File Information
File: 05-lr/acl_arc_1_sum/cleansed_text/xml_by_section/metho/88/p88-1012_metho.xml
Size: 36,308 bytes
Last Modified: 2025-10-06 14:12:11
<?xml version="1.0" standalone="yes"?> <Paper uid="P88-1012"> <Title>Interpretation as Abduction</Title> <Section position="3" start_page="95" end_page="95" type="metho"> <SectionTitle> 2 Local Pragmatics </SectionTitle> <Paragraph position="0"> The fbur local pragmatics problems we have addressed can be illustrated by the following &quot;sentence&quot; from the casualty reports: (2) Disengaged compressor after lube-oil alarm.</Paragraph> <Paragraph position="1"> Identifying the compressor and the alarm are reference resolution problems. Determinlug the implicit relation between &quot;lube-oil&quot; and &quot;alarm&quot; is the problem of compound nominal interpretation. Deciding whether &quot;after lube-oil alarm&quot; modifies the compressor or the disengaging is a problem in syntactic ambiguity resolution.</Paragraph> <Paragraph position="2"> The preposition &quot;after&quot; requires an event or condition as its object and this forces us to coerce &quot;lube-oil alarm&quot; into &quot;the sounding of the lube-oil alarm&quot;; this is an example of metonymy resolution. We wish to show that solving the farst three of these problems amounts to deriving the logical form of the sentence. Solving the fourth amounts to deriving the constraints predicates impose on their arguments, allowing for coercions. For each of these problems, our approach is to frame a logical expression whose derivation, or proof, constitutes an interpretation.</Paragraph> <Paragraph position="3"> Reference: To resolve the reference of &quot;compressor&quot; in sentence (1), we need to prove (constructively) the following logical expression:</Paragraph> </Section> <Section position="4" start_page="95" end_page="97" type="metho"> <SectionTitle> (3) (B c)comFeessor(c) </SectionTitle> <Paragraph position="0"> If, for example, we prove this expression by using axioms that say (71 is a starting air compressor, and that a starting air compressor is a compressor, then we have resolved the reference of &quot;compressor&quot; to 6'i.</Paragraph> <Paragraph position="1"> In general, we would expect definite noun phrases to refer to entities the hearer already knows about and can identify, and indefinite noun phrases to refer to new entities the speaker is introducing. However, in the casually reports most noun phrases have no determiner. There are sentences, such as Retained oil sample and filter for future analysis.</Paragraph> <Paragraph position="2"> where &quot;sample&quot; is indefinite, or new information, and &quot;filter&quot; is definite, or already known to the hearer. In this case, we try to prove the existence of both the sample and the filter. When we fail to prove the existence of the sample, we know that it is new, and we simply assume its existence.</Paragraph> <Paragraph position="3"> Elements in a sentence other than nominals can also function referentially. In Alarm sounded.</Paragraph> <Paragraph position="4"> Alarm activated during routine start of compressor.</Paragraph> <Paragraph position="5"> one can argue that the activation is the same as, or at least implicit in, the sounding. Hence, in addition to trying to derive expressions such as (3) for nominal reference, for possible non-nomlnal reference we try to prove similar expressions.</Paragraph> <Paragraph position="6"> (3 ... e, a,...)... ^ activate'(e, a) ^ ...s That is, we wish to derive the existence, from background knowledge or the previous text, of some known or implied activation. Most, but certainly not all, information conveyed non-nominally is new, and hence will be assumed. Compound Nominals: To resolve the reference of the noun phrase &quot;lube-oi\] alarm&quot;, we need to Find two entities o and a with the appropriate properties. The entity o must be lube oil, a must be an alarm, and there must be some implicit relation betwee~ them. Let us call that implicit relation nn. Then the expression that must be proved is</Paragraph> <Paragraph position="8"> In the proof, instantiating nn amounts to interpreting the implicit relation between the two nouns in the compound nominal. Compound nominal interpretation is thus just a special case of reference resolution.