Focus (linguistics)

Focus directly affects the semantics, or meaning, of a sentence. Different ways of pronouncing the sentence affects the meaning, or, what the speaker intends to convey. Focus distinguishes one interpretation of a sentence from other interpretations of the same sentence that do not differ in word order, but may differ in the way in which the words are taken to relate to each other. To see the effects of focus on meaning, consider the following examples:

(6) John only introduced Bill to SUE.

In (6), accent is placed on Sue. There are two readings of (6) – broad focus shown in (7) and narrow focus shown in (8):

(7) John only [introduced Bill to SUE] _f.

(8) John only introduced Bill to [SUE] _f.

The meaning of (7) can be summarized as the only thing John did was introduce Bill to Sue. The meaning of (8) can be summarized as the only person to whom John introduced Bill is Sue.

In both (7) and (8), focus is associated with the focus sensitive expression only. This is known as association with focus. The class of focus sensitive expressions in which focus can be associated with includes exclusives (only, just) non-scalar additives (merely, too) scalar additives (also, even), particularlizers (in particular, for example), intensifiers, quantificational adverbs, quantificational determiners, sentential connectives, emotives, counterfactuals, superlatives, negation and generics.[12] It is claimed that focus operators must c-command their focus.

In the alternative semantics approach to focus pioneered by Mats Rooth, each constituent ${\displaystyle \alpha }$ has both an ordinary denotation ${\displaystyle [\![\alpha ]\!]_{o}}$ and a focus denotation ${\displaystyle [\![\alpha ]\!]_{f}}$ which are composed by parallel computations. The ordinary denotation of a sentence is simply whatever denotation it would have in a non-alternative-based system while its focus denotation can be thought of as the set containing all ordinary denotations one could get by substituting the focused constituent for another expression of the same semantic type. For a sentence such as (9), the ordinary denotation will be the proposition which is true iff Mary likes Sue. Its focus denotation will be the set of each propositions such that for some contextually relevant individual 'x', that proposition is true iff Mary likes 'x'.[30][19][20]

(9) Mary likes [SUE]_f.

In formal terms, the ordinary denotation of (9) will be as shown below:

• ${\displaystyle [\![{\text{Mary likes SUE}}]\!]_{o}={\textit {like}}({\textit {Mary}})({\textit {Sue}})}$.

Focus denotations are computed using the alternative sets provided by alternative semantics. In this system, most unfocused items denote the singleton set containing their ordinary denotations.

• ${\displaystyle [\![{\text{Mary}}]\!]_{f}=\{Mary\}}$
• ${\displaystyle [\![{\text{likes}}]\!]_{f}=\{\lambda x\,.\,\lambda y\,.\,likes(y)(x)\}}$

Focused constituents denote the set of all (contextually relevant) semantic objects of the same type.

• ${\displaystyle \{like(Mary)(y)|y\in E\}}$, where E is the domain of entities or individuals.

In alternative semantics, the primary composition rule is Pointwise Functional Application. This rule can be thought of as analogous to the cross product.

• Pointwise Functional Application: If ${\displaystyle \alpha }$ is a constituent with daughters ${\displaystyle \beta }$ and ${\displaystyle \gamma }$ which are of type ${\displaystyle \langle \sigma ,\tau \rangle }$ and ${\displaystyle \sigma }$ respectively, then ${\displaystyle [\![\alpha ]\!]=\{f(x)|f\in [\![\beta ]\!],x\in [\![\gamma ]\!]}$

Applying this rule to example (9) would give the following focus denotation if the only contextually relevant individuals are Sue, Bill, Lisa, and Mary

• ${\displaystyle [\![{\text{Mary likes SUE}}]\!]_{f}=\{like(Mary)(Sue),\,like(Mary)(Bill),\,like(Mary)(Lisa),\,like(Mary)(Mary)\}}$

The focus denotation can be "caught" by focus-sensitive expressions like "only" as well as other covert items such as the squiggle operator.[19][20][30]

