Intentionality in the Abductive Framework

The issue of what the assertion of the composite segment in Axiom (1) should be requires us to build up some more machinery. The assertion of the composite segment is of no significance when that segment is viewed in isolation. It plays a role only when we try to embed the segment in a larger context. We can see the problem without moving beyond the informational aspect of discourse by embedding (3) in a dialogue. Suppose the reply to (3) is

(15)	That's wonderful!

We need to be able to figure out whether ``that'' refers to the happiness or the promotion. Clearly it is the promotion. The Evaluation relation of Hobbs (1985) requires that the second segment (15) be a comment on the assertion of the first (3). This will be satisfied if we resolve ``that'' to the assertion of composite segment (3). But that means the assertion of composite segment (3) must be e₂, not e₁ as provided by Axiom (1).

However, when we hear or read (3) in isolation, we already know the main point of the composite segment is the promotion; we do not need to wait for the response. The reason is that the promotion is a newsworthy event, whereas happiness is generally not, or at least that promotions are much more newsworthy than happiness.

To accomodate this observation in the formal framework, we have to move beyond the text and consider the environment in which the text is embedded. We have to take into account that discourse is intentional, goal-directed action. An approach that incorporates this basic assumption into the abductive framework is sketched in Hobbs (1996b). What we present here is a very simplified version of that approach.

The key idea is that an intelligent agent's interpretation of the world in general is an abductive process. An agent is presented with a multitude of observables occurring in a history of observables, and the job of the agent is to figure out the best explanation for that set of observables, consistent with the history. As before, this explanation requires that assumptions be made, and optimality involves factors such as minimizing the number of assumptions, minimizing the length of the chains of inference used, maximizing plausibility and salience, maximizing consistency with the rest of what the agent knows, exploiting redundancy in explanation, and so on.

In discourse, the observable to be explained is that someone uttered a string of sounds. The most reasonable explanation for this is that the action was intentional and was intended to convey some meaning to an addressee. It serves the speaker's goals, and one of the speaker's goals is to report newsworthy events. Skipping over several steps, we can represent this consideration by the following axiom:

(16)	$Segment(w,e) \& newsworthy(e) \, \supset \,utter(i,u,w)$

That is, if w is a coherent segment of discourse that describes a situation e where e is newsworthy, then (defeasibly) some speaker i will utter w to some hearer u.

Although our notion of newsworthiness is context-relative and not restricted to eventualities that are intrinsically newsworthy, we will simplify the example by assuming that promotions are intrinsically newsworthy:

(17)	$promotion(e_{2},x) \, \supset \,newsworthy(e_{2})$

That is, if e₂ is x's promotion, then e₂ is newsworthy.

A coherent segment may consist of a single sentence, or it may consist of more than one sentence. In the latter case, it must have been composed of smaller segments related by coherence relations. The following axiom, from IA, Section 6.3, captures this:

(18)	$Segment(w_{1},e_{1}) \& Segment(w_{2},e_{2}) \& CoRel(e_{1},e_{2},e)$
	$\, \supset \,Segment(w_{1} w_{2},e)$

If the string w₁ is a coherent segment conveying e₁, string w₂ is a coherent segment conveying e₂, and there is a coherence relation relating e₁ and e₂ yielding e, then the concatenation w₁ w₂ is a coherent segment conveying e.

A single, grammatical, interpretable sentence is also a coherent segment. In Hobbs (1996c) a substantial fragment of the syntax of English is developed in a manner somewhat similar to the treatment in IA, Section 6.1, integrating syntax with the other processes of interpretation in a thorough fashion. In this treatment, the predication

(19)	$Syn(w,e,\ldots)$

says that the string w is a grammatical, interpretable string of words describing the situation or entity e. The arguments of Synindicated by the dots include information about complements and various agreement features. The interface between syntax and discourse is effected by the axiom

(20)	$Syn(w,e,\ldots) \, \supset \,Segment(w,e)$

A grammatical, interpretable sentence w describing eventuality eis a coherent segment of discourse describing e. Composition in this framework is effected by axioms of the form

(21)	$Syn(w_{1},e,\ldots,y,\ldots) \& Syn(w_{2},y,\ldots) \, \supset \, Syn(w_{1} w_{2},e,\ldots)$

A string w₁ whose head describes the eventuality e and which has an unsaturated argument y can be concatenated with a string w₂describing y, yielding a string describing e. (This axiom, by the way, is a specialization of Axiom (18), in which the relation conveyed by adjacency is the predicate-argument relation.) The interface between syntax and world knowledge in this approach is effected by ``lexical axioms'' of a form illustrated by

(22)	$read'(e,x,y) \& text(y) \, \supset \,Syn($``read'' $,e,\ldots,x,\ldots,y,\ldots)$

If e is the eventuality of x reading y (the logical form fragment supplied by the word ``read''), where y is a text (the selectional constraint imposed by ``read''), then e can be described by a phrase headed by the word ``read'' provided it picks up, as subject and object, phrases of the right sort describing x and y.

In this note, where possible, we avoid the details of syntax by drawing links from the logical form fragment for a sentence or phrase directly to its Syn predication.

With this machinery we can now embed example (3) in its context of utterance. This is illustrated in Figure .

  

Figure: Explanation of the Uttering of (3).

The uttering of example (3) is the observable to be explained. Using Axiom (16) this can be explained by being a coherent segment conveying newsworthy information. By Axiom (18), we can show it is a coherent segment of discourse by showing it is composed of two coherent segments of discourse related by a coherence relation. By Axiom (20) each of the component strings can be shown to be coherent segments by showing them to be grammatical sentences. We skip over the details of syntax by generating the logical forms for the sentences immediately below the Syn predications. The remainder of the proof is as in Figure .

There is a problem here however. Axiom (16) insists that the assertion e associated with the segment of discourse w₁ w₂ be newsworthy. By Axiom (17) the promotion e₂ is newsworthy, and is thus a good candidate. But the assertion provided by the Explanation pattern, Axiom (1), is the happiness e₁. There is a mismatch. We have now pinpointed in the formal framework exactly where the objection of Redeker (in press) has its force.