</Paragraph> <Paragraph position="9"> Treating nn as a predicate variable in this way seems to indicate that the relation between the two nouns can be anything, and there are good reasons for believing this to be the case (e.g., Downing, 1977). In &quot;lube-oil alarm&quot;, for example, the relation is ~x, y \[y sounds if pressure of z drops too low\] However, in our implementation we use a first-order simulation of this approach. The symbol nn is treated as a predicate constant, and the most common possible relations (see Levi, 1978) are encoded in axioms. The axiom (v=, v)r~,~(y, =) ~ --(=,y) allows interpretation of compound nominals of the form &quot;<whole> <part>&quot;, such as &quot;filter element&quot;. Axioms of the form (Vz, y)sample(y, z) D nn(z, y) handle the very common ease in which the head noun is a relational noun and the prenominal noun fills one of its roles, as in &quot;oil sample&quot;. Complex relations such as the one in &quot;luhe-oil alarm&quot; can sometimes be glossed as &quot;for&quot;. (v=, v)fo~Cy, =) ~ --(=, y) Syntactic Ambiguity: Some of the most common types of syntactic ambiguity, including prepositional phrase and other attachment ambiguities and very compound nominal ambiguities, can be converted into constrained coreference problems (see Bear and Hobbs, 1988). SSee Hobbs (1985a) for explanation of this notation for events. For example, in (2) the first argument of after is taken to be an existentially quantified variable which is equal to either the compressor or the alarm. The logical form would thus include (3...e,c,y,a .... )... A aftcr(y,a) A ye {c,~} A ...</Paragraph> <Paragraph position="10"> That is, however after(y, a) is proved or assumed, y must be equal to either the compressor c or the disengaging c. This kind of ambiguity is often solved as a byproduct of the resolution of metonymy or of the merging of redundancies. Metonymy: Predicates impose constraints on their arguments that are often violated. When they are violated, the arguments must be coerced into something related which satisfies the constraints. This is the process of metonymy resolution. Let us suppose, for example, that in sentence (2), the predicate after requires its arguments to be events:</Paragraph> <Paragraph position="12"> To allow for coercions, the logical form of the sentence is altered by replacing the explicit arguments by &quot;coercion variables&quot; which satisfy the constraints and which are related somehow to the explicit arguments. Thus the altered logical form for (2) would include (3 ... kt, k2, y, a, rela, eel2,...).., h after(k1, k2) A event(ka) A rcll(kl, y) A event(k~) A ret2(k2,a) A ...</Paragraph> <Paragraph position="13"> As in the most general approach to compound nominal interpretation, this treatment is second-order, and suggests that any relation at all can hold between the implicit and explicit arg~unents. Nunberg (1978), among others, has in fact argued just this point. However, in our implementation, we are using a first-order simulation. The symbol eel is treated as a predicate constant, and there are a number of axioms that specify what the possible coercions are. Identity is one possible relation, since the explicit arguments could in fact satisfy the constraints.</Paragraph> <Paragraph position="14"> (Vx)rel(=, x) In general, where this works, it will lead to the best interpretation. We can also coerce from a whole to a part and from an object to its function. Hence,</Paragraph> <Paragraph position="16"> Putting it all together, we find that to solve all the local pragnaatics problems posed by sentence (2), we must derive the following expression:</Paragraph> <Paragraph position="18"> But this is just the logical form of the sentence 4 together with the constraints that predicates impose on their arguments, allowing for coercions. That is, it is the first half of our characterization (1) of what it is to interpret a sentence.</Paragraph> <Paragraph position="19"> When parts of this expression cannot be derived, assumptions must be made, and these assumptions are taken to be the new information. The likelihood of different atoms in this expression being new information varies according to how the information is presented, linguistically. The main verb is more likely to convey new information than a definite noun phrase. Thus, we assign a cost to each of the atoms--the cost of assuming that atom. Tlus cost is expressed in the same currency in which other factors involved in the &quot;goodness&quot; of an interpretation are expressed; among these factors are likely to be the length of the proofs used and the salience of the axioms they rely on. Since a definite noun phrase is generally used referentially, an interpretation that simply assumes the existence of the referent and thus falls to identify it should be an expensive one. It is therefore given a high assumability cost.