Minimalist grammars

MCFG rules describe directly how string tuples concatenate. What would a grammar look like if lexical features instead determined the available syntactic operations? Minimalist grammars (MGs) formalize a feature-driven system of Merge and Move (Stabler 1997). An MG lexical item describes which of those operations it can trigger or satisfy.

Reading

Read Stabler (1997) on lexical feature sequences, Merge, and Move.

Feature sequences

An MG lexicon pairs a phonological form with a finite sequence of features. Four common feature shapes are:

$=x$: select an expression of category $x$;
$x$: project or satisfy category $x$;
$+f$: trigger movement associated with feature $f$; and
$-f$: mark an expression that must undergo that movement.

For instance, a transitive verb might have the sequence $=d\;=d\;v$: it selects two determiner phrases and then behaves as a verbal expression. The order and interpretation of the two selectors depend on the chosen MG definition.

Merge and Move

Merge applies when a selector $=x$ matches category $x$. It combines the two expressions and removes the matched features.

Move applies when a licensor $+f$ in an expression matches a licensee $-f$ contained within it. It reorders the licensed subexpression and removes the matched movement features.

These are formal operations over feature-bearing expressions. Calling an operation Move does not by itself determine its linguistic analysis; the lexicon determines which dependencies the grammar derives.

Question

What prevents Merge from combining any two lexical items?

Answer

Merge requires a matching selector and category. An expression with initial feature $=d$ can select an expression whose relevant category feature is $d$, but it cannot select an arbitrary $n$ or $v$ expression.

Compilation to string-tuple grammars

Formal versions of MGs and MCFGs or LCFRSs are weakly equivalent: each system can be translated into the other while preserving the generated strings (Michaelis 2001a, 2001b; Harkema 2001). This is a statement about weak generative capacity. It does not identify MG derivation trees with MCFG derivation trees, nor does it imply that every linguistic analysis transfers unchanged.

The equivalence supplies a computational route from feature-driven grammars to tuple-based recognition. An MG can be compiled into an MCFG and then recognized with an MCFG parsing algorithm (Kobele et al. 2007). The compiled grammar records the string components needed to track expressions whose surface material is discontinuous.

Research on subregular constraints over MG derivation trees asks a different question: how complex are the well-formed sets of derivations once those derivations are represented as trees (Graf 2013)? That connection returns to the subregular perspective from phonology, but it changes the objects under study from surface strings to derivation structures.

The next section demonstrates both directions of this equivalence slowly. It first identifies the tuple of string pieces associated with a partial MG expression, then shows how Merge and Move preserve that tuple invariant, and finally reverses the construction for a normalized LCFRS.

The five formalisms in this unit thus should not be collapsed into one class. TAG and suitably restricted CCG are weakly equivalent; MG and general MCFG or LCFRS are weakly equivalent under the cited formal definitions; and the general MCFG family properly contains the TAG language class. The final project works at the MCFG level because tuple-valued rules expose the information a recognizer must store.

References

Graf, Thomas. 2013. “Local and Transderivational Constraints in Syntax and Semantics.” PhD thesis, UCLA.

Harkema, Hendrik. 2001. “Parsing Minimalist Languages.” PhD thesis, University of California, Los Angeles. https://linguistics.ucla.edu/people/stabler/paris12/Harkema01.pdf.

Kobele, Gregory M., Christian Retoré, and Sylvain Salvati. 2007. “An Automata-Theoretic Approach to Minimalism.” Model Theoretic Syntax at 10.

Michaelis, Jens. 2001a. “Derivational Minimalism Is Mildly Context-Sensitive.” Logical Aspects of Computational Linguistics: Third International Conference, LACL ’98, Selected Papers, Lecture notes in computer science, vol. 2014: