Introduction:
Blutner's (1999) bi-directional OT is both (i) theoretically appealing, and (ii) has proven to be empirically successful. To a large extend, Blutner's bi-directional OT was motivated by Atlas & Levinson's (1981) reduction of Grice's (1975) maxims to the so-called Q and I-principles. In this paper I want to argue that (i) there are major problems for reducing Gricean pragmatics to these two principles, and (ii) that, in fact, the Q and I principles of bi-directional OT should be replaced by two other opposing principles; Relevance versus Effort.
The Q and I principle:
The Q principle (implementing Grice's first maxim of Quantity) advises the speaker to say as much as he can to fulfil his communicative goals, while the I-principle (implementing Grice's other maxims, except for quality) advises the speaker to say no more than he must to fulfil these goals. Both principles help to strengthen what is communicated by a sentence. The Q-principle induces inferences from the use of one expression to the assumption that the speaker did not intend to communicate a contrasting, and informationally stronger, one. This principle is thus essentially metalinguistic in kind, and accounts for both `scalar' and `clausal' implicatures. It allows us, for instance, to conclude from ``John ate SOME of the cookies'' to ``John didn't eat ALL of the cookies'' (scalar implicature), and from ``A or B'' to ``A or B, but not both'' (clausal + scalar implicature). The I principle allows us to infer from the use of an expression to its most informative or stereotypical interpretation. It is used, for instance, to enrich the interpretation of a conjunction to a temporal sequential, or causal, relation, and it allows us to interpret a conditional like `John walks, if Mary walks' as the biconditional `John walks if and only Mary walks'.
Problems for the Q and I principles:
Although the Q and I principles are intuitively appealing, they give rise to a number of conceptual and empirical problems. Let's start with some cases where it is predicted that Q-implicatures arise, although in fact they don't. First, at least when implemented as Gazdar (1979) did, we can derive from the existential ``Someone is sick'' as a Q-implicature that (the speaker knows that) `a' is not sick, for any individual `a'. Second, it is predicted that we can infer from `B, if A' to the conclusion that it is not the case that the stronger `B if and only if A' holds, although in a lot of situations this is exactly what we can conclude. Levinson and others have argued that these two problems can be prevented by (i) weakening the force of Q-implicatures from know-not to not-know (for the first problem), and by stipulating that for some cases Q implicatures do not arise for lack of a corresponding contrasting expression (for the second problem). The biconditional interpretation is then said to be due to an I-implicature. The most serious problematic cases where Q-implicatures overgenerate, however, cannot be explained away in this way; The Horn/Gazdar/Levinson/Atlas analysis of Q-implicartures as GENERALISED conversational implicatures (PCIs) triggered solely by lexical expressions cannot explain why from A's answer ``John has 2 children'' to Q's question ``Who has 2 children?'' the implicature ``John has only 2 children'' does not even arise as a default (cf. van Kuppevelt). This latter example seems to suggest that these so-called Q-implicatures are, after all, dependent on the conversational situation, in particular on the question being asked.
Not only does the standard analysis of Q-implicatures overgeneralize, it also doesn't seem to be general enough. First, as discussed extensively by Hirschberg (1985), the standard analysis is of no help to account for certain examples that intuitively should be analysed as scalar implicatures. If Mary's potential new boss asks her at her job-interview whether she speaks French, and she answers by saying ``My sister does'', he can conclude that Mary herself does not. The standard analysis fails to account for this, because (a) scalar implicatures are all analysed in terms of the Q-principle, (b) the Q-principle is stated in terms of INFORMATIVITY, but (c) the proposition that Mary speaks French is not more INFORMATIVE (i.e. entails) than the proposition that her sister does. This example suggests (i) that scalar implicatures should not exclusively be accounted for in terms of informativity, and (ii) that just like in the previous example, also here the relevant implicature crucially depends on the conversational situation (i.e. the beliefs and preferences of the agents inolved). A second example where the standard analysis of Q-implicatures isn't general enough was discussed by Groenendijk & Stokhof (1984). They observe that when A answers Q's question ``Who comes?'' by saying ``Peter comes'', we typically interpret the answer as being exhaustive. That is, we interpret A's answer as ``Only Peter comes''. They claim that this kind of inference should intuitively be accounted for in terms of Grice's maxim of Quantity (as a Q-implicature), but note that the standard implementation does not predict the exhaustivity of the answer. Still, it seems that the exhaustive interpretation of the answer should be derived by Gricean pragmatics on the assumption that answers are as informative as the question requires.
