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Lexical Pragmatics: Some Principles and Formalisms: 

Lexical Pragmatics: Some Principles and Formalisms Anne L. Bezuidenhout Trondheim, September 18-22, 2006

Lexical Pragmatics: 

Lexical Pragmatics Lexical Pragmatics is a particular account of the division of labor between lexical semantics and pragmatics … It combines the idea of (radical) semantic underspecification in the lexicon with a theory of pragmatic strengthening (based on conversational implicatures). In the core of this approach is a precise treatment of Atlas and Levinson’s (1981) Q- and I-Principles and the formalization of the balance between informativeness and efficiency in natural language processing (Horn’s (1984) division of pragmatic labor). In a roughly simplified formulation, the I-Principle seeks to select the most coherent interpretation, and the Q-Principle acts as a blocking mechanism which blocks all the outputs which can be grasped more economically by an alternative linguistic input. Recently, these mechanisms have been implemented within a bi-directional version of optimality theory…which aims to integrate expressive and interpretive optimization. (Blutner andamp; Solstad: 11)

Components of OT: 

Components of OT It assumes three formal components, namely a Generator, an Evaluator and a system Con of ranked constraints. Given some input, Gen creates a set of candidate outputs, and Eval then selects the optimal candidate for that input. The optimal candidate is the one that violates the fewest constraints. The principal innovation of a bi-directional version of OT is that Gen delivers a set of input-output pairs.

Lexical-Pragmatics Interface: 

Lexical-Pragmatics Interface Comprehension Perspective

The Generator: 

The Generator Applying BOT to lexical pragmatics, and thinking of the encoded meaning of an expression as its context change potential, we assume that Gen delivers a set of expression-interpretation pairs andlt;u, iandgt;, defined as follows: Gencg = {andlt;u, iandgt;: cg([[ u ]]) = i} Here i is a potential result of updating the common ground cg with [[ u ]], which is the encoded meaning associated with the expression u. This encoded meaning is assumed to be semantically underspecified.

The Cost Function: 

The Cost Function We also need to assume that there is an ordering relation ‘«’ (being less costly than) that ranks the elements in Gencg. The total cost function can be represented as follows:  cost(u, i) = compl(u) . c([[ u ]], i) In English: Cost = Complexity of expression  Surprise value of interpretation (The less complex and the less surprising, the less costly)

Bi-Directional OT: 

Bi-Directional OT BOT (strong version) asserts that an expression-interpretation pair andlt;u, iandgt; is optimal if and only if it satisfies both of the following constraints: (Q): There is no other pair andlt;u, iandgt;  Gencg such that andlt;u, iandgt; « andlt;u, iandgt; (I): There is no other pair andlt;u, iandgt;  Gencg such that andlt;u, iandgt; « andlt;u, iandgt; These constraints (formulated from the Comprehension perspective) could be formulated in English as follows: (Q) There is no less costly way for the speaker to express her meaning. (I) There is no meaning that is less costly to attach to the speaker’s utterance.

Lexical Blocking: 

Lexical Blocking Total blocking is a situation in which some productive form is disallowed because there is already a lexicalized form that serves to cover the intended range of meaning. E.g, although one can talk of ‘pale yellow’, ‘pale blue’, and ‘pale green’, one would not talk of ‘pale red’, since ‘pink’ already exists as an expression covering the relevant range of the color spectrum. The strong version of BOT would explain why the pair andlt; ‘pale red’, andgt; is non-optimal, because there is another pair andlt; ‘pink’, andgt; that is less costly than it (in this case because the lexicalized form ‘pink’ is less complex than the productive form ‘pale red’).

Partial Blocking: 

Partial Blocking Partial blocking is the phenomenon in which a lexicalized or more productive expression exists to cover some (stereotypical) part of some relevant domain of meaning, and a less productive form is used to refer to the remaining (somehow unusual or special) elements in the domain. E.g., consider the contrast between lexical and productive causatives: a. Black Bart killed the sheriff b. Black Bart caused the sheriff to die.

Weak Version of BOT: 

Weak Version of BOT An expression-interpretation pair andlt;u, iandgt; is optimal in the weak sense if and only if it satisfies both of the following constraints: (Qw): There is no other pair andlt;u, iandgt;  Gencg that satisfies the I-principle such that andlt;u, iandgt; « andlt;u, iandgt; (Iw): There is no other pair andlt;u, iandgt;  Gencg that satisfies the Q-principle such that andlt;u, iandgt; « andlt;u, iandgt; The weak version of BOT is one in which the directions of optimization make reference to each other.

Horn’s Division of Pragmatic Labor: 

Horn’s Division of Pragmatic Labor The weak version of BOT can explain why marked expressions are associated with stereotypical meanings/ situations and unmarked forms are associated with non-stereotypical situations. The marked, less productive form is not totally blocked by the unmarked form, because it is less costly to associate the unmarked form with the typical rather than the atypical interpretation.