</Paragraph> <Paragraph position="20"> For purposes of concreteness, let's call this $10. Indefinite noun phrases arc not usually used referentially, so they are given a low cost, say, $1. Bare noun phrases are given an inte~ediate cost, say, $5. Propositions presented non-nominally are usually new information, so they are given a low cost, say, $3. One does not usually use selectional constraints to convey new information, so they are given the same cost as definite noun phrases. Coercion relations and the compound nominal relations are given a very high cost, say, $20, since to assume them is to fail to solve the interpretation problem. If we superscript the atoms in the above logical form by their assumability costs, we get the following expression:</Paragraph> <Paragraph position="22"> While this example gives a rough idea of the relative assumability costs, the real costs must mesh well with the inference processes and thus must be determined experimentally. The use of numbers here and throughout the next section constitutes one possible regime with the needed properties. Vv'e are at present working, and with some optimism, on a semantics for the numbers and the procedures that operate on them. In the course of this work, we may modify the procedures to an extent, but we expect to retain their essential properties.</Paragraph> </Section> <Section position="5" start_page="97" end_page="98" type="metho"> <SectionTitle> 3 Abduction </SectionTitle> <Paragraph position="0"> We now argue for the last half of the characterization (I) of interpretation.</Paragraph> <Paragraph position="1"> Abduction is the process by which, from (Vz)p(z I D q(r) and q(A), one concludes p(A I. One can think of q(A) as the observable evidence, of (Vz)p(z) D q(z) as a general principle that could explain q(A)'s occurrence, and of p(A) as the inferred, underlying cause of q(A). Of course, this mode of inference is not valid; there may be many possible such p(A)'s. Therefore, other criteria are needed to choose among the possibilities. One obvious criterion is consistency of p(A I with the rest of what one knows.</Paragraph> <Paragraph position="2"> Two other criteria are what Thasard (1978) has called consilience and simplicity. Roughly, simplicity is that p(A) should be as small as possible, and consilience is that q(A) should be as big as possible. We want to get more bang for the buck, where q(A) is bang, and p(A) is buck.</Paragraph> <Paragraph position="3"> There is a property of natural language discourse, noticed by a number of linguists (e.g., Joos (19721, Wilks (1972)), that su~ests a role for simplicity and consilience in its interpretation--its high degree of redundancy. Consider null Inspection of oll filter revealed metal particle~.</Paragraph> <Paragraph position="4"> An inspection is a looking at that causes one ~o learn a property relevant to the j~nc~io~ of the inspected object. The ~nc~ioC/ of a falter is to capture p,~eticle~ from a fluid. To reveal is to os~e one ~o/earn. If we assume the two causings to learn are identical, the two sets of particles are identical, and the two functions are identical, then we have explained the sentence in a minimal fashion. A small number of inferences and assumptions have explained a large number of syntactically independent propositions in the sentence. As a byproduct, we have moreover shown that the inspector is the one to whom the particles are revealed and that the particles are in the filter.</Paragraph> <Paragraph position="5"> Another issue that arises in abduction is what might be called the &quot;informativeness-correctness tradeotP'. Most previous uses of abduction in AI from a theorem-proving perspective have been in diagnostic reasoning (e.g., Pople, 1973; Cox and Pietrzykowski, 1986), and they have asmaned &quot;most specific abduction&quot;. If we wish to explain chest palna~ it is not su~cient to assume the cause is simply chest pains. We want something more specific, such as &quot;pneumonia&quot;. We want the most specific possible explanation. In natural language processing, however, we often want the least specific assumption. If there is a mention of a fluid, we do not necessarily want to assume it is lube oil.