Our conclusion that the scales relevant for the implicatures depend on the conversational situation (i.e. question asked) and the beliefs and preferences of the agents involved is in correspondence with Hirschberg's claim that scales are dependent on context. However, we would like to say something more; we would also like to say HOW the relevant scale depends on the question asked and the relevant beliefs and desires.
Relevance:
In this respect, important progress has been made recently by Merin (1997). Following the lead of Anscombre & Ducrot (1983), Merin argues that scales should be defined not in terms of informativity, but rather in terms of a notion of RELEVANCE. The relevance of a proposition is determined in terms of the ARGUMENTATIVE FORCE force the proposition would have in that particular conversational situation. The relevance of an assertion is then defined in information/decision/game theoretical terms, based on the assumption that the participants of the conversation have strictly opposing preferences, i.e. that the participants play a zero-sum game.
Although Merin convincingly shows that some scalar implicatures (in particular the Hirschberg examples) can be accounted for appropriately on the assumption that players argue for particular hypotheses, and that their contribution should be interpreted in the most relevant way (i.e. strongest argument), it is intuitively clear that not all conversations can, and should, be modeled as zero-sum games. It makes little sense, for instance, to assume that the exhaustive interpretation of ``John has 2 children'' as answer to the question ``How many children does John have?'' can be explained in terms of opposing preferences between questioner and answerer, for the latter typically cooperates with the former. What is called for, then, is a GENERALISATION of Merin's notion of relevance that also measures the relevance of propositions in COOPERATIVE conversational situations. It seems only natural, on the assumption that speakers are relevance optimizers, that once we can define such a measure, not only the typical Q-implicatures can be accounted for in terms of relevance, but also the I-implicatures from conditional to biconditional, and Groenendijk & Stokhof's (1984) observation that answers are normally interpreted in an exhaustive way.
In this respect it is highly relevant that Groenendijk & Stokhof (1984) show that almost all typical Q-implicatures can be analysed alternatively in terms of their explicit exhaustivity-operator, when the clause that gives rise to the implicature is used as an answer to a question.
It turns out, fortunately, that the searched for quantitative notion of relevance of assertions (answers) in cooperative situations has already been defined by van Rooy (1999, 2000, to appear) in terms of the way it helps to resolve the questioner's decision problem. In this talk I will show how the exhaustive interpretation of an answer follows from the principle of relevance optimiziation (i.e. maximal reduction of entropy of the decision problem corresponding to the question) in cooperative conversational situations. This will (a) enable us to give a uniform analysis of lots of standard I-implicatures (i.e. conditional to biconditional) and standard Q-implicatures (i.e. some cookies to not all cookies), but (b) still allows us to account for van Kuppevelt's observation that the existence of scalar implicatues depends crucially on the question being asked, or (as I would say) the decision problem of the relevant agents. Accounting for scalar implicatures in terms of Relevance is in line with Merin's proposal, and it is also noteworthy that our explanation of the so-called I implicatures in terms of relevance was already anticipated by Grice (1975) himself.
Effort, and Bidirectional OT:
But if we reduce both the Q and the I principle to the principle that assumes that speakers are Relevance optimizers (the R principle), doesn't that mean that as a result we have to give up on Blutner's bi-directional OT and its Game theoretic implementation of Dekker & van Rooy (to appear)? In particular, how could we now account for Horn's (1984) division of pragmatic labour, so elegantly explained in terms of Blutner's OT, and so important to explain why marked expressions typically get non-stereotypical interpretations?
I will show in the talk that this can be explained if we assume that optimal interpretations do not simply follow from the assumption that speakers are relevance maximizers; the optimal interpretation should rather be thought of as a BALANCE, or game-theoretic equilibrium, between relevance maximalization and EFFORT minimalization. The principle that effort should be as minimal as possible - the E principle - is clearly important to explain, for instance, why `salience' is so crucial for the interpretation of pronouns, and I will show how effort is relevant to account for markedness-phenomena, too.
Notice that when we explain interpretation as a balancing act between relevance and effort, our analysis comes very close to Sperber & Wilson's (1986) analysis of natural language in terms of their Theory of Relevance. This is interesting for two reasons. First, because it suggests that Sperber & Wilson's theory is much closer to the standard pragmatic theories on which we build our analysis than they claim themselves, and second because it opens up the possibility of a mathematical sophisticated implementation of their rather informal suggestions.
References:
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