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<Paper uid="H90-1012">
  <Title>Making Abduction More Efficient</Title>
  <Section position="1" start_page="0" end_page="61" type="abstr">
    <SectionTitle>
SRI International
</SectionTitle>
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    <Section position="1" start_page="0" end_page="60" type="sub_section">
      <SectionTitle>
Menlo Park, California
Introduction
</SectionTitle>
      <Paragraph position="0"> The TACITUS system uses a cost-based abduction scheme for finding and choosing among possible interpretations for natural language texts. Ordinary Prologstyle, backchaining deduction is augmented with the capability of making assumptions and of factoring two goal literals that are unifiable (see Hobbs et al., 1988).</Paragraph>
      <Paragraph position="1"> Deduction is combinatorially explosive, and since the abduction scheme augments deduction with two more options at each node--assumption and factoring--it is even more explosive. We have been engaged in an empirical investigation of the behavior of this abductive scheme on a knowledge base of nearly 400 axioms, performing relatively sophisticated linguistic processing. So far, we have begun to experiment, with good results, with three different techniques for controlling abduction--a type hierarchy, unwinding or avoiding transitivity axioms, and various heuristics for reducing the branch factor of the search.</Paragraph>
      <Paragraph position="2"> The Type Hierarchy The first example on which we tested the abductive scheme was the sentence There was adequate lube oil.</Paragraph>
      <Paragraph position="3"> 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="4"> It is clear what went wrong here. Pressure is a magnitude whereas lube oil is a material, and magnitudes can't be materials. In principle, abduction requires a check for the consistency of what is assumed, 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, eliminate a very large number of possible assumptions that are likely to result in an inconsistency. We have consequently implemented a module that 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 magnitude.</Paragraph>
      <Paragraph position="5"> A further use of the type hierarchy speeds up processing by a factor of 2 to 4. The types provide prefiltering of relevant axioms for compound nominal, coercion, and other very general relations. Suppose, for example, that we wish to prove rel(a, b), and we have the two axioms Without a type hierarchy we would have to backchain on both of these axioms. If, however, the first of the axioms is valid only when x and y are of types tl and t2, respectively, and the second is valid only when x and y are of types t3 and t4, respectively, and a and b have already been determined to be of types tl and t2, respectively, then we need only backchain on the first of the axioms.</Paragraph>
      <Paragraph position="6"> There is a problem with the type hierarchy, however.</Paragraph>
      <Paragraph position="7"> In an ontologically promiscuous notation, there is no commitment in a primed proposition to truth or existence in the real world. Thus, lube-oill(e,o) does not say that o is lube oil or even that it exists; rather it says that e 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 Rexists(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 &amp;quot;The eventuality e of o's being lube oil does not exist,&amp;quot; or simply as &amp;quot;o is not lube oil.&amp;quot; Or e may exist only in someone's beliefs or in some other possible world. While the axiom (Vx)press=re(x) l be-oiZ(x) is certainly true, the axiom</Paragraph>
      <Paragraph position="9"> would not be true. The fact that a variable occupies the second argument position of the predicate lube-oil ~ does not mean it is lube oil. We cannot properly restrict that argument position tobe lube oil, or fluid, or even a material, for that would rule out perfectly true sentences like &amp;quot;Truth is not lube oil.&amp;quot; Generally, when one uses a type hierarchy, one assumes the types to be disjoint sets with cleanly defined 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. Rather 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 say. When 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 failing on certain rare examples. We could not, for example, deal with the sentence, &amp;quot;It then assumed that the pressure was lube oil.&amp;quot; Unwinding or Avoiding Transitivity Axioms In general, one must exercise a certain discipline in the axioms one writes. At one point, in order to conclude from the sentence Bombs exploded at the offices of French-owned firms in Catalonia.</Paragraph>
      <Paragraph position="10"> that the country in which the terrorist incident occurred was Spain, we wrote the following axiom: (V x, y, z)in(x, y) A partof(y, z) D in(x, z) That is, if x is in y and y is a part of z, then x is also in z. The interpretation of this sentence was taking an extraordinarily long time. When we examined the search space, we discovered that it was dominated by this one axiom. We replaced the axiom with several axioms that limited the depth of recursion to three, and the problem disappeared.</Paragraph>
      <Paragraph position="11"> In general, one must exercise a certain discipline in the axioms one writes. Which kinds of axioms cause trouble and how to replace them with adequate but less dangerous axioms is a matter of continuing investigation. Reducing the Branch Factor of</Paragraph>