</Paragraph> <Paragraph position="6"> Assuming simply the existence of a fluid may be the best we can do. s However, if there is corroborating evidence, we may want to make a more specific assumption. In Alarm sounded. Flow obstructed.</Paragraph> <Paragraph position="7"> SSometimes a cigar is just a cigar.</Paragraph> <Paragraph position="8"> we know the alarm is for the lube oil pressure, and this provides evidence that the flow is not merely of a fluid but of lube oil. The more specific our assumptions are, the more informative our interpretation is. The less specific they are, the more likely they are to be correct.</Paragraph> <Paragraph position="9"> We therefore need a scheme of abductive inference with three features. First, it should be possible for goal expressions to be assumable~ at varying costs. Second, there should be the possibility of making assumptions at various levels of specificity. Third, there should be a way of exploiting the natural redundancy of texts.</Paragraph> <Paragraph position="10"> We have devised just such an abduction scheme, s First: every conjunct in the logical form of the sentence is given an assumability cost, as described at the end of Section 2.</Paragraph> <Paragraph position="11"> Second, this cost is passed back to the antecedents in Horn clauses by assigming weights to them. Axion~s are stated in the form (4) Pp ^Pp ~ Q This says that Pl and P2 imply Q, but also that if the cost of assuming Q is c, then the cost of assuming PI is wlc, and the cost of assuming P2 is w2c. Third, factoring or synthesis is allowed. That is, goal wi~s may be unified, in which case the resulting wi~ is given the smaller of the costs of the input wi~s. This feature leads to minimality through the exploitation of redundancy.</Paragraph> <Paragraph position="12"> Note that in (41, if wl + w2 <= 1, most specific abduction is favored--why assume Q when it is cheaper to assume PI and P~. Hwlq-w2 I, least specific abduction is favored--why assume PI and P2 when it is cheaper to assume Q. But in pis ^ P~s ~ Q if PI has already been derived, it is cheaper to assume P2 than ~. P1 has provided evidence for Q, and assumlug the &quot;remainder&quot; P2 of the necessary evidence for Q should be cheaper.</Paragraph> <Paragraph position="13"> Factoring can also override least specific abduction.</Paragraph> <Paragraph position="14"> Suppose we have the axioms</Paragraph> <Paragraph position="16"> and we wish to derive ~i ^ ~2, where each conjunct has an assumability cost of $10. Then assuming QI ^ ~2 will cost $20, whereas assuming Pl ^ P2 ^ Ps will cost only $18, since the two instances of P2 can be unified. Thus, the abduction scheme allows us to adopt the careful policy of favoring least specific abduction while also allowing us to exploit the redundancy of texts for more specific interpretations.</Paragraph> <Paragraph position="17"> In the above examples we have used equal weights on the conjuncts in the antecedents. I~ is more reasonable, SThe ~bduction scheme is due to Mark Stickel, and it, or a variant of it, is described at ~-eater length in Stickel (1988).</Paragraph> <Paragraph position="18"> however, to assign the weights according to the &quot;semantic contribution&quot; each conjunct makes to the consequent. Consider, for example, the axiom</Paragraph> <Paragraph position="20"> We have an intuitive sense that ear contributes more to convertible than no-top does. r In principle, the weights in (4) should be a function of the probabilities that instances of the concept Pi are instances of the concept Q in the corpus of interest. In practice, all we can do is assign weights by a rough, intuitive sense of semantic contribution, and refine them by successive approximation on a representative sample of the corpus.</Paragraph> <Paragraph position="21"> One would think that since we are deriving the logical form of the sentence, rather than determining what can be inferred from the logical form of the sentence, we could not use super~et information in processing the sentence. That is, since we are back-chaining from the propositions in the logical form, the fact that, say, lube oil is a fluid, which would be expressed as</Paragraph> <Paragraph position="23"> could not play a role in the analysis. Thus, in the text Flow obstructed. Metal particles in lube oil filter.