LIN 3021 Formal Semantics Lecture 7 Albert Gatt

LIN 3021 Formal Semantics Lecture 7 Albert Gatt

In this lecture �We finish our discussion of referring expressions �How pronouns work. �Plural reference. �Generic reference

Part 1 A bit about pronouns

Pronouns are variables �Pronouns like she and her seem to contain very little descriptive information (beyond the fact that x is female. . . ). �How do we determine what a pronoun refers to in contexts like these? Denise went shopping. She bought a sword. Denise met Sally. She chatted with her.

Types of pronominal use � Referential: �It’s really ugly [spoken by someone looking at a painting] �Denise met Sally. She chatted with her. �Pronoun depends on context for interpretation. The antecedent for the pronoun is not completely specified grammatically. � Bound: �Only John loves his mother. �Pronoun depends on an antecedent in the linguistic context (its binder). � E-type: �Few politicians admire Kennedy and they are very junior. �Pronoun doesn’t seem to be bound by few politicians: this sentences doesn’t mean few politicians admire Kennedy and few politicians are junior. �(Compare: Jenny admires Kennedy and she is very junior)

Pronouns as variables Denise met Sally. She chatted with her. �In different contexts, she can refer to lots of different things. �Logically, we can think of the way they are interpreted in terms of an assignment function. �Very roughly, let’s think of the above as �meet(d, s) �chat(x, y) If we assume an assignment function g, then in this context: g(x) = Denise. g(y) = Sally But how does the assignment function know which is which?

Pronouns and context 1. Denise met Sally. She chatted with her. 2. Denise met Sally. She chatted with her. �Note that alternative (2) seems possible (though less likely). �Clearly, one way in which variable assignments work with pronouns is through salience: �Denise is the most salient antecedent for she. �Sally is the most salient antecedent for her. �Context interacts with grammatical role information (subject/object) to let us come to the most likely conclusion.

Bound pronouns Only John likes his mother. �This sentence seems to allow two interpretations: 1. John is the only person who likes his mother (nobody else likes their mother) �the reference of his shifts depending on who we assign his to �a bound pronoun 2. John’s mother is only liked by John (nobody else likes her) �his = John �Note further that the two interpretations are mutually exclusive: �We can’t have an interpretation where John likes his mother, Steve like’s John’s mother (=2) and Frank

Pronouns and grammar Only John likes his mother. �This sentence also has particular truth conditions, where only is playing a role. 1. John’s mother is only liked by John (nobody else likes her) �his = John �Sentence is true iff John likes John’s mother and for all x different from John, x doesn’t like John’s mother. �Pronoun his here seems to exhibit a referential use. 2. John is the only person who likes his mother (nobody else likes their mother) �the reference of his shifts depending on who we assign his to �Sentence is true iff John likes John’s mother and for all x different from John, x doesn’t like x’s mother. �How do we obtain interpretation (2)?

Digression: relative clauses (reminder) �In a sentence such as John is who Mary killed �the phrase who Mary killed is also a predicate �(i. e. an unsaturated proposition, that yields a complete proposition when combining with John) �We’ve dealt with the internal structure of this complex predicate by thinking of it as a property in the underlying logical form.

Relative clauses: a rough estimation � [[who Mary killed]] = the proposition that Mary killed someone �underlined part represents who Mary killed whatever’s missing and needs to saturate the proposition. ei � Assume who has moved to the front of the sentence. � The underlying proposition is Mary killed e. 1. 2. 3. 4. We start with Mary killed e: the placeholder ei temporarily saturates kill We add who indicates that the logical object of kill is no longer in place this can be interpreted as an instruction to (re-)unsaturate kill, before combining it with an NP to saturate it.

