Multiple Simultaneous Inter pr etations of Ambiguous Sentences Peter Norvig  Uni ve rsity of California Berk ele Intr oduction This paper is concerned with the problem of semantic and pragmatic inter
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Multiple Simultaneous Inter pr etations of Ambiguous Sentences Peter Norvig Uni ve rsity of California Berk ele Intr oduction This paper is concerned with the problem of semantic and pragmatic inter

We s tart by of fering a simple yet commonly adopted interpretation strate gy Strategy 1 Apply syntactic rules to the sentence to deri ve a s et of parse trees Ne xt apply seman tic rules to the trees to get a set of logical formulae and discard an

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Multiple Simultaneous Inter pr etations of Ambiguous Sentences Peter Norvig Uni ve rsity of California Berk ele Intr oduction This paper is concerned with the problem of semantic and pragmatic inter

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Multiple Simultaneous Inter pr etations of Ambiguous Sentences Peter Norvig * Uni ve rsity of California, Berk ele Intr oduction This paper is concerned with the problem of semantic and pragmatic interpretation of ambiguous sentences. We s tart by of fering a simple yet commonly adopted interpretation strate gy: Strategy 1: Apply syntactic rules to the sentence to deri ve a s et of parse trees. Ne xt apply seman- tic rules to the trees to get a set of logical formulae, and discard an yi nconsistent formulae. Do a pragmatic interpretation of each formula, and gi ve a s core to

each possibility based on consistenc or lik elihood in the gi ve nc onte xt. Finally ,c hoose the interpretation with the highest score. In this frame wo rk, the le xicon, grammar ,a nd semantic and pragmatic interpretation rules determine a map- ping between sentences and meanings. As tring with e xactly one interpretation is unambiguous, one with no interpretation is anomalous, and one with multiple interpretations is ambiguous. To e numerate the pos- sible parses and logical forms of a sentence is the proper job of a linguist; to then choose from the possibili- ties the one ‘correct ’o r

‘intended ’m eaning of an utterance is an e xe rcise in pragmatics or Artificial Intelligence. One major problem with Strate gy 1 is that it ignores the dif ference between sentences that seem truly ambiguous to the listener ,a nd those that are only found to be ambiguous after careful analysis by the lin- guist. F or e xample, each of the follo wing is technically ambiguous ( with could signal the instrument or accompanier case, and port could be a harbor or the left side of a ship), b ut only the third w ould be seen as ambiguous in a neutral conte xt. (1) I sa wt he w oman with long

blond hair (2) I drank a glass of port. (3) I sa wh er duck. Zadeh (personal communication) has suggested that ambiguity is a matter of de gree. He assumes each interpretation has a lik elihood score attached to it. As entence with a lar ge g ap between the highest and second rank ed interpretation has lo wa mbiguity; one with nearly-equal rank ed interpretations has high ambiguity; and in general the de gree of ambiguity is in ve rsely proportional to the sharpness of the drop-of in ranking. So, in (1) and (2) abo ve ,t he de gree of ambiguity is belo ws ome threshold, and thus is not

noticed. In (3), on the other hand, there are tw os imilarly rank ed interpretations, and the ambiguity is per cei ve da ss uch. Man yr esearchers, from Hock ett (1954) to Jack endof f( 1987), ha ve s uggested that the inter pretation of sentences lik e( 3) beha ve sl ik et he perception of visual illusions such as the Neck er cube or the va se/f aces or duck/rabbit illusion. In other w ords, it is possible to shift back and forth between alternate interpretations, b ut it is not possible to percei ve b oth at once. This leads us to Strate gy 2: Strategy 2: Do syntactic, semantic, and

pragmatic interpretation as in Strate gy 1. Retain only the highest-ranking interpretation(s), according to some threshold function. If there is more than one interpretation remaining, alternate between them. Ap roblem with Strate gy 2 is that it assumes all possible interpretations will be considered and rank ed. Ho we ve r, m an ys entences ha ve a p rohibiti ve ly lar ge or infinite number of interpretations. Consider the fol- lo wing: (4) He seems older no w. Here he can refer to one of se ve ral billion males, and now can refer to one of an infinite number of time points.

