Minimalist Parsing Scott Drellishak CompLing Lab Meeting 2/1/2006

Overview Four parts: Four parts: 1. Whirlwind tour of Minimalism 2. Formal definition of a Minimalist Grammar 3. Algorithms for parsing MGs 4. Software and web sites

Four parts: Four parts: 1. Whirlwind tour of Minimalism 2. Formal definition of a Minimalist Grammar 3. Algorithms for parsing MGs 4. Software and web sites

Minimalism Minimalism Minimalism Recent version of transformational generative grammar. Chomsky’s (1995) The Minimalist Program. Recent version of transformational generative grammar. Chomsky’s (1995) The Minimalist Program. Updates and supersedes earlier GB/P&P Updates and supersedes earlier GB/P&P Explores “the extent to which previous empirical coverage can be maintained with fewer grammatical devices.” (Stabler 1999: 299) Explores “the extent to which previous empirical coverage can be maintained with fewer grammatical devices.” (Stabler 1999: 299)

Minimalism Sentence derivations proceed according to this (famous) diagram: Sentence derivations proceed according to this (famous) diagram: Lexicon Phonetic Form (PF) Logical Form (LF)

Minimalism Items come out of the lexicon fully inflected and with features: interpretable and uninterpretable. Items come out of the lexicon fully inflected and with features: interpretable and uninterpretable. Uninterpretable features must cancel out before the derivation reaches LF. Uninterpretable features must cancel out before the derivation reaches LF. The branch to PF allows the surface form to “peek” into the middle of the derivation. The branch to PF allows the surface form to “peek” into the middle of the derivation. Cross-linguistic differences are accounted for by variations in the lexicon. Cross-linguistic differences are accounted for by variations in the lexicon.

Minimalism Trees are derived by starting with singleton trees (lexical items) and combining them. Trees are derived by starting with singleton trees (lexical items) and combining them. Only two operations: Only two operations: On two trees: merge them together into a single tree (with one “projecting over” the other). On two trees: merge them together into a single tree (with one “projecting over” the other). On a single tree: move a node in the tree up to the root to cancel a feature. On a single tree: move a node in the tree up to the root to cancel a feature. (We’ll see a couple of derivations later.) (We’ll see a couple of derivations later.)

Four parts: Four parts: 1. Whirlwind tour of Minimalism 2. Formal definition of a Minimalist Grammar 3. Algorithms for parsing MGs 4. Software and web sites

Minimalist Grammars For parsing, Minimalism needs formalization. For parsing, Minimalism needs formalization. Stabler (1997) defines a MG as: Stabler (1997) defines a MG as: V =phonetic and interpretable features Cat =categories, selectors, licensors, licensees Lex =expressions (trees) built from V and Cat F ={ merge, move } (Based on an earlier grammar formalism, so the names don’t mean what you think.) (Based on an earlier grammar formalism, so the names don’t mean what you think.)

V = Lexicon Lexical entries like: Lexical entries like: =n d –case every (category D, selects a N, needs case) n language (category N) =d +case =d v speaks (category V, 2 DPs, assigns case to 1) This is a DP analysis This is a DP analysis “speaks” stands for /speaks/(speaks) “speaks” stands for /speaks/(speaks)

Cat = Features Base: c, t, v, d, n, … (parts of speech) Base: c, t, v, d, n, … (parts of speech) Select: =x, =X, X= (selects arguments) Select: =x, =X, X= (selects arguments) Select features trigger merge Select features trigger merge Upper-case moves phonetic content to merged node; “=” determines prefix or postfix Upper-case moves phonetic content to merged node; “=” determines prefix or postfix Licensees: -case, -wh, … (needs…) Licensees: -case, -wh, … (needs…) Licensors: +case, +wh, … (provides…) Licensors: +case, +wh, … (provides…) L* features trigger move; upper-case = “strong” L* features trigger move; upper-case = “strong”

Lex = Trees A set of nodes and three relations: A set of nodes and three relations: Dominance (x ⊳ y = x is y ’ s parent) Dominance (x ⊳ y = x is y ’ s parent) Who ’ s higher in the tree? Who ’ s higher in the tree? Precedence (x ≺ y = x precedes y) Precedence (x ≺ y = x precedes y) Who ’ s before who in the tree? Who ’ s before who in the tree? Projection (x < y = x projects over y) Projection (x < y = x projects over y) Whose features percolate up to the parent? Whose features percolate up to the parent?

