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 Robert Levine 2019 5201 1 / 9

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 S NP VP NP NP \ S Mary V NP Mary (NP \ S)/NP NP criticized Bill criticized Bill ◮ Seemingly, all that has happened is the replacement of category names based on parts of speech with category names based on valence. ◮ BUT. . . Robert Levine 2019 5201 2 / 9

Trees as proof histories? ◮ What is happening at each step in the tree in (2)? (2) S NP NP \ S Mary (NP \ S)/NP NP criticized Bill ◮ 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 ’. Robert Levine 2019 5201 3 / 9

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? Robert Levine 2019 5201 4 / 9

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’): ϕ ⊃ ψ ϕ (3) 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. Robert Levine 2019 5201 5 / 9

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 X \ Y X Y 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. Robert Levine 2019 5201 6 / 9

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 NP \ S Mary (NP \ S)/NP NP criticized Bill ◮ 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. Robert Levine 2019 5201 7 / 9

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. Robert Levine 2019 5201 8 / 9

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 of 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. Robert Levine 2019 5201 9 / 9