Thus, while syntax and semantics may be producing discrete lists of possibilities, it seems that pragmatic interpretation must operate by proposing lik ely interpretations, rather than enumerating all possi- bilities and then choosing among them. Hobbs (1983) has ar gued that enumeration should be minimized *T he author has been sponsored by the Defense Adv anced Research Projects Agenc y( DoD), Arpa Order No. 4871, monitored by Space and Na va lW arf are Systems Command under Contract N00039-84-C-0089. -1-
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ev e ni ns yntactic and semantic analysis. Accepting that intuition,

we get Strate gy 3, which is similar to the approachs used by se ve ral recent authors, including Hobbs (1987), Stallard (1987), and Charniak (unpub- lished). Strategy 3: Do le xical, syntactic and semantic analysis to produce one (or occasionally more) neutral representation of the input, which can contain ambiguous and v ague predications. Prag- matics then attempts to ‘solv e’ for the ambiguous predications and some of the v ague ones. Solu- tions are generated in a roughly best-first manner ,a nd when there is a lar ge drop-of fi nt he ranking of solutions, we stop and the

final interpretation alternates between the high ranking one(s). This might represent an ef ficient interpretation mechanism, b ut it doesn tm irror the human interpretation mechanism particularly well. Sentences lik e( 5-9) each ha ve o nly one good pragmatic interpretation, which wo uld be found easily by Strate gy 3. But (5-9) are notoriously hard for humans to get right without at least ac onscious sense of ha ving to back up and re-parse the sentence. (5) The horse raced past the barn fell. (6) The astronomer married a star (7) The rabbi w as hit on the temple. (8) The

landlord painted all the w alls with cracks. (9) Ross w as told what to do by the ri ve r. Strate gies lik eK imball s( 1973) or Frazier and F odor s( 1978) try to account for phenomena lik et hese in terms of general syntactic preference principles, which appeal to performance issues such as limits on a va il- able memory space. Schubert (1984, 1986) and K urtzman (1984) ar gue con vincingly that no simple syn- tactic preference will do. Rather ,m an yf actors must be considered, as in Strate gy 4: Strategy 4: Do le xical, syntactic, and semantic analysis on a w ord-by-w ord basis,

identifying points of ambiguity along the w ay ,a nd using all sources of e vidence to rank alternati ve s. Evi- dence for a particular choice can include le xical frequenc yp references, pragmatic associations, and other f actors outside of the simple logical form. Ah igh-ranking interpretation can be accepted (and its alternati ve sd iscarded) before the parse is complete, if its score remains suf ficiently abo ve the alternati ve sf or a suf ficient amount of time. In addition, if at an yp oint there are more than a maximum number =3 ?) alternati ve s, discard the lo west

ranking alternati ve ,e ve ni fi ts score is close to others. At the end, alternate between the highest ranking interpretations, as before. Mutually Compatible Inter pr etations and Connotations Consider the follo wing quote from Richard P arsons, of the American Fur Industry Inc., on their ne wa dv er tising slog an Fur is for Life: It has a good sound, a good connotation. Ye s, the yl ast a long time. Ye s, the y re a good product. Ye s, furs support wildlife conserv ation. Pa rsons (although not a professional linguist) is making a claim about language use: that the proper or intended

meaning of a phrase can be a combination of a number of interpretations and connotations. Strate gies 2-4 assume that the reader e ve ntually arri ve sa tas ingle interpretation, or a Neck er -cube-lik alternation between interpretations. But P arsons is saying that his slog an Fur is for Life is dif ferent. The slog an seems to ha ve t wo p rimary interpretations, (10) and (11) belo w. B ut it also has important connota- tions, listed as (12-14), as well as another interpretation, (15), that P arsons presumably w ants the public to ignore. (10) Fur lasts a lifetime. (11) The fur industry is