Scalar and Clausal Implicatures: 

Scalar and Clausal Implicatures BOT can explain why ‘P or Q’ gets interpreted in the exclusive sense, as ruling out the joint truth of the two disjuncts. E.g., ‘You can have soup or salad’ gets interpreted as The hearer can have either soup or salad but not both soup and salad. This is because there is an alternative expression, ‘P and Q’, that is a less costly way of expressing the possibility of the joint truth of ‘P’ and ‘Q’. It is less costly because the surprise value of learning that the state of the world is such that both ‘P’ and ‘Q’ hold is less after learning that ‘P and Q’ is true than after learning that ‘P or Q’ is true. See Blutner (1998: 134); van Rooy (2002a: 3). So the Q-principle blocks the joint truth of ‘P’ and ‘Q’ being part of the interpretation of ‘P or Q’, forcing an exclusive interpretation of the disjunction.

Pragmatic Scales: 

Pragmatic Scales Bob has just returned from a visit to the Kruger National Park game reserve. Suppose that it is part of the common ground that on visits to game reserves it is desirable to see lions, and that hippo sightings are not as prized as lion sightings. In this context, consider the following dialog:  Anne: Did you see any lions? Bob: I saw some hippos. Implicature: Bob did not see any lions. The 'scale' here only exists because of assumptions in the common ground. It wouldn’t exist if assumptions were changed. For example, suppose it is part of the common ground that lions are always to be spotted whenever hippos are spotted. The implicature would disappear.

Problem 1 for BOT: 

Problem 1 for BOT This implicature is derived by means of what has been called a pragmatic scale. Unlike the elements in a Horn scale or other comparable linguistic scale, we cannot say that the lexical entry for the expression ‘lion’ records the fact that ‘lion’ is informationally stronger than the expression ‘hippo’. ‘Lion’ and ‘hippo’ are not expression-alternates. So, it looks as though the blocking function of the Q-principle cannot work in this case to yield the desired implicature. So BOT cannot account for such cases.

Abductive Extension of BOT: 

Abductive Extension of BOT The idea is to extend the coverage of BOT beyond the sort of cases mentioned in the previous section (cases of lexical blocking, scalar and clausal implicatures, etc.) to cases where interpretation depends on specific aspects of world and discourse knowledge. Blutner discusses the pragmatics of adjectives and cases of systematic polysemy in particular.

Pragmatics of Adjectives: 

Pragmatics of Adjectives (1) a. The apple is red. b. Its peel is red. c. Its pulp is red. Blutner (1998: 148) claims that (1b) but not (1c) is a conversational implicature of (1a). He argues that part of the underspecified meaning of ‘apple’ is that apples have parts that are colored and so the underspecified meaning of (1a) is that the apple in question has a part that is red. Context will have to supply something to fill the part-slot in this underspecified representation.

Adjectives (cont.): 

Adjectives (cont.) Blutner (1998: 149) writes: Given the assumption that the colour of the peel is more diagnostic for classifying apples than the colour of other apple parts, for example, the colour of the pulp, the red peel-specification is arguably the cost minimal specification…. The red peel-specification comes out as the cost-minimal specification if its total costs are smaller than the costs of any other specification. … Suppose that, as is rather plausible, this condition is satisfied, then the I-principle selects the red peel-interpretation and blocks the red pulp-interpretation.

Adjectives (cont.): 

Adjectives (cont.) Notice here that it is the I-principle that is said to do the blocking, not the Q-principle. ‘Red peel’ and ‘red pulp’ are not expression-alternates of ‘red’. Rather, the red peel- and red pulp-specifications are what Blutner (1998: 144) calls abductive variants. Presumably it is our world knowledge of apple parts that will suggest what variants are to be considered by the comprehension mechanism and are to be ruled in or out by the I-principle.

Systematic Polysemy: 

Systematic Polysemy (2) a. The school has strict hiring policies. b. The school has a flat roof. c. The school building has a flat roof. ‘School’ is polysemous, and can be understood as referring either to an institution, as in (2a), or to the physical buildings that house that institution, as in (2b). Blutner (1998: 152-155) argues that the abductive extension of his basic BOT mechanism can explain why (2b) is interpreted as (2c).

Systematic Polysemy (cont.): 

Systematic Polysemy (cont.) Blutner claims that the institution and building senses of ‘school’ are equally salient, but that the building interpretation can be integrated into the conceptual frame created by the predicate ‘has a flat roof’ more readily than the institution interpretation can. So, since the building interpretation is less costly, it is selected by the I-principle and the institution interpretation is blocked, resulting in the conversational implicature in (2c). Note that the blocking of the institution interpretation of ‘school’ in (2b) is not a result of the operation of the Q-principle.

Some Initial Worries…: 

Some Initial Worries… No longer have a bi-directional version of OT, if the Q-principle drops out of the picture. Not clear that the blocking that I-principle does is blocking in the same sense as done by the Q-principle. (Abductive variants are not expression-alternates). If the Q-principle drops out of the picture, we can’t account for pragmatic scales. Lion is not an abductive variant of the underspecified meaning of ‘hippo’.

