On Idioms and Compositionality Stefan Keine ling 720 · 12/10/2013 1 Introduction are compositional. Only entire interpretations can be. What we can ask is whether we can capture idioms in a compositional semantics. • The overwhelming majority of theories of semantics presuppose the Principle of • Outlook: Compositionality in (1), standardly attributed to Gottlob Frege. Westerståhl (2002) is a detailed study of idioms and compositionality. He argues that idioms are unproblematic for compositionality. (1) Principl e of C ompositionality The meaning of a complex expression is a ‘function of’ 2 The Compositionality of Idioms: Westerst å hl (2002) (i) the meanings of its component expressions and (ii) their mode of syntactic composition. • Westerståhl (2002) develops three ways in which idioms can be implemented in a compositional system. His first develops a system and then shows three ways this • Within Montague Grammar, this principle is implemented as a homomorphism system has to be amended to include idioms. We will go through them and then step between the syntax and the semantics (Montague 1970). The definition in (2) is from back to draw some general conclusions about compositionality. Westerståhl (1998: 635f.). 2.1 The Basic System (2) C ompositionality as a H omomorphism Given the syntactic algebra A = ( A , ( F γ ) γ ∈ Γ ) and a meaning function m from A to a set of meanings M . Let F be a k -ary operation of A . m is F - compositional (3) G rammar if there is a k -ary partial function G on M such that whenever F ( a 1 , . . . , a k ) is A grammar E = ( E , A , α ) α ∈ Σ defined, m ( F ( a 1 , . . . , a k )) = G ( m ( a 1 ) , . . . , m ( a k )) . consists of a set E of expressions , a set A ⊆ E of atomic expressions and for each function symbol α ∈ Σ a corresponding syntactic rule : a partial With G as above we say that m is F - compositional with G , and we say that m is map α from E n to E , for some n . compositional if it is F -compositional for all operations F of A . • The Problem with Idioms: (4) G rammatical T erms The set GT ( E ) of grammatical terms and the function val ∶ GT ( E ) → E are Idioms seem to be in direct contrast with the requirement in (2). The meaning of, e.g., kick the bucket seems to be unrelated to its parts and their combination. given by: α ∈ A is an atomic grammatical term, and val ( a ) = a . • Central Question: a. b. Suppose α ∈ Σ in an n -ary function symbol, and p 1 , . . . , p n ∈ GT ( E ) with Do idioms force us to abandon (2) (and perhaps the basic idea that natural languages val ( p i ) = e i . If α ( e 1 , . . . , e n ) is defined, say α ( e 1 , . . . , e n ) = e , the term are compositional)? α ( p 1 , . . . , p n ) is in GT ( E ) , and val ( α ( p 1 , . . . , p n )) = e . • A Terminological Point: Given the definition in (2), it does not make sense to ask whether certain expressions 1
• Note: 2.3 Treating Idioms 2: Indexed Operations NB: grammatical terms are analysis trees/derivations; val gives back t he string associ- ated with an analysis tree; E is the set of surface expressions (9) G rammar We define a new grammar E i = ( E , A , α ) α ∈ Σ i , (5) S emantics A semantics for E is a function µ whose domain is a subset of GT ( E ) . p ∈ GT ( E ) where Σ i = Σ ∪ { α i 0 } , and α i 0 = α 0 . is µ - meaningful if p ∈ dom ( µ ) . 0 is a new k -ary function sumbols such that α i 0 = α i 0 ( q 01 , . . . , q 0 k ) . E i is called a duplicated rule extension of E . Let q i (6) C ompositionality µ is compositional if dom ( µ ) is closed under subterms and for each α ∈ Σ there (10) Example is a function r α such that, whenever α ( p 1 , . . . , p n ) is µ -meaningful, ‘John kicked the bucket.’ α ( John , α 0 ( kick , β ( the, bucket ))) ↝ literal µ ( α ( p 1 , . . . , p n )) = r α ( µ ( p 1 ) , . . . , µ ( p n )) a. α ( John , α i 0 ( kick , β ( the, bucket ))) ↝ idiomatic b. (11) s − = the result of deleting all superscripts i in s . 2.2 Treating Idioms 1: Atomic Extensions • Intuition: (12) S emantics The semantics for E i , µ i , is defined as follows: Idioms are syntactically unanalyzable atoms. Its domain is K i = { p ∶ p − ∈ dom ( µ )} ; a. µ i ( a ) = µ ( a ) for all a ∈ A (whenever defined); (7) G rammar Let e 0 ∈ E − A . The the new grammar E a is defined as b. Let p = α ( p 1 , . . . , p n ) be a complex term in GT ( E i ) . p − is of the form c. β ( p − n ) , where β = α if α ∈ Σ , and β = α i 0 if α = α i ( E , A ∪ { e 0 } , α ) α ∈ Σ . 