pro-conserv ation. (12) Fur wearers are li ve ly (13) The recipient of a fur may become indebted to the gi ve rf or life. (14) Life is a good thing; hence fur is a good thing. -2-
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(15) Fur ,w hile on an animal, protects its life. Although we w ould not be lik ely to say that an yo f( 12-14) are good candidates for the final interpretation, it seems that the intended ef fect of the slog an is for the reader to entertain some or all of these simultane- ously .W hile this is a radical departure from the Hock ett/Jack endof f/Neck er theory of ‘one interpretation at at ime,

’i ta ppears to be quite common in poetry ,p olitics, and adv ertising (see Burli-Storz, 1980). The f acts are admittedly slippery; I am suggesting that alternati ve p arses can sometimes be combined into one interpretation, b ut it is hard to distinguish between distinct parses that ha ve b een combined together ,a nd a v ague interpretation that has se ve ral possible entailments. Also, it is notoriously hard to introspect about the phenomenology of these cases. Perhaps the follo wing e xample, from the last line of Gerard Manle yH opkins God sG ra ndeur will be more compelling: (16) Because

the Holy Ghost o ve rt he bent Wo rld broods with w arm breast and with ah! bright wings. The w ord br oods is le xically ambiguous between ‘to sit on e ggs to hatch them’ and ‘to think long and deeply or resentfully .’ T his is clearly not a case of v agueness. Y et it seems that the most natural interpreta- tion is of a bird-lik eg od sitting on an e gg-lik ew orld (or w orld-lik ee gg), pensi ve ly surv ey ing his creation, and w aiting for it to come to fruition. This interpretation clearly in vo lv es no Neck er -lik ea lternation between senses for br oods; rather ,i ti nv o lv es a

simultaneous synthesis of tw oi mages. Note that not just an yi mages can be superimposed this w ay; if the w orld were flat, or if e ggs were cubical, the combined image w ould not w ork. It is permissible to combine the images e ve nt hough the wo rld is quite a bit lar ger and composed of dif ferent material than the a ve rage e gg, and e ve nt hough the prototypical image of God does not include wings. Poetry ,l ik ea dv ertising, seems to sanction this superimposition of distinct parses. To s upport this claim, I opened a poetry anthology at random, finding the opening line of

to Dylan Thomas’ poem In the Be ginning: In the be ginning w as the three-pointed star . ’A st he rest of the poem mak es clear ,t he three- pointed star should be tak en as referring to a stellar body in primordial space, to the light in God sp erfor mati ve s peech act ‘Let there be light, ’’ t ot he star of Bethlehem, and to the Holy T rinity .T here does not seem to be a clear feeling of shifting between these referents; rather the ys eem to be entertained simultane- ously Lak of fa nd T urner (1988) cite, b ut do not fully analyize, another Dylan Thomas poem, Do not go ge ntle into that

good night: (17) Do not go gentle into that good night, Old age should b urn and ra ve a tc lose of day; Rage, rage ag ainst the dying of the light. Understanding this passage requires kno wledge of at least six metaphors for life and death. While these metaphors of fer conflicting vie ws on the nature of death, there is no feeling of ha ving to switch between them in understanding the poem; the ya re all acti ve a to nce. In fa ct, metaphors (18-23) are all used in the interpretation of the six w ords go g entle into that good night :( 18) for go ,( 19) for ge ntle ,( 20) for into ,(