Towards an analysis Only John loves his mother. �In this example, Only John is binding the variable his. �The variable assignment can’t always depend on context. Sometimes, it’s down to grammar and semantics. Surface form along John 1 think likes of his. Only �Only We can John loves his mother 1 mother. these lines: = Only John 1 [e 1 likes his 1 mother] Underlying logical form A property, which we predicate of only John

The semantics Only John 1 likes his 1 mother. = Only John 1 [e 1 likes his 1 mother] Surface form Underlying logical form A property �If the bracketed part is a property, then it’s an unsaturated proposition: something like love-hismother(x). �The variable x plays a dual role as shown in the diagram: �the one who loves (the subject e 1 in the open proposition) �the person whose mother we’re talking about (his)

The semantics Only John 1 likes his 1 mother. = Only John 1 [e 1 likes his 1 mother] Surface form Underlying logical form A property � When we combine the property with Only John we get a proposition which: �Is true if John saturates the property loves-his-mother �False otherwise. � This corresponds to our desired interpretation: �John likes his mother. For every other x, x doesn’t like x’s mother. � Notice that here, the bound variable isn’t getting its meaning from a context outside of the sentence. There’s a semantic restriction on the interpretation of his.

Two analyses? � So we seem to have two ways in which the assignment function for pronouns is determined: �Through context (She likes him) �Semantically, via grammar (only John likes his mother) � It seems we need both: �Sometimes pronouns obviously depend on context, when they don’t have linguistic antecedents: � It’s really ugly. [Spoken by someone looking at a painting] �Binding also doesn’t seem to work across sentences: � Only John loves his mother. His father’s bad. � The second his takes John as antecedent. It doesn’t mean Only John loves his mother and has a bad father.

A note about e-type pronouns �Few politicians admire Kennedy and they are very junior. 1. The politicians who admire Kennedy are few and they are junior. (And there are no other politicians who admire Kennedy) 2. #There are few junior politicians who admire Kennedy (but there may be senior ones who do). � Here, they can’t be a bound variable. Interpretation (2) is excluded. � It seems as if this is a case where the pronoun has some descriptive content: �they = the politicians who admire Kennedy �So maybe this pronoun is unlike the others? I. e. Maybe we don’t have variable binding here?

A note about e-type pronouns Few politicians admire Kennedy and they are very junior �We can account for this in two ways: 1. Treat they on a par with purely referential uses (It’s really ugly), where we have an assignment function that assigns the variable they to “those politicians who admire Kennedy”. �This turns the pronoun interpretation into a pragmatic issue. It leaves open the question of how the function actually determines that this is the right interpretation. 2. Assume that they is (semantically) interpreted as “the politicians who admire Kennedy” This is the position known as the “E-type” theory. � Under this theory, these kinds of pronouns aren’t just �

E-type pronouns: other examples � The E-Type theory has been used to explain examples like these: �Every girl who deserved it won the prize she wanted. �Here it seems to mean “the prize she wanted”. �It’s not referring to a particular prize – the specific prize changes depending on who the girl is we’re talking about. �So there’s no specific prize that the assignment function can bind the pronoun to. � But notice: �if it = the prize she wanted �Then we have a pronoun (she) inside the meaning of the pronoun it. �This pronoun would be bound by every girl in our example. �So even if the pronoun it isn’t just a variable, its meaning must itself contain a variable!

Part 2 Plurals

Plural NPs �For our purposes, a plural NP is an NP that denotes several individuals. This includes both morphologically plural and conjoined NPs: �John and Bill �the horses �etc

Question 1 �How can we account, semantically, for plural predicates? What is the difference between: �horse – horses �girl – girls �etc?

Plurals and predication � Consider: �The horse ran �The horses ran � We’ve thought of run as a predicate and analysed it as a property (type <e, t>). So it requires an individual to saturate it. � With the horse, we know what to do: the predicate horse denotes a set of individuals; the definite article turns the predicate into a reference to the most salient one (type e). � How do we deal with the plural? �Horses can’t just denote a set of individuals (otherwise, the horses would be an individual) �An idea (due to Godehard Link, 1983) is to think of plurals as denoting a plural individual or sum – an individual made up of parts.

Revising our models � What is the meaning of horses? �Of course, this depends on the model (world) in which we’re carrying out our interpretation. �Assume a model M with only three horses: {A, B, C} � [[horse]]M = {A, B, C} �The meaning of singular horse is just the set of individual horses as usual. � [[horses]]M = the set of plural individuals formed from the set of horses = {A+B, B+C, A+B+C} �In other words, the extension of a semantically plural predicate involves: � taking the individuals in the singular extension; � creating all the possible sub-groups (sums) of more than one individual.