</Paragraph> <Paragraph position="24"> we know from the first sentence that there is a fluid. We would like to identify it with the lube oil mentioned in the second sentence. In interpreting the second sentence, we must prove the expression</Paragraph> <Paragraph position="26"> If we had as an axiom (Vz)/tuid(z) ~ tub,-al(:) then we could establish the identity. But of course we don't have such an axiom, for it isn't true. There are lots of other kinds of fluids. There would seem to be no way to use superset information in our scheme.</Paragraph> <Paragraph position="27"> Fortunately, however, there is a way. We can make use of this information by converting the axiom into a biconditional. In general, axioms of the form species D genus can be converted into a bieonditional axiom of the form genus A differentiae _= species rTo prime this intuition, imagine two doom. Behind one is n ear. Behind the other is something with no top. You pick a door. If there's a convertible behind it, you get to keep it. Which door would you pick? Often, of course, as in the above example, we will not be able to prove the differentiae, and in many cases the differentiae can not even be spelled out. But in our abductive scheme, this does not matter. They can simply be assumed. In fact, we need not state them explicitly. We can simply introduce a predicate which stands for all the remaining properties. It will never be provable, but it will be assumable. Thus, we can rewrite (5) as (Vz)fluid(z) h etcl(z) _ lube-oil(z) Then the fact that something is fluid can be used as evidence for its being lube oil. With the weights distributed according to semantic contribution, we can go to extremes and use an axiom like</Paragraph> <Paragraph position="29"> to allow us to use the fact that something is a mammal as (weak) evidence that it is an elephant.</Paragraph> <Paragraph position="30"> In principle, one should try to prove the entire logical form of the sentence and the constraints at once. In this global strategy, any heuristic ordering of the individual problems is done by the theorem prover. From a practical point of view, however, the global strategy generally takes longer, sometimes significantly so, since it presents the theorem-prover with a longer expression to be proved.</Paragraph> <Paragraph position="31"> We have experimented both with this strategy and with a bottom-up strategy in which, for example, we try to identify the lube oil before trying to identify the lube oil alarm. The latter is quicker since it presents the theorem-prover with problems in a piecemeal fashion, but the former frequently results in better interpretations since it is better able to exploit redundancies; The analysis of the sentence in Section 4.2 below, for example, requires either the global strategy or very careful axiomatization. The bottom-up strategy, with only a view of a small local region of the sentence, cannot recognize and capitalize on redundancies among distant elements in the sentence. Ideally, we would like to have detailed control over the proof process to allow a number of different factors to interact in deterr-ln~ng the allocation of deductive resources. Among such factors would be word order, lexlcal form, syntactic structure, topic-comment structure, and, in speech, pitch accent .s</Paragraph> </Section> <Section position="6" start_page="98" end_page="101" type="metho"> <SectionTitle> 4 Examples </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="98" end_page="99" type="sub_section"> <SectionTitle> 4.1 Distinguishing the Given and New </SectionTitle> <Paragraph position="0"> We will examine two difllcult definite reference problems in which the given and the new information are intertwined and must be separated. In the first, new and old information about the same entity are encoded in a single noun phrase.</Paragraph> <Paragraph position="1"> SPereira and Pollnck's CANDIDE system (1988) is specifically designed to aid investigation of the question of the most effective order of interpretation.</Paragraph> <Paragraph position="2"> There was adequate lube oil.</Paragraph> <Paragraph position="3"> We know about the lube oil already, and there is a corresponding axiom in the knowledge base.</Paragraph> <Paragraph position="5"> Its adequacy is new information, however. It is what the sentence is telling us.</Paragraph> <Paragraph position="6"> The logical form of the sentence is, roughly,</Paragraph> <Paragraph position="8"> This is the expression that must be derived. The proof of the existence of the lube oil is immediate. It is thus old information. The adequacy can't be proved, and is hence assumed as new information.