Autumn 2019 Ling 5201 Syntax I 2: Syntax as deduction?aria7dne - - PowerPoint PPT Presentation

Autumn 2019 Ling 5201 Syntax I 2: Syntax as deduction?aria7dne

Robert Levine

Ohio State University levine.1@osu.edu

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Where we left off. . .

◮ Since we can treat VP as characterizing a string of words looking for

an NP to the left to form a sentence, we can write VP as NP\S.

◮ A transitive verb such as discuss or criticize will then be (NP\S)/NP. ◮ How does this approach change our view of syntactic structure? ◮ One one level, not all that much. Compare the trees:

(1)

S VP NP Bill V criticized NP Mary S NP\S NP Bill (NP\S)/NP criticized NP Mary

◮ Seemingly, all that has happened is the replacement of category names

based on parts of speech with category names based on valence.

◮ BUT. . .

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Trees as proof histories?

◮ What is happening at each step in the tree in (2)?

(2)

S NP\S NP Bill (NP\S)/NP criticized NP Mary

◮ At the lowest point in the tree,

◮ a symbol of the form A/B appears on the left of a symbol of the form

B

◮ with the node dominating them labeled A.

◮ ‘Give me a B to my right and I’ll give you back an A’ meets ‘B’. . . ◮ with the result ‘A’.

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Proof histories, cont’d.

◮ At the next level up,

◮ a symbol of the form B\A appears on the right of a symbol of the form

B

◮ with the node dominating them labeled A.

◮ ‘Give me a B to my left and I’ll give you back an A’ meets ‘B’. . . ◮ with the result ‘A’.

The essential story

◮ a syntactic type defined by a guarantee to combine with a category of

a different type so that a particular category is the result. . .

◮ combines with that indicated type. . . ◮ . . . and the promised category does indeed result. ◮ Does this remind you of anything from. . . say. . . elementary logic?

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Syntax as deduction

◮ We can see each step in the proof in (2) as an instance of the ancient

rule Modus Ponens (lit. ‘the way that validates’): (3) ϕ ⊃ ψ ϕ ψ

◮ When Modus ponens holds, the truth of one proposition (the

antecedent) is a guarantor of the truth of a second proposition (the consequent).

◮ But we’re not talking about truth here. . . ◮ . . . we’re talking about valid descriptions of the syntactic types which

correspond to the combination of other syntactic types.

◮ So what we have is not Modus ponens in some version of

propositional logic,

◮ but rather a strict analogue of Modus ponens in a logic of syntactic

types,

◮ where both / and \ correspond to logical implication.

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A (very) simple type logic

◮ So now: given that we are constructing a logical analogue to (some

subportion of) propositional logic, what is the analogue of (3)? (4) / Elim(ination) \ Elim(ination) X Y/X Y X\Y X Y

◮ Slashed categories combine with the element they’re ‘slashed for’ to

yield the promised syntactic type

◮ which is the type on the side from which the slash is falling away.

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But what about the prosodic and semantic ‘labels’?

◮ Something is definitely missing from the rules in (4), however.

◮ In particular: what’s missing from (4) so far as (2) is concerned? ◮ Let’s look at (2) one more time:

(2)

S NP\S NP Bill (NP\S)/NP criticized NP Mary

◮ I’ve been talking about a slashed category ‘looking to the left’ or

‘looking to the right’ for the right kind of category to combine with.

◮ But the rules given so far say nothing about the directionality of the

actual words in the sentence.

◮ There is nothing about linear prosodic ordering here, ◮ and there is nothing about the semantic result of combining the

linguistic signs described by these types.

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A not-so-simple type logic

◮ Our logic is a logic of types, as propositional logic is a logic of

propositions.

◮ But in propositional logic, the proof terms are simple formulæ, ◮ whereas our type logic, to be useful, must be a logic not only of types

(‘formulæ’) but of labels for those types which have their own (possibly quite complex) structure.

◮ The labels ‘go along for the ride’, ◮ so that the deduction of a particular syntactic type on the basis of

prosodically and semantically labeled premises will simultaneously yield the prosodic and semantic labels for that deduced type.

◮ Or, in terms more familiar to the linguist, given a set of signs each of

which has a specified syntactic type,

◮ we can deterministically infer the prosody and meaning of the

combination.

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Rules of the labeled deduction system

◮ What do we want our rules to do? ◮ On the prosodic side,

◮ we want the combination of syntactic types to order the pronunciation

• f the word sequences corresponding to the combined types as dictated

by the direction of the slash,

◮ so that if Y/X combines with X, the result is a category Y whose

pronunciation consists of the prosodic string labeling Y/X followed by the string labeling X,

◮ and likewise for X\Y

criticized; (NP\S)/NP bill; NP criticized • bill; NP\S criticized • bill; NP\S mary; NP mary • criticized • bill; S

◮ where a • b connects two phonological strings a,b by the

concatenation operator.

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