Revising our models �If we make these assumptions, then we’ve implicitly added structure to our model. � It no longer has just an unstructured set U of individuals; we need some kind of part-whole structure. A+B+C A+B A+C B+C A B C

Revising our models �This kind of structure is called a lattice. A+B+C sums (complex individuals) Denotation of horses A+B A A+C B B+C C atoms (simple individuals) Denotation of horse

The meaning of plurals � [[horse]]M = {A, B, C} � A property that describes any individual horse. A+B+C A+B A+C B+C � [[horses]]M = {A+B, A+C, B+C, A+B+C} � A property which describes any plural A B C � [[the horse]]M = the unique most salient individual consisting of horses individual in context, described by horse � [[the horses]]M = the unique, most salient individual described by horses � = by default, the plural individual A+B+C � NB: uniqueness with plurals also tends to carry a maximality presupposition

Conjoined NPs �As we said at the outset, j+b+g j b g conjoined NPs like John, Bill and George or the girl and the boy work in much the same way.

An aside on Chinese �Some languages don’t have a singular-plural distinction. �E. g. Chinese ma = horse or horses �Perhaps in these languages, the word ma covers both singular and plural individuals. A+B+C Sums English horses A+B A A+C B B+C C Atoms English horse Chinese ma

An aside on Chinese san pi ma three classifier horses �San indicates we’re counting three horses �Pi, a measure word, indicates large-animal-sized individuals. �Ma is the predicate. �(“Three individual-sized things with the property of horsehood”) �Suggests that we’re right in thinking of plurals as involving two things: a plural-sum formation + a property �Compare to English: three pieces of furniture �Furniture is a mass noun. �It requires us to specify pieces if we want to count individuals.

Mass terms �The furniture is of poor quality �The gold was precious. �NPs like much water, the furniture and the water seem not to be understood as sets/groups/collections of individuals. �We can sometimes specify the parts �Some mass terms are inherently made up of parts: furniture �Others, like gold are not. But we can “divide” them into portions: the gold in these two rings

Mass terms cumulative reference �Mass terms allow cumulative readings: �If a is a P and b is a P, then a+b is a P �Consider: �If a is water and b is water, then the sum of a and b is water.

Question 2 �Can we handle mass terms in roughly the same way as plurals?

Mass terms � Not all mass terms behave like furniture. �Mass nouns like gold can be thought of in lattice-theoretic terms, but they don’t have individual parts. �However, we can individuate portions of these masses. For example, the gold making up a ring is a portion of gold. � The lattice approach does allow us to account for the cumulativity with mass terms: �If A is gold and B is gold, then A+B is also gold. �If the gold (A) in this ring is old, and the gold (B) in that ring is old, then the gold (A+B) in the two rings is old. A+B Lattice structure for gold A B

Mass terms and count nouns �The utility of the lattice is best seen when we create mappings between mass and count nouns. �Suppose we have two rings of gold, R 1 and R 2. �Then the material in R 1 is gold, and the material in R 2 is gold. �Taken together, the material in the rings R 1+R 2 is also gold. G 1+G 2 R 1+R 2 G 1 G 2 Lattice structure for gold R 1 R 2 Lattice structure for ring

Distributivity and collectivity �The children built a raft. �Suppose there are three children. �How many rafts were built? �Collective interpretation: �The children built a raft (together). �True, just in case three children built one raft. �Distributive interpretation: �The children built a raft (each). �True, just in case the children built three rafts.

Distributivity and collectivity �Some predicates allow only one or the other interpretation, not both. �Collective predication: �The children are a good team. �The children gathered around their teacher. �Distributive predication: �The children are tall.

Collectives versus distributives �Collective predication involves: �Predicating a property of a plurality viewed as a whole (a group). �Distributive predication involves: �Predicating a property of a plurality understood as a set of individuals, where the property applies to each individual.

Question 3 �When we have distributive or collective readings, how does the meaning of the plural NP change? �Should we treat the NP as ambiguous, since it is interpreted differently in distributive/collective contexts? �The children are tall. (distributive) �The children are a good team. (collective)

An argument against NP ambiguity Sue and Pete got dressed and gathered in the playground distributive collective �If we localise the difference in the NP itself, and say it’s ambiguous, then in this case we’d have to say that the NP exhibits two different meanings in the same context! �This suggests that the ambiguity between distributive/collective readings lies in the VP. �Distributivity/collectivity of a plural NP arises as a result of the predication (the VP).