F = Operations merge: Combines two trees. A head selects and combines with a phrase to its right: merge: Combines two trees. A head selects and combines with a phrase to its right: =d =d v make + d lunch ⇒ < =d v makelunch

F = Operations If the selector feature is upper case, only the phonetic features combine: If the selector feature is upper case, only the phonetic features combine: D= =d v make + d lunch ⇒ < =d v /lunch make/(make)(lunch)

F = Operations move: One tree’s head’s +x feature attracts the nearest –x feature to the root of the tree: move: One tree’s head’s +x feature attracts the nearest –x feature to the root of the tree: < +case v speak-case Nahuatl ⇒ > (Nahuatl) (Nahuatl)< v speak/Nahuatl/

A Sample Derivation Let’s take a look at the derivation of a simple sentence from Stabler (1997)… Let’s take a look at the derivation of a simple sentence from Stabler (1997)…

Four parts: Four parts: 1. Whirlwind tour of Minimalism 2. Formal definition of a Minimalist Grammar 3. Algorithms for parsing MGs 4. Software and web sites

Parsing MGs Stabler (2000 and 2001) describes a CYK-like algorithm for parsing MGs. Stabler (2000 and 2001) describes a CYK-like algorithm for parsing MGs. Defines a set of operations on strings of features that are arranged in “chains” (forests of incomplete trees). Defines a set of operations on strings of features that are arranged in “chains” (forests of incomplete trees). Each of these operations operates on a contiguous range of the forest, so they can be chart-parsed to recognize input sentences. Each of these operations operates on a contiguous range of the forest, so they can be chart-parsed to recognize input sentences.

MG Operations

CYK? Somewhat different from the version of CYK used to parse CFGs, but it’s still the same idea. Somewhat different from the version of CYK used to parse CFGs, but it’s still the same idea. Each operation transforms a string of features, canceling out selection and licensing features, producing more strings, which are stored in the chart. Each operation transforms a string of features, canceling out selection and licensing features, producing more strings, which are stored in the chart. Then, look for further operations that take them as input, building a hierarchy. Then, look for further operations that take them as input, building a hierarchy.

Another Recognizer Stabler refers to Harkema (2000), which defines a MG recognizer that works more like an Earley parser. Stabler refers to Harkema (2000), which defines a MG recognizer that works more like an Earley parser. It has an agenda and a chart. As operations are applied to make new items, those go into the agenda. Stop when a “goal item” appears in the chart. It has an agenda and a chart. As operations are applied to make new items, those go into the agenda. Stop when a “goal item” appears in the chart. Overall time complexity is O(n 4k+4 ) Overall time complexity is O(n 4k+4 )

Another Sample Derivation Here’s a derivation from Stabler (2000)—a slightly different format; note indices: Here’s a derivation from Stabler (2000)—a slightly different format; note indices: 1. (0,1)::=d v –wlexical 2. (1,2)::d –caselexical 3. (x,x)::=v +case acclexical 4. (x,x)::=acc +w wlexical 5. (0,1):v -w,(1,2):-casemerge3(1,2) 6. (x,x):+case acc,(0,1):-w,(1,2):-casemerge3(3,5) 7. (1,2):acc,(0,1):-wmove1(6) 8. (1,2):+w w,(0,1):-wmerge1(4,7) 9. (0,2):wmove1(8)

Four parts: Four parts: 1. Whirlwind tour of Minimalism 2. Formal definition of a Minimalist Grammar 3. Algorithms for parsing MGs 4. Software and web sites

Parsers Stabler’s parsers: MG parsers in Ocaml and two flavors of Prolog. (Also requires tcl/tk.) Stabler’s parsers: MG parsers in Ocaml and two flavors of Prolog. (Also requires tcl/tk.) Stabler’s parsers Stabler’s parsers Sourabh Niyogi: Stabler-based MG parser in Scheme, does verb subcategorization. Sourabh Niyogi: Stabler-based MG parser in Scheme, does verb subcategorization. Sourabh Niyogi Sourabh Niyogi Willemijn Vermaat: Stabler-based MG parser w/ web interface (that I couldn’t figure out). Willemijn Vermaat: Stabler-based MG parser w/ web interface (that I couldn’t figure out). Willemijn Vermaat Willemijn Vermaat Dekang Lin: MINIPAR. Executable only, based on PRINCIPAR, not clear what the internals are like. Dekang Lin: MINIPAR. Executable only, based on PRINCIPAR, not clear what the internals are like. Dekang Lin Dekang Lin

References Chomsky (1995). The Minimalist Program. Harkema (2000). A Recognizer for Minimalist Grammars. Stabler (1997). Derivational Minimalism. Stabler (1999). Remnant Movement and Structural Complexity. Stabler (2000). Minimalist Grammars and Recognition.