21) for good night ,a nd (22) for night .T hus, the w ord night is being used simultaneously as a time, a destina- tion, a container ,a nd an adv ersary ,a ll without promoting a conscious feeling of Neck er -lik ea mbiguity (18) Life is a journe y. (19) Life is a struggle; death is an adv ersary (20) Life is ‘here’; death is a another w orld. (21) Death is sleep. (22) A lifetime is a day; death is night. (23) Life is a fire that blazes and b urns out. At this point let us try to modify Strate gy 4 to account for these ne w ndings. There are tw op ossibilities; we can treat the

combination of tw oi nterpretations as an abnormality ,a nd try to sho wh ow i tc an be sanc- tioned, or we can treat it as the ne wb asic interpretation mechanism, and try to sho wh ow i tc an be con- -3-
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strained. Strategy 5a: The Conser va ti ve S imultaneity Strategy: Ammend Strate gy 5 to allo was imulta- neous amalg am of tw oo rm ore competing top-rank ed interpretations, b ut only when sanctioned by some as-yet-unspecified f actors, and only when the result is a coherent combination of the tw o. Strategy 5b: The Radical Simultaneity Strategy: Always try to

combine top-ranking interpreta- tions into one image. When a coherent combination is impossible, alternate between interpreta- tions as in Strate gy 5. To t ry to choose between the tw o, we will first consider Strate gy 5b, as it is applied to sentence (24), and its interpretation, the disjunction (24’): (24) The chick en is ready to eat. (24’) chick en(x) & ready(x,e) & eating(e) & (agent(e,x) | patient(e,x)) Using Strate gy 5b, we could combine the tw oi nterpretations simply by accepting both parts of the disjunc- tion, yielding ‘the chick en is ready to eat the chick en. ’T his is

by no means a normal interpretation of (24), so we ha ve a na rg ument ag ainst 6b .H ow ev e r, t hat ar gument only goes through if the proposed logical form (24’) is accurate. Suppose we use the follo wing logical form instead: chick en(x) & ready(x,e) & eating(e) & ((agent(e,x) & ali ve (x) & location(e,barn yard) & patient(e,seed) & ...) | (patient(e,x) & not ali ve (x) & location(e,table) & agent(e,human) & ...)) Then we ha ve t wo i nterpretations that cannot be combined coherently ,n either under Strate gy 5b nor 5a. Thus, we see that for 5b to be feasible, we need to insist on full

frame-lik es emantic interpretations, com- plete with def ault assumptions. We n eed a rich set of def aults to rule out unw anted unification of the tw interpretations, e ve nt hough we w ant to allo wt he possibility of o ve rriding some of the def aults, as in ‘The chick en on the table is ready to eat her asparagus. ’’ N ow l et st ry an e xample that does not bring as much background kno wledge into play: (25) She opened the door with a k ey The ambiguity is between with a k ey as an instrument of opening, and as a modifier of the door .H ere there seems to be nothing to stop

5b from accepting both interpretations for the phrase, whereas we kno wt hat if this were the intended meaning, one w ould ha ve t ou se something lik et he follo wing: (26) She opened the door with the k ey t hat w as in/near it. Thus, Strate gy 5b as it stands is rejected. To e va luate Strate gy 5a, we need to de ve lop a better notion of sanctioning ac ombined interpretation, which we will address in the ne xt section. Jo ke sa nd Puns Consider the follo wing adv ertisement for Flintstones brand V itamins: (27) W ea re Flintstones kids, ten million strong and gro wing. The coordinate and

gr owing can attach to either ar or ten million str ong ,w ith the respecti ve i nterpretations that the indi vidual children are gro wing, or that the number of children is increasing. Most informants rec- ognize both alternati ve s, b ut report an ability to fuse the tw ot ogether into a single image where each indi- vidual child in an e xpanding group is gro wing. (Ho we ve r, n oo ne interpreted str ong as possibly modifying kids, perhaps because of the idiomatic nature of the phrase ten million str ong .) My analysis of this e xample is that the listener arri ve sa tt he tw oi