The simple cases �Sue and Pete are tall. (distributive only) �Sue and Pete gathered. (collective only) �Following Link, we could stipulate that: �lexically collective predicates like gather and be a good team take only plural individuals (i. e. sums). �[[gather]]M = {s+p} �Lexically distributive predicates like be tall take both individuals and sums: �[[tall]]M = {s, p, s+p}

The ambiguous cases �Sue and Pete danced. (collective or distributive) �Link’s view: �Under a collective reading, the predicate combines directly with the plural argument: dance(s+p) �In the distributive case, we have a special operator, DIST which “distributes” the meaning of the predicate over the arguments. �The effect is that if we apply the distributive predicate to a plurality, the predicate is applied both to the plural sum, and to the atoms making it up.

The ambiguous cases �Sue and Pete danced �Collective: dance(s+p) �True just in case s+p is in the denotation of dance �(I. e. s+p danced together) �Distributive: DISTdance(s+p) �True just in case s, p and s+p are in the denotation of dance. �Note: this makes the “collective” more basic than the distributive in the semantic analysis of the plural.

Distributivity and collectivity with plural NPs �The examples so far involved a conjoined NP, just to keep things simple. �We can also consider how the system works with (morphologically) plural NPs: �All the boys danced �[[the boys]]M = a+b+c �So this is true just in case a+b+c is in the denotation of dance A+B+C A+B A A+C B C

Part 3 A few words about reference to kinds

Genericity � Tigers are protected. � Tigers are animals � Tigers are fierce. � Tigers ran in the forest. � (as a group) � (all of them, individually) � (generally, not necessarily always) � (some tigers, at some point in time, in a particular place) �Do we have ambiguous NPs here? Do we want to say that tigers is ambiguous between three readings? �Probably not. The different readings seem to be due to the predicates, not the NPs.

Bare and non-bare plurals English Maltese �Tigers are protected. �It-tigri protetti. �Tigers are animals �It-tigri (huma) annimali. �Tigers are fierce. �It-tigri (huma) feroċi. �Tigers ran in the forest. �Ġrew it-tigri fil-foresta. �Some languages use bare plurals where others use definites. �But roughly, the meanings are the same. �Once again, the different readings seem to be down to the properties of the predicates.

Adding more structure to our models �In addition to the structure proposed by Link, we could introduce some more structure (as proposed by Carlson). �We need to think in terms of: �the individuals themselves �their kinds (i. e. the “sorts” of things they are) – an abstraction over the individuals that make up a kind. �their stages (i. e. Spatio-temporal “slices” of the individuals)

Properties at different levels � Tigers are rare �The property of being rare is most naturally interpreted as belonging to a kind. Here, we seem to have kind predication � That tiger has claws. � Tigers have claws. �The property of having claws is most naturally interpreted as pertaining to individuals. Here, we have individual-level predication. �But in the second case, we seem to be able to predicate the individual-level predicate of a whole kind or species. �Carlson proposed that if we start out with an object-level predicate, we can “genericise” it to raise it to the kind level.

Properties at different levels � Tigers ran in the forest �The predicate run-in-the-forest seems to apply to individual tigers. �But note: we’re talking not of the tigers across time and space, but of the tigers in a specific time and place. �So here we have stage-level predication. �We predicate run of particular spatiotemporal stages of the tigers in question. � The stage-level predicate can be predicated of an individual: �Hans the tiger ran. �Just as we can “genericise” individual-level predicates, we can also “individualise” stage-level predicates.

Carlson’s model The structure The operators - I �Gn (“genericise”) Tige r Kinds Han s Individua ls Stages s 1 Mac k s 2 . . . �Tigers have tails. �Have tails is individual level. We shift it: �Gn(have-tail)(tigers) �Shifted meaning Gn(P)(K) of predicate P: �P is true of kind K just in case the individuals of K generally have P.

Carlson’s model The structure The operators - II �R (“realise”) Han s Individua ls Stages �Hans ran. Tige r Kinds s 1 Mac k s 2 . . . �Run is stage-level. We shift it: �R(run)(Hans) �Shifted meaning R(P)(x) of predicate P: �x has a stage such that x is/was P at that stage