Following Jacobs[22] and Williams,[29] Krifka[21] argues differently. Krifka claims focus partitions the semantics into a background part and focus part, represented by the pair:

The syntactic/semantic tree of the sentence John only introduced [BILL] _f to [SUE] _f.[21]

${\displaystyle \langle B,F\rangle }$

The logical form of which represented in lambda calculus is:

${\displaystyle \langle \lambda x.x,A\rangle }$

This pair is referred to as a structured meaning. Structured meanings allow for a compositional semantic approach to sentences that involve single or multiple foci. This approach follows Frege's (1897) Principle of Compositionality: the meaning of a complex expression is determined by the meanings of its parts, and the way in which those parts are combined into structured meanings. Krifka’s structured meaning theory represents focus in a transparent and compositional fashion it encompasses sentences with more than one focus as well as sentences with a single focus. Krifka claims the advantages of structured meanings are twofold: 1) We can access the meaning of an item in focus directly, and 2) Rooth's[19][20] alternative semantics can be derived from a structured meaning approach but not vice versa. To see Krifka’s approach illustrated, consider the following examples of single focus shown in (10) and multiple foci shown in (11):

(10) John introduced Bill to [SUE] _f.

(11) John only introduced [BILL] _f to [SUE] _f.

Generally, the meaning of (10) can be summarized as John introduced Bill to Sue and no one else, and the meaning of (11) can be summarized as the only pair of persons such that John introduced the first to the second is Bill and Sue.

Specifically, the structured meaning of (10) is:

${\displaystyle \langle introd(j,b,x),s\rangle }$ where introd is the denotation of introduce, j John, b Bill and s Sue.

The background part of the structured meaning is; introd (j, b, x); and the focus part is s.

Through a (modified) form of functional application (or beta reduction), the focus part of (10) and (11) is projected up through the syntax to the sentential level. Importantly, each intermediate level has distinct meaning.

It has been claimed that new information in the discourse is accented while given information is not. Generally, the properties of new and given are referred to as a word's discourse status. Definitions of new and given vary. Halliday[31] defines given as "anaphorically" recoverable, while new is defined to be "textually and situationally non-derivable information". To illustrate this point, consider the following discourse in (12) and (13):

(12) Why don’t you have some French TOAST?

(13) I’ve forgotten how to MAKE French toast.[32]

In (13) we note that the verb make is not given by the sentence in (12). It is discourse new. Therefore, it is available for accentuation. However, toast in (13) is given in (12). Therefore, it is not available for accentuation. As previously mentioned, pitch accenting can relate to focus. Accented words are often said to be in focus or F-marked often represented by F-markers. The relationship between accent placement is mediated through the discourse status of particular syntactic nodes.[33] The percolation of F-markings in a syntactic tree is sensitive to argument structure and head-phrase relations.[15]

Selkirk[13][14] develops an explicit account of how F-marking propagates up syntactic trees. Accenting indicates F-marking. F-marking projects up a given syntactic tree such that both lexical items, i.e. terminal nodes and phrasal levels, i.e. nonterminal nodes, can be F-marked. Specifically, a set of rules determines how and where F-marking occurs in the syntax. These rules are shown in (1) and (2):

(14) Basic Rule: An accented word is f-marked.

(15) Focus Projection:

a. F-marking the head of a phrase licenses F-marking of the phrase.

b. F-marking of the internal argument of a head licenses the F-marking of the head.

c. F-marking of the antecedent of a trace left by NP or wh-movement licenses F-marking of the trace.