</Paragraph> <Paragraph position="9"> The second example is from Clark (1975), and illustrates what happens when the given and new information are combined into a single lexical item.</Paragraph> <Paragraph position="10"> John walked into the room.</Paragraph> <Paragraph position="11"> The chandelier shone brightly.</Paragraph> <Paragraph position="12"> What chandelier is being referred to? Let us suppose we have in our knowledge base the fact that rooms have lights.</Paragraph> <Paragraph position="14"> Suppose we also have the fact that lights with numerous fixtures are chandeliers.</Paragraph> <Paragraph position="16"> The first sentence has given us the existence of a room m room(R). To solve the definite reference problem in the second sentence, we must prove the existence of a chandelier. Back-chaining on axiom (7), we see we need to prove the existence of a light with fixtures. Back-chaining from light(1) in axiom (6), we see we need to prove the existence of a room. We have this in room(R). To complete the derivation, we assume the light I has fixtures. The light is thus given by the room mentioned in the previous sentence, while the fact that it has fl.xtures is new information. null</Paragraph> </Section> <Section position="2" start_page="99" end_page="100" type="sub_section"> <SectionTitle> 4.2 Exploiting Redundancy </SectionTitle> <Paragraph position="0"> We next show the use of the abduction scheme in solving internal coreference problems. Two problems raised by the sentence The plain was reduced by erosion to its presen t level.</Paragraph> <Paragraph position="1"> are determining what was eroding and determining what &quot;it&quot; refers to. Suppose our knowledge base consists of the following axioms: (Vp, l, s)decrease(p, l, s) A vertical(s) A etc3(p, I, s) = (3 el)reduce'(el, p, l) or el is a reduction of p to l if and only if p decreases to l on some vertical scale s (plus some other conditions).</Paragraph> <Paragraph position="3"> or e is the condition of l's being the level of y if and only if e is the condition of y's being at I on some vertical scale s and It is fiat (plus some other conditions).</Paragraph> <Paragraph position="4"> (Vz, I, s )decrease( z, I, s) A landform(z) A altitude(a) A etce(y, l, s) -- (3 e)erode'(e, z) or * is an eroding of z if and only if z is a landform that decreases to some point I on the altitude scale s (plus some other conditions)deg (Vs)vertical(s) A etcr(p) - altitude(s) or s is the altitude scale if and only if s is vertical (plus some other conditions).</Paragraph> <Paragraph position="5"> Now the analysis. The logical form of the sentence is roughly (3 ca, p, l, z, e2, It)reduce'(el, p, l) A plain(p) A erode'(el, z) A present(e2) A level'(e2, l, y) Our characterization of interpretation says that we must derive this expression from the axioms or from assumptions. Back-chainlng on reducer(el, p, l) yields decrease(p, l, sl) A vertical(s1 ) A etcs(p, l, sl ) Back-cb~r~ing on erode'(e:, z) yields decrease(z, 12,s2) A landform(z) ^ altitude(s2) A etc4( z,12, s2 ) and back-chaining on altitude(s2) in turn yields vertical(s2) A etcr( s2 ) We unify the goals decrease(p, I, st) and decrease(z, 12, s2), and thereby identify the object of the erosion with the plain. The goals vertical(sl ) and vertical(s2) also unify, telling us the reduction was on the altitude scale. Back-chaining on plain(p) yields landform(p) A flat(p) A ete,(p) and landform(z) unifies with landform(p), reinforcing our identification of the object of the erosion with the plain. Back-chainlng on level'(e2, I, y ) yields</Paragraph> <Paragraph position="7"> and vertical(s3) and vertical(s2) unify, as do flat(y) and flat(p), thereby identifying &quot;it&quot;, or y, as the plain p. We have not written out the axioms for this, but note also that &quot;present&quot; implies the existence of a change of level, or a change in the location of &quot;it&quot; on a vertical scale, and a decrease of a plain is a change of the plain's location on a vertical scale. Unifying these would provide reinforcement for our identification of &quot;it&quot; with the plain. Now assuming the most specific atoms we have derived including all the &quot;et cetera&quot; conditions, we arrive at an interpretation that is minimal and that solves the internal coreference problems as a byproduct.</Paragraph> </Section> <Section position="3" start_page="100" end_page="101" type="sub_section"> <SectionTitle> 4.3 A Thorough Integration of Syntax, Semantics, and Pragmatics </SectionTitle> <Paragraph position="0"> By combining the idea of interpretation as abduction with the older idea of parsing as deduction (Kowalski, 1980, pp.