Interpretation as abduction

TL;DR: In this article, the TACITUS project at SRI developed an approach to abductive inference, called "weighted abduction" that has resulted in a significant simplification of how the problem of interpreting texts is conceptualized.

About: This article is published in Artificial Intelligence.The article was published on 1993-10-01 and is currently open access. It has received 856 citations till now. The article focuses on the topics: Pragmatics & Abductive reasoning.

Summary

1 Introduction

• Abductive inference is inference to the best explanation.
• The process of interpreting sentences in discourse can be viewed as the process of providing the best explanation of why the sentences would be true.
• In a discourse situation, the speaker and hearer both have their sets of private beliefs, and there is a large overlapping set of mutual beliefs.
• In Section 2 of this paper, the authors justify the first clause of the above characterization by showing that solving local pragmatics problems is equivalent to proving the logical form plus the constraints.

Local Pragmatics

• The fbur local pragmatics problems the authors have addressed can be illustrated by the following "sentence" from the casualty reports: (2) Disengaged compressor after lube-oil alarm.
• The authors wish to show that solving the farst three of these problems amounts to deriving the logical form of the sentence.
• In general, the authors 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.
• Where "sample" is indefinite, or new information, and "filter" is definite, or already known to the hearer.
• To resolve the reference of the noun phrase "lube-oi] alarm", the authors need to Find two entities o and a with the appropriate properties.

(3 o, a, nn)tu~-oit(o) ^ atarm(a) ^ nn(o, a)

• 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.
• 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) .
• The symbol nn is treated as a predicate constant, and the most common possible relations (see Levi, 1978) are encoded in axioms.

.).., h after(k1, k2)

• 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.
• 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.

A nn(o, a) A tube-oil(o)

• But this is just the logical form of the sentence 4 together with the constraints that predicates impose on their arguments, allowing for coercions.
• When parts of this expression cannot be derived, assumptions must be made, and these assumptions are taken to be the new information.
• The main verb is more likely to convey new information than a definite noun phrase.
• Tlus cost is expressed in the same currency in which other factors involved in the "goodness" 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.
• Bare noun phrases are given an inte~ediate cost, say, $5.

^ cornpreJsor(c) ss ^ aftcr(kt, k2)" ^event(k~) .2° ^ rel(kt,y) *~ ^ y ~ {c,e} A event(k2) sa° A rel(k2,a) s2° A alarm(a) gs ^ nn(o, a) s~° ^ tube-oil(o)"

• 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.
• 4For justification for this kind of logical form for sentences with quantifiers and inteusional operators, see Hobbs(1983) and Hobbs (1985a) .

3 Abduction

• The authors now argue for the last half of the characterization (I) of interpretation.
• One obvious criterion is consistency of p(A I with the rest of what one knows.
• Consider Inspection of oll filter revealed metal particle~.
• Another issue that arises in abduction is what might be called the "informativeness-correctness tradeotP'.
• The authors want the most specific possible explanation.

SSometimes a cigar is just a cigar.

• The authors 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 their assumptions are, the more informative their interpretation is.
• 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.
• 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.
• In the above examples the authors have used equal weights on the conjuncts in the antecedents.

(Vz)ear(z) "s A no-top(z) "4 D convertible(x)

• The authors have an intuitive sense that ear contributes more to convertible than no-top does.
• One would think that since the authors are deriving the logical form of the sentence, rather than determining what can be inferred from the logical form of the sentence, they could not use super~et information in processing the sentence.
• That is, since the authors are back-chaining from the propositions in the logical form, the fact that, say, lube oil is a fluid, which would be expressed as (.

5) (Vz)lube-oil(z) D fluid(z)

• The authors know from the first sentence that there is a fluid.
• The authors would like to identify it with the lube oil mentioned in the second sentence.
• In interpreting the second sentence, the authors must prove the expression.

(Vz)/tuid(z) ~ tub,-al(:)

• The authors 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.
• If there's a convertible behind it, you get to keep it.
• But in their abductive scheme, this does not matter.
• The authors can simply introduce a predicate which stands for all the remaining properties.

(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, the authors can go to extremes and use an axiom like.

