure Theory: A Frame- phy, 9, 63-82. work for the Analysis of Texts. International Joshi, Aravind, Webber, Bonnie L. & Pragmaties Association Papers in Pragmatics, 1, Weischedel, Ralph [1984] Default Reasoning in 79-105. Interaction. In Proceedings of the Non-Monotonic Webber, Bonnie [1988] Tense as Discourse Reasoning Workshop, AAAI, New York, October, Anaphor. Computational Linguistics, 14, 61-73. 1984, 144-150. Kamp, Hans [1981] A Theory of Truth and Se- mantic Representation. In Groenendijk, J. A. G., Janssen, T. M. V. and Stokhof, M. B. J. (eds.) Formal Methods in the Study of Language, Vol-
62