</Paragraph> <Paragraph position="1"> 52-53; Pereira and Warren, 1983), it becomes possible to integrate syntax, semantics, and pragmatics in a very thorough and elegant way. 9 Below is a simple grammar written in Prolog style, but incorporating calls to local pragmatics.</Paragraph> <Paragraph position="2"> The syntax portion is represented in standard Prolog manner, with nonterminals treated as predicates and having as two of its arguments the beginning and end points of the phrase spanned by the nonterminal. The one modification we would have to make to the abduction scheme is to allow conjuncts in the antecedents to take costs directly as well as weights. Constraints on the application of phrase structure rules have been omitted, but could be incorporated in the usual way.</Paragraph> <Paragraph position="3"> (Vi,j, k, x,p, args, req, e, c, rel)np(i, j, x) A vp(j, k,p, args, req) A 'pt(e, c) $3 A rel(c, z) $2deg A subst(req, cons(c, args)) $1deg D s(i, k, e) (V i, j, k, e, p, ar gs, req, et, c, ~el)s( i, j, e) A pp(j, k,p, args, req) A p'(el, c) s3 A tel(c, e) 12deg A subst(req, cons(c, args)) *xdeg D s(i, k, e&el)</Paragraph> <Paragraph position="5"> A pp(j, k,p2, args, req) (Vi,j, k, w, z, c, rel)prep(i, j, w) ^ np(j, k, x) A rel(c, z) Indeg 3 ptXi, k, ,~z\[w(c, z)\], <c>, Req(w)) For example, the first axiom says that there is a sentence from point i to point k asserting eventuality e if there is a noun phrase from i to j referring to z and a verb phrase from j to k denoting predicate p with arguments arg8 and having an associated requirement req, and there is (or, for $3, can be assumed to be) an eventuality e of p's being true of C/, where c is related to or coercible from x (with an assumability cost of $20), and the requirement req associated with p can be proved or, for $10, assumed to hold of the arguments of p. The symbol c&el denotes the conjunction of eventualities e and el (See Hobbs (1985b), p. 35.) The third argument of predicates corresponding to terminal nodes such as n and det is the word itself, which then becomes the name of the predicate. The function Req returns the requirements associated with a predicate, and subst takes care of substituting the right arguments into the requirements. <c> is the list consisting of the single element c, and cons is the LISP function cons. The relations re/and nn are treated here as predicate variables, but they could be treated as predicate constants, in which case we would not have quantified over them.</Paragraph> <Paragraph position="6"> In this approach, s(0, n, e) can be read as saying there is an interpretable sentence from point 0 to point n (asserting e). Syntax is captured in predicates like np, vp, and s. Compositional semantics is encoded in, for example, the way the predicat e p' is applied to its arguments in the first axiom, and in the lambda expression in the third argument of vp in the third axiom. Local pragmatics is captured by virtue of the fact that in order to prove s(O, n, e), one must derive the logical form of the sentence together with the constraints predicates impose on their arguments, allowing for metonymy.</Paragraph> <Paragraph position="7"> Implementations of different orders of interpretation, or different sorts of interaction among syntax, compositional semantics, and local pragmatics, can then be seen as different orders of search for a proof of s(O, n, e). In a syntax-first order of interpretation, one would try first to prove all the &quot;syntactic&quot; atoms, such as np(i,j,x), before any of the &quot;local pragmatic&quot; atoms, such as p'(e, c). Verb-driven interpretation would first try to prove vp(j, k, p, args, req) by proving v(i, j, w) and then using the information in the requirements associated with the verb to drive the search for the arguments of the verb, by deriving subst(req, cons(c, args)) before trying to prove the various np atoms. But more fluid orders of interpretation are obviously possible. This formulation allows one to prove those things first which are easiest to prove. It is also easy to see how processing could occur in parallel.</Paragraph> <Paragraph position="8"> It is moreover possible to deal with ill-formed or unclea~ input in this framework, by having axioms such as this revision of our first axiom above.