nterpretations using something lik eS trate gy 4, and in the process of trying to choose between them, realizes that both were intended interpretations, and successfully superim- poses the tw oi mages. In short, (27) is a kind of pun. In a re gular pun, the main point of the utterance is that the speak er has been cle ve r, p roducing tw om eanings in one sentence. As econdary point is one of the meanings (and, for a good pun, both of the meanings tak en separately). But in (27) we ha ve a s pecial kind of pun, where the point is that both meanings are to be tak en simultaneously .A similar e

xample comes from another ad, for -4-
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Michelin tires: (28) Because you ve g ot a lot riding on your tires. Here the ambiguous phrase got a lot riding on is ambiguous between ‘much depends on your tires’ and ‘much rides in the car which is on the tires, ’w ith the resulting combined interpretation ‘your f amily ss afety while in the car depends on the tires. ’H ere ag ain the reader must recognize the ‘pun, ’a nd the intended ef fect of combining the tw oi nterpretations, b ut here there is an added hitch: it is the combination of the tw interpretations that resolv es the

phrase al ot to ‘your f amily’; neither of the tw oi nterpretations strongly point to this interpretation singly ,b ut together the yd o. Let us compare these puns to the follo wing e xample from Freud (1916): (29) I met Baron Rothschild, and he treated me quite as his equal−quite f amillionairely This is funn y, F reud claims, because of the une xpected ease of combining familiarly with millionair to cre- ate a ne ww ord meaning ‘as f amiliarly as is possible for a millionaire. ’( In German, f amili ¨ ar + Million ¨a r= fa milion ¨ ar .) Freud also presents the standard definition

of joking as the ability to find hidden similarities between dissimilar things. This is amended to allo wf or the disco ve ry of dif ferences, or just ‘to bind into a unity ,w ith surprising rapidity ,s ev e ral ideas which are in f act alien to one another . ’I no ther w ords, the combination of disparate ambiguous interpretations is an unusual e ve nt, b ut one that we ha ve a na utomatic capacity for Ar emaining problem is to e xplain wh ys ome such ambiguities are funn y, w hile others are not. Wh is it that, to my ears at least, the r abbi was hit on the temple is funn y, w hile the

plumber lit his pipe is merely confusing? Freud claims that the laughter response is illicited by the release of suppressed violent or se xual thoughts. That e xplains, perhaps, wh yt he follo wing is a f airly good jok e, while other le xical and structural ambiguities in this paper are not: (30) She criticized his apartment, so he knock ed her flat. Minsk y( 1980) recasts Freud sn otions into the terminology of mental agents acting as censors to violent or se xual thoughts. In Minsk y st erms, certain mental agents are good at combining ambiguous interpreta- tions, b ut other agents

notice that this is not the normal mode of operation, and act to censor them. The laughter response serv es to ‘shak eu p’ the mind, get it back on track, and post a w arning to a vo id such thoughts. Presumably ,t he simultaneous combinations that sneak by uncensored are ones that do not repre- sent ‘dangerous’ modes of thought. Simultaneous Inter pr etation in ‘Normal’ Language There are also cases of combined simultaneous interpretation which don ti nv o lv ep oetic license or puns. Consider the use of book in (31). Book is polysemous between a ph ysical object, a string of w ords, and an

abstract plot or sequence of situations. The use of beautifully bound refers to the ph ysical object, one ne idea refers to the abstract content, and 50,000 wor ds refers to a particular (abstract) instantiation of the con- tent. (If the book were reprinted in paperback it w ould still ha ve t he same number of w ords, whereas if it were translated into another language, it w ould ha ve a d if ferent number of w ords, b ut the same number of ideas.) All three polysemous interpretations of book are used simultaneously (31) This book, although beautifully bound, contains only one ne wi dea in

