LIN3021 Formal Semantics Lecture 7

1. LIN3021 Formal SemanticsLecture 7 Albert Gatt

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

3. Part 1 A bit about pronouns

4. 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.

5. 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)

6. Pronouns as variables • 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) • Denise met Sally. She chatted with her. 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?

7. Pronouns and context • Notethat 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. • 1. Denise met Sally. She chatted with her. • 2. Denise met Sally. She chatted with her.

8. Bound pronouns Only John likes his mother. • This sentence seems to allow two interpretations: • 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 • 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 doesn’t like his own mother (=1)

9. Pronouns and grammar Only John likes his mother. • This sentence also has particular truth conditions, where only is playing a role. • 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. • 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)?

10. 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.

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

12. 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. • We can think of Only John loves his mother along these lines: Only John1 likes his1 mother. = Only John1[e1 likes his1 mother] Surface form Underlying logical form A property, which we predicate of only John

13. The semantics Only John1 likes his1 mother. = Only John1[e1 likes his1 mother] Surface form • If the bracketed part is a property, then it’s an unsaturated proposition: something like love-his-mother(x). • The variable x plays a dual role as shown in the diagram: • the one who loves (the subject e1in the open proposition) • the person whose mother we’re talking about (his) Underlying logical form A property

14. The semantics Only John1 likes his1 mother. = Only John1[e1 likes his1 mother] Surface form • 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’smother. • 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. Underlying logical form A property

15. 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.

16. A note about e-type pronouns • Few politicians admire Kennedy and they are very junior. • The politicians who admire Kennedy are few and they are junior. (And there are no other politicians who admire Kennedy) • #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?

17. A note about e-type pronouns Few politicians admire Kennedy and they are very junior • We can account for this in two ways: • 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. • 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 variables.

18. 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!

19. Part 2 Plurals

20. 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

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

22. 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.

23. 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 Mwith 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+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.

24. 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 C A B

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

26. The meaning of plurals • [[horse]]M = {A,B,C} • A property that describes any individual horse. • [[horses]]M = {A+B,A+C,B+C,A+B+C} • A property which describes any plural individual consisting of horses • [[the horse]]M = the unique most salient 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 A+B+C A+B A+C B+C C A B

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

28. 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 Chinese ma A+B A+C B+C Atoms English horse C A B

29. 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. • Otherwise, we’re referring to the furniture as a whole.

30. Mass terms • Mass terms • The furniture is of poor quality • The gold was precious. • NPs like much water, the furnitureand 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

31. 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.

32. Question 2 • Can we handle mass terms in roughly the same way as plurals?

33. Mass terms • Not all massterms 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

34. 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, R1 and R2. • Then the material in R1 is gold, and the material in R2 is gold. • Taken together, the material in the rings R1+R2 is also gold. G1+G2 R1+R2 G1 G2 R1 R2 Lattice structure for gold Lattice structure for ring

35. 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 the three children built one raft. • Distributive interpretation: • The children built a raft (each). • True, just in case the children built three rafts.

36. 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.

37. 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.

38. 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)

39. An argument against NP ambiguity Sue and Pete got dressed and gathered in the playground • 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). distributive collective

40. 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}

41. 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.

42. 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.

43. 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+C B+C C A B

44. Part 3 A few words about reference to kinds

45. 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.

46. Bare and non-bare plurals English Maltese Tigers are protected. Tigers are animals Tigers are fierce. Tigers ran in the forest. It-tigriprotetti. It-tigri (huma) annimali. It-tigri (huma) feroċi. Ġrew it-tigrifil-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.

47. 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)

48. 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.

49. 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.

50. Carlson’s model The structure The operators - I Gn (“genericise”) 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.