0 . If p − is in 1 , . . . , p − dom ( µ ) then so is each p − j , so µ i ( p j ) is defined, by induction hypothesis, E a is the atomic extension of E . and µ i ( p ) = r α ( µ i ( p 1 ) , . . . , µ i ( p n )) (8) Example e 0 = kick-the-bucket = val ( α 0 ( kick , β ( the, bucket ))) a. (13) D efinition of r α i if m j = µ ( q 0 j ) , 1 ≤ j ≤ k b. ‘John kicked the bucket.’ 0 α ( John , α 0 ( kick , β ( the, bucket ))) ↝ literal 0 ( m 1 , . . . , m k ) = { m 0 (i) r α 0 ( m 1 , . . . , m k ) r α i (ii) α ( John , e 0 ) ↝ idiomatic otherwise where each q 0 j is a specified meaning (e.g., µ ( kick ) , µ ( the bucket ) ). • Remarks: • Consequence: This treatment is clearly unsatisfactory for the majority of idioms. It leaves entirely Nothing bad happens if α i 0 applies to elements that lack an idiomatic interpretation unaccounted for the fact that idioms overwhelmingly are syntactically regular, and 0 = r α 0 . (e.g., see John ). In this case r α i that parts of them may be targeted by syntactic operations (e.g., Strings were pulled to secure Henry his position; John kick+ed the bucket ). • A Drawback: Because the definition of r α i 0 is stated in terms of the output of µ , i.e., in meaning, it • Possible candidate: follows that substitution of synonymous expressions should preserve the idiomatic by and large interpretation. If q and q 01 are synonymous, then µ i ( α i 0 ( q 01 , q 02 , . . . . , q 0 k )) = µ i ( α i 0 ( q , q 02 , . . . . , q 0 k )) = m 0 2
• If, e.g., bucket and pale are synonymo us, then kick the pale should mean die. Likewise, (17) I dioms We then add new, idiomatic, elements a i 1 , . . . , a i cemetery shif or burial ground shif should mean what graveyard shif means. k to A such that v ( a i j ) = v ( a j ) , 1 ≤ j ≤ k 2.4 Treating Idioms 3: Indexed Terminals That is, superscripted elements are syntactically identical to their non-indexed counterpart. • Many idioms, like pull strings , may appear in various syntactic constructions: (18) The final grammar has the form E ∗ = (( E , A ∪ { a i (14) a. Strings were pulled to get John his position. k } , α ) α ∈ Σ , v ∗ ) 1 , . . . , a i b. Mary tried to pull a lot of strings. where v ∗ ⊇ v and v ∗ ( a i j ) = v ( a j ) . c. We could pull yet more strings. d. Those strings, he wouldn’t pull for you. (19) Example • Analysis: ‘Mary tried to pull several strings.’ α ( Mary , α 0 ( δ ( try-to, pull ) , γ ( several, strings ))) ↝ literal There are special homophones of pull and string — pull i and strings i , respectively—that a. α ( Mary , α 0 ( δ ( try-to, pull i ) , γ ( several, strings i ))) ↝ idiomatic give rise to the idiomatic meaning. b. • Similar accounts have been argued for by Nunberg et al. (1994) for some and by (20) S emantics Marantz (1996, 1997) for all idioms. The semantics for E ∗ is µ ∗ , which has the following properties: Its domain is K ∗ = { p ∶ p − ∈ dom ( µ )} , (15) G rammar a. µ ∗ ( a i j ) = m i We first adopt a new general definition of a grammar b. j (( E , A , α ) α ∈ Σ , v ) µ ∗ ( α ( q 1 , . . . , q n )) = r α ( µ ∗ ( q 1 ) , . . . , µ ∗ ( q n )) c. where E and Σ are as before but A no longer has to be a subset of E . Instead • A Problem: there is function v from A to E . How do we constrain the distribution of indexed expressions? In particular, how we • We now slightly revise our definition of GT ( E ) (only the clause for simplex expres- make sure that strings in Mary tried to tie several strings does not get an idiomatic interpretation. sions changes): • Westerst å hl’s Solution: (16) G rammatical T erms Make the occurrence of strings i dependent on the occurrence of pull i and vice versa. The set GT ( E ) of grammatical terms and the function val ∶ GT ( E ) → E are (21) A term in GT ( E ∗ ) is meaningful iff it belongs to K ∗ and for each subterm of given by: α ∈ A is an atomic grammatical term, and val ( a ) = v ( a ) . the form α ( p , α 0 ( q 1 , q 2 )) it holds that pull i occurs in q 1 iff strings i occurs in a. b. Suppose α ∈ Σ in an n -ary function symbol, and p 1 , . . . , p n ∈ GT ( E ) with either q 2 or p . val ( p i ) = e i . If α ( e 1 , . . . , e n ) is defined, say α ( e 1 , . . . , e n ) = e , the term α ( p 1 , . . . , p n ) is in GT ( E ) , and val ( α ( p 1 , . . . , p n )) = e . • What about Passives? Passives are treated as underlyingly active and then derived by applying a passive rule NB: grammatical terms are analysis trees; val gives back the string associated α P . Thus, Several strings were pulled by Mary would have the structure with an analysis tree α P ( α ( Mary , α 0 ( δ ( pull i , γ ( several, strings i ))))) and (21) is respected. 3
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