Problem 2 for BOT: 

Problem 2 for BOT Accounting for novel uses: Suppose that we are playing a board game where the game pieces are Granny Smith apples and the game board consists of a grid of colored squares. If a speaker were to utter: ‘Play the red apple’ she would be taken to have suggested that the hearer play the Granny Smith apple on the red square of the game board. The apple counts as red in this context not in virtue of the color of any of its parts, but in virtue of the fact that it is currently placed on the red square of the game board.

Problem 3 for BOT: 

Problem 3 for BOT Pragmatic loosening: Blutner (1998: 131) says that a pair andlt;u, iandgt;  Gencg iff [[u]] holds in i, written as i |= [[u]]. This would allow only interpretations that are logical strengthenings. Pragmatic strengthenings that result in logical weakenings (e.g., cases in which the domain of a universal quantifier is restricted) or pragmatic loosenings are not covered by this definition. Since the RT comprehension mechanism deals in the same way with both loosenings and strengthenings (see Carston, 1997), its mechanism is more general than the BOT mechanism.

van Rooy’s LOT: 

van Rooy’s LOT The utility value of a proposition B, UV(B), can be thought of as the increase in expected utility that results from adding B to the common ground. One interpretation B is better than another C just in case UV(B) andgt; UV(C). A special case of this can be applied in a situation in which we have a partition of logical space Q, and we must decide which element of Q is true. The addition of new information might make this decision problem easier, by eliminating cells in the partition. We say that the entropy value of a proposition B with respect to a decision problem Q, EVQ(B), is its usefulness in resolving this decision problem. So if learning a proposition B eliminates more cells of the partition Q than learning C, EVQ(B) andgt; EVQ(C).

Argumentative Value: 

Argumentative Value Another special case is the argumentative value of a proposition B relative to a hypothesis h, AVh(B). Learning B might increase or decrease the probability of h. We can say that B is positively relevant to h if the conditional probability of h given B is greater than the prior probability of h, i.e., p(h/B) andgt; p(h). It is negatively relevant if p(h/B) andlt; p(h). The argumentative value of B with respect to h is thus a measure of its degree of relevance to the argument, and B is a better argument for h than is C if AVh(B) andgt; AVh(C).

AVh vs. Informativeness: 

AVh vs. Informativeness The argumentative value of a proposition B with respect to a hypothesis h may be greater than the argumentative value of a proposition C with respect to h even though C entails B. For example: B = Bob’s knife was found at the scene of the murder. C = Carol’s blood (as well as the victim’s blood) was found on the knife. h = Bob is the murderer. p(h/B) andgt; p(h/ B  C) So AVh(B) andgt; AVh(B  C) Yet (B  C) entails B. Hence (B  C) is more informative than B. van Rooy notes that in this situation it would be more useful/ relevant to say only B, even though this would not be very cooperative.

Problem for LOT?: 

Problem for LOT? (1) (a) People who are getting married should consult a doctor about possible hereditary risks to their children. (b) Two people both of whom have thalassemia should be warned against having children. (c) Susan has thalassemia. (2) (a) Susan, who has thalassemia, is getting married to Bill. (b) Bill, who has thalassemia, is getting married to Susan. (c) Bill, who has thalassemia, is getting married to Susan, and 1967 was a very good year for French wines.

Problem (cont.): 

Problem (cont.) RT says (2b) is more relevant than (2a) because (2b) has more contextual effects than (2a), while we can assume that they are roughly equal in terms of processing costs. As van Rooy puts it, we can think of the above discourse as raising the following questions: (i) Who should consult a doctor? (ii) Who should be warned against having children? (2a) resolves question (i) for both Susan and Bill. But (2b) resolves both questions for both individuals. Thus it has greater entropy value and hence is more useful/ relevant than (2a). So far, RT and LOT are in agreement.

van Rooy’s Full Account: 

van Rooy’s Full Account However, RT says that (2c) is less relevant than (2b), intuitively because (2c) gives extra irrelevant information that adds to the processing costs without any compensatory contextual effects. On the other hand, it appears that LOT has to say that (2b) and (2c) are equally relevant, because they resolve the same questions. van Rooy proposes the following as a solution: Proposition B is more relevant than proposition C just in case: Either UV(B) andgt; UV(C) or UV(B) = UV(C) and inf(B) andlt; inf(C) On this definition it will turn out that (2c) is less relevant than (2b). So once more RT and LOT are in agreement.



A Meta-Framework?: 

A Meta-Framework? Does LOT allow us to unify RT and the neo-Gricean theories of Horn/Levinson? No, because to construe RT in terms of LOT is to ignore RT’s central aim of offering a psychological theory. One could of course construe LOT as a psychological processing account too, where processing effort is measured in quantitative terms (e.g., in terms of duration). Such quantitative measures of effort are routinely used in psycholinguistics. Moreover, RT (with certain provisos) can accept a methodology that measures effort quantitatively. Does this make unification any more likely? No. There are still the incompatibilities between BOT and RT that I’ve already catalogued in my discussion of Blutner’s views. Besides, RT and neo-Gricean accounts make differential predictions about processing, and there is at least some psycholinguistic evidence that favors RT over neo-Gricean accounts.