(Vz)rnammal(z) "2 A atc2(z) "s D elephant(z)

• In principle, one should try to prove the entire logical form of the sentence and the constraints at once.
• 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.
• The authors have experimented both with this strategy and with a bottom-up strategy in which, for example, they try to identify the lube oil before trying to identify the lube oil alarm.
• The analysis of the sentence in Section 4.2 below, for example, requires either the global strategy or very careful axiomatization.
• Among such factors would be word order, lexlcal form, syntactic structure, topic-comment structure, and, in speech, pitch accent .s 4 Examples 4.1 Distinguishing the Given and New We will examine two difllcult definite reference problems in which the given and the new information are intertwined and must be separated.the authors.the authors.

lube-oil( O)

• This is the expression that must be derived.
• The proof of the existence of the lube oil is immediate.
• The adequacy can't be proved, and is hence assumed as new information.
• The second example is from Clark (1975) , and illustrates what happens when the given and new information are combined into a single lexical item.

What chandelier is being referred to?

• Let us suppose the authors have in their knowledge base the fact that rooms have lights.
• (6) (Vr)roorn(r) D (31)light (1) A in(l,r) Suppose the authors also have the fact that lights with numerous fixtures are chandeliers.

(7) (Vl)light(l) A has-fiztures(l) D chandelier(l)

• To solve the definite reference problem in the second sentence, the authors must prove the existence of a chandelier.
• To complete the derivation, the authors 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.

4.2 Exploiting Redundancy

• The authors next show the use of the abduction scheme in solving internal coreference problems.
• The plain was reduced by erosion to its presen t level.
• Are determining what was eroding and determining what "it" refers to.

vertical(s2) A etcr( s2 )

• The authors 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.
• Backchaining on plain(p) yields landform(p) A flat(p) A ete,(p) and landform(z) unifies with landform(p), reinforcing their identification of the object of the erosion with the plain.
• Unifying these would provide reinforcement for their identification of "it" with the plain.
• Now assuming the most specific atoms the authors have derived including all the "et cetera" conditions, they arrive at an interpretation that is minimal and that solves the internal coreference problems as a byproduct.

Semantics, and Pragmatics

• By combining the idea of interpretation as abduction with the older idea of parsing as deduction (Kowalski, 1980 , pp. 52-53; Pereira and Warren, 1983) , it becomes possible to integrate syntax, semantics, and pragmatics in a very thorough and elegant way.
• Below is a simple grammar written in Prolog style, but incorporating calls to local pragmatics.
• 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.
• Constraints on the application of phrase structure rules have been omitted, but could be incorporated in the usual way.

3 ptXi, k, ,~z[w(c, z)], <c>, Req(w))

• 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.
• In a syntax-first order of interpretation, one would try first to prove all the "syntactic" atoms, such as np(i,j,x), before any of the "local pragmatic" atoms, such as p'(e, c).
• But more fluid orders of interpretation are obviously possible.
• This formulation allows one to prove those things first which are easiest to prove.

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.
• 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.

5 Controlling Abduction: Type Hierarchy

• The first example on which the authors tested the new abductive scheme was the sentence.
• The authors 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 eventuality may or may not exist in the real world.
• But e's existential status could be something different.
• The authors could not, for example, deal with the sentence, ~It then assumed that the pressure was lube oily.

Frequently asked questions

Q1. What are the contributions in this paper?

An approach to abductive inference developed in the TACITUS project has resulted in a dramatic simplification of how the problem of interpreting texts is conceptualized. It also suggests an elegant and thorough integration of syntax, semantics, and pragmatics. 

Q2. What is the meaning of r e / a n d n?

The relations r e / a n d nn are treated here as predicate variables, but they could be treated as predicate constants, in which case the authors would not have quantified over them. 

Q3. What is the meaning of s(O, n, e)?

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). 

Q4. What are the main components of the study?

In addition to type checking, the authors have introduced two other tevhnlques that are necessary for controlling the exploslon~unwinding recursive axioms and making use of syntactic noncoreference information. 

Q5. What is the syntax of the sentence?

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. 

Q6. What is the syntax portion of the grammar?

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.