</Paragraph> <Paragraph position="9"> (V i, j, k, z, p, args, req, e, c, tel)rip(i, j, z) '4 ^ vp(j, k,p, args, req) &quot;s ^ p'(e, c) Is A re/(c, :)12o A subst(req, cons(c, args)) stdeg D s(i, k, e) This says that a verb phrase provides more evidence for a sentence than a noun phrase does, but either one can constitute a sentence if the string of words is otherwise interpretable.</Paragraph> <Paragraph position="10"> It is likely that this approach could be extended to speech recognition by using Prolog-style rules to decompose morphemes into their phonemes and weighting them according to their acoustic prominence.</Paragraph> </Section> </Section> <Section position="7" start_page="101" end_page="101" type="metho"> <SectionTitle> 5 Controlling Abduction: Type </SectionTitle> <Paragraph position="0"> Hierarchy The first example on which we tested the new abductive scheme was the sentence There was adequate lube oil.</Paragraph> <Paragraph position="1"> The system got the correct interpretation, that the lube oil was the lube oil in the lube oil system of the air compressor, and it assumed that that lube oil was adequate. But it also got another interpretation. There is a mention in the knowledge base of the adequacy of the lube oil pressure, so it identified that adequacy with the adequacy mentioned in the sentence. It then assumed that the pressure was lube oil.</Paragraph> <Paragraph position="2"> It is clear what went wrong here. Pressure is a ma~irude whereas lube oil is a material, and magnitudes can't be materials. In principle, abduction requires a check for the consistency of what is e.mumed, and our knowledge base should have contained axioms from which it could be inferred that a magnitude is not a material. In practice, unconstrained consistency checking is undecidable and, at best, may take a long time. Nevertheless, one can, through the use of a type hierarchy, eI~minate a very large number of possible assumptions that are likely to result in an inconsistency. We have consequently hnplemented a module which specifies the types that various predicate-argument positions can take on, and the likely disjointness relations among types. This is a way of exploiting the specificity of the English lexicon for computational purposes. This addition led to a speed-up of two orders of magn/tude.</Paragraph> <Paragraph position="3"> There is a problem, however. In an ontologically promiscuous notation, there is no commitment in a primed proposition to truth or existence in the real world. Thus, \]ubeoil'(e, o) does not say that o is lube oil or even that it exists; rather it says that * is the eventuality of o's being lube oil. This eventuality may or may not exist in the real world. If it does, then we would express this as Re,fists(e), and from that we could derive from axioms the existence of o and the fact that it is lube oil. But e's existential status could be something different. For example, e could be nonexistent, expressed as not(e) in the notation, and in English as &quot;The eventuality e of o's being lube oil does not exist,&quot; or as &quot;o is not lube oil.&quot; Or e may exist only in someone's beliefs. While the axiom</Paragraph> <Paragraph position="5"> is certainly true, the axiom (Vel,z)~essure'(e,,=) ~ -,(3 eDtu~e-oir(e2, =) would not be true. The fact that a variable occupies the second argument position of the predicate lube-o/l' does not mean it is lube oil. We cannot properly restrict that ar~Btment position to be lube oil, or fluid, or even a material, for that would rule out perfectly true sentences like &quot;~uth is not lube oil.&quot; Generally, when one uses a type hierarchy, one assumes the types to be disjoint sets with cleanly dei~ed boundaries, and one assumes that predicates take arguments of only certain types. There are a lot of problems with this idea- In any case, in our work, we are not buying into this notion that the universe is typed. P~ther we are using the type hierarchy strictly as a heuristic, as a set of guesses not about what could or could not be but about what it would or would not occur to someone to 5~zI/. ~'hen two types are declared to be disjoint, we are saying that they are certainly disjoint in the real world, and that they are very probably disjoint everywhere except in certain bizarre modal contexts. This means, however, that we risk fmling on certain rare examples. We could not, for example, deal with the sentence, ~It then assumed that the pressure was lube oily</Paragraph> </Section> class="xml-element"></Paper>