To see how (14) and (15) apply, consider the following example:

Judy _f [adopted _f a parrot _f] _f] _foc[33]

Because there is no rule in (14) or (15) that licenses F-marking to the direct object from any other node, the direct object parrot must be accented as indicated in bold. Rule (15b) allows F-marking to project from the direct object to the head verb adopted. Rule (15a) allows F-marking to project from the head verb to the VP adopted a parrot. Selkirk[13][14] assumes the subject Judy is accented if F-marked as indicated in bold.[33]

Schwarzschild[15] points out weaknesses in Selkirk’s[13][14] ability to predict accent placement based on facts about the discourse. Selkirk’s theory says nothing about how accentuation arises in sentences with entirely old information. She does not fully articulate the notion of discourse status and its relation to accent marking. Schwarzschild differs from Selkirk in that he develops a more robust model of discourse status. Discourse status is determined via the entailments of the context. This is achieved through the definition in (16):

(16) Definition of given: An utterance of U counts as given if it has a salient antecedent A and

a. if U is type e, then A and U corefer;

b. otherwise: modulo ${\displaystyle \exists }$-type-shifting, A entails the existential F-closure of U.

The operation in (16b) can apply to any constituent. ${\displaystyle \exists }$-type-shifting "is a way of transforming syntactic constituents into full propositions so that it is possible to check whether they are entailed by the context".[33] For example, the result of ${\displaystyle \exists }$-type-shifting the VP in (17) is (18):

(17) [hums a happy tune]

(18) ${\displaystyle \exists }$x[x hums a happy tune][33]

Note that (18) is a full proposition. The existential F-closure in (16b) refers to the operation of replacing the highest F-marked node with an existentially closed variable. The operation is shown in (19) and (20):

(19) ${\displaystyle \exists }$x[x hums [a happy _f tune _f] _f]

(20) ${\displaystyle \exists }$Y${\displaystyle \exists }$x[x hums Y][33]

Given the discourse context in (21a) it is possible to determine the discourse status of any syntactic node in (21b):

(21)

a. Sean [hummed a happy tune] _VP

b. Angie [hummed [Chopin’s Funeral March] _f] _VP[33]

If the VP in (21a) is the salient antecedent for the VP in (21b), then the VP in (21b) counts as given. ${\displaystyle \exists }$-type-shifed VP in (21a) is shown in (22). The existential F-closure of the VP in (21b) is shown in (23):

(22) ${\displaystyle \exists }$x[x hums a happy tune]

(23) ${\displaystyle \exists }$Y${\displaystyle \exists }$x[x hums Y][33]

(22) entails (23). Therefore, the VP of (21b) counts as given. Schwarzschild[15] assumes an optimality theoretic grammar.[34] Accent placement is determined by a set of violable, hierarchically ranked constraints as shown in (24):

(24)

a. GIVENness: A constituent that is not F-marked is given.

b. Foc: A Foc-marked phrase contains an accent

c. AvoidF: Do not F-mark

d. HeadArg: A head is less prominent than its internal argument.

The ranking Schwarzschild[15] proposes is seen in (25):

(25) GIVENness, Foc >> AvoidF >> HeadArg

As seen, GIVENness relates F-marking to discourse status. Foc relates F-marking to accent placement. Foc simply requires that a constituent(s) of an F-marked phrase contain an accent. AvoidF states that less F-marking is preferable to more F-marking. HeadArg encodes the head-argument asymmetry into the grammar directly.[33]

Recent empirical work by German et al.[33] suggests that both Selkirk’s[13][14] and Schwarzschild’s[15] theory of accentuation and F-marking makes incorrect predictions. Consider the following context:

(26) Are the children playing their game?

(27) Paul took down their tent that they play their game in.[33]

It has been noted that prepositions are intrinsically weak and do not readily take accent.[32][33] However, both Selkirk and Schwarzschild predict that in the narrow focus context, an accent will occur at most on the preposition in (27) as shown in (28):

(28) Paul took down their tent that they [play their game [in _f t _f] _foc].[33]

However, the production experiment reported in German et al.[33] showed that subjects are more likely to accent verbs or nouns as opposed to prepositions in the narrow focused context, thus ruling out accent patterns shown in (28). German et al. argue for a stochastic constraint-based grammar similar to Anttila[35] and Boersma[36] that more fluidly accounts for how speakers accent words in discourse.