    </Section>
    <Section position="2" start_page="60" end_page="61" type="sub_section">
      <SectionTitle>
the Search
</SectionTitle>
      <Paragraph position="0"> It is always useful to reduce the branch factor of the search for a proof wherever possible. There are several heuristics we have devised so far for accomplishing this.</Paragraph>
      <Paragraph position="1"> The first heuristic is to prove the easiest, most specific conjuncts first, and then to propagate the instantiations.</Paragraph>
      <Paragraph position="2"> For example, in the domain of naval operations reports, words like &amp;quot;Lafayette&amp;quot; are treated as referring to classes of ships rather than to individual ships. Thus, in the sentence Lafayette sighted.</Paragraph>
      <Paragraph position="3"> &amp;quot;Lafayette&amp;quot; must be coerced into a physical object that can be sighted. We must prove the expression</Paragraph>
      <Paragraph position="5"> The predicate Lafayette is true only of the entity LAFA YETTE-CLASS. Thus, rather than trying to prove tel(y, x) first, leading to a very explosive search, we try first to prove Lafayette(x). We succeed immediately, and propagate the value LAFAYETTE-CLASS for x. We thus have to prove rel(y, LAFAYETTE-CLASS). Because of the type of LAFAYETTE-CLASS, only one axiom applies, namely, the one allowing coercions from types to tokens that says that y must be an instance of LAFAYETTE-CLASS.</Paragraph>
      <Paragraph position="6"> Similar heuristics involve solving reference problems before coercion problems and proving conjuncts whose source is the head noun of a noun phrase before proving conjuncts derived from adjectives.</Paragraph>
      <Paragraph position="7"> Another heuristic is to eliminate assumptions wherever possible. We are better off if at any node, rather than having either to prove an atomic formula or to assume it, we only have to prove it. Some predicates are therefore marked as nonassumable. One category of such predicates are the &amp;quot;closed-world predicates&amp;quot;, those predicates such that we know all entities of which the predicate is true. Predicates representing proper names, such as Enterprise, and classes, such as LafayeLte, are examples. We don't assume these predicates because we know that if they are true of some entity, we will be able to prove it.</Paragraph>
      <Paragraph position="8"> Another category of such predicates is the &amp;quot;schemarelated&amp;quot; predicates. In the naval operations domain, the task is to characterize the participants in incidents described in the message. This is done, as described in Section 5.4. A schema is encoded by means of a schema predication, with an argument for each role in the schema. Lexical realizations and other consequences of schemas are encoded by means of schema axioms.</Paragraph>
      <Paragraph position="9"> Thus, in the jargon of naval operations reports, a plane can splash another plane. The underlying schema is called Init-Act. There is thus an axiom (V x, y, . . .)Init-Act(x, y, attack,...) D splash(x, y) Schema-related predicates like splash occurring in the logical form of a sentence are given very large assumption costs, effectively preventing their being assumed. The weight associated with the antecedent of the schema axioms is very very small, so that the schema predication can be assumed very cheaply. This forces backchaining into the schema.</Paragraph>
      <Paragraph position="10"> In addition, in the naval operations application, coercion relations are never assumed, since this is what drives the use of the type hierarchy.</Paragraph>
      <Paragraph position="11">  Factoring also multiplies the size of the search tree wherever it can occur. As explained above, it is a very powerful method for coreference resolution. It is based on the principle that where it can be inferred that two entities have the same property, there is a good possibility that the two entities are identical. However, this is true only for fairly specific properties. We don't want to factor predicates true of many things. For example, to resolve the noun phrase ships and planes we need to prove the expression</Paragraph>
      <Paragraph position="13"> where Plural is taken to be a relation between the typical element of a set and the set itself. If we applied factoring indiscriminately, then we would factor the conjuncts Plural(x, sl) and Plural(y, s2), identifying x with y and Sl with s2. If we were lucky, this interpretation would be rejected because of a type violation-planes aren't ships. But this would waste time. It is more reasonable to say that very general predicates such as Plural provide no evidence for identity.</Paragraph>
      <Paragraph position="14"> The type hierarchy, the discipline imposed in writing axioms, and the heuristics for limiting search all make the system less powerful than it would otherwise be, but we implement these techniques for the sake of efficiency.</Paragraph>
      <Paragraph position="15"> There is a kind of scale, whose opposite poles are efficiency and power, on which we are trying to locate the system. It is a matter of ongoing investigation where on that scale we achieve optimal performance.</Paragraph>
    </Section>
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