50,000 w ords. (32) He is the author of o ve r1 00 books. It can tb et hat book is a single sense implying all these aspects, because in (32), book must refer only to the ‘plot or sequence of ideas’ sense. One could not felicitously use (32) to describe someone who had written as ingle book which has had a hundred copies printed, or a single book which w as translated by others into ah undred languages. Len T almy (1977) pro vides a good e xample of image combination in non-ambiguous language. In (33), the single interpretation is ‘she tra ve led lightly and easily through the room and the

guests at the party her path displaying a topology similar to a leaf w afting through air .’ ( 33) forces the reader to combine the image of a w oman w alking through a party with the image of a leaf w afting through the air (or something similar) to arri ve a tt he result. Ta lmy e xplains just what properties of the v erb are maintained, and which -5-
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are tak en from the complements. (33) She w afted through the party Image combination is more ob vious in the case of metaphors and cliches where the deri ve dm eaning is remo ve dt han the surf ace form. Compare (34), which is

a consistent use of metaphor ,w ith (35). Sentence (35) pro vides a topological clash that cannot easily be resolv ed into a single interpretation, e ve nt hough the meaning of the tw oc liches is consistent. (34) I ve a lwa ys been 100% behind my husband, pushing him on as best I can. (35) I ve a lwa ys been at my husband ss ide, 100% behind him. (36) The yc an ta ff ord to get out from under the rat-hole of rent payments. Sentence (36), tak en from a ne wspaper article on real estate prices, is an e xample of a mix ed metaphor with va rying ef fecti ve ness; some find it to be

fine, while most report that the topology is all wrong: one should be stri ving to get out of a rat-hole, not out from under it. Conclusion In this paper I ha ve i nv e stig ated se ve ral strate gies for pragmatic interpretation, and ha ve p resented a ne strate gy which (1) accounts for the little-mentioned phenomenon of a simultaneous combination of ambigu- ous interpretations, (2) is not inconsistent with e xperimentally deri ve dh uman preference results, and (3) uses a combination mechanism that is needed for non-ambiguous language as well. Bibliograph Burli-Storz, Claudia, Deliber

ate Ambiguity in Advertising Bern, 1980. Frazier ,L yn and Janet Dean F odor , ‘The sausage machine: A ne wt wo -stage parsing model, Co gnition, (4), December 1978, 291-325. Freud, Sigmund, Jo ke sa nd Their Relation to the Unconscious, Tr anslated by James Strache y, 1 960, Nor ton, NY ,o riginally published 1916. Hobbs, Jerry , ‘Representing ambiguity , Pr oceedings of the Second W est Coast Confer ence on F ormal Lin- guitics, Stanford Uni ve rsity 1983 Hobbs, Jerry ,a nd P aul Martin, ‘Local pragmatics, Pr oceedings of the International J oint Confer ence on Artificial Intellig ence

1987. Hock ett, Charles F ., ‘T wo m odels of grammatical description, ’’ W ord, 1954, 386-399. Jack endof f, Ray Consiousness and the Computational Mind, MIT Press, 1987. Kimball, John, ‘Se ve np rinciples of surf ace parsing in natural language, Co gnition (1), 1973, 15-47. Ku rtzman, Ho wa rd S., ‘A mbiguity resolution in the human syntactic parser: An e xperimental study , Col- ing ,1 984. Lak of f, Geor ge, and Mark T urner Mor eT han Cool Reason, to appear ,1 988. Minsk y, M arvin, ‘Jok es and the logic of the cogniti ve u nconscious, AI memo No. 603, MIT AI Lab, 1980. Schubert, Lenhart

K., ‘On parsing preferences, Pr oceedings of Coling84, Stanford, CA, July 1984. Schubert, Lenhart K., ‘A re there preference trade-of fs in Attachment Decisions?, ’’ P roceedings of AAAI, 1986, 601-605. Stallard, Da vid, ‘The logical analysis of le xical ambiguity , ’2 5th Annual Meeting of the A CL, 1987, 179-185. Ta lmy ,L eonard, ‘Rubber -sheet cognition in language, Chica go Linguistics Society 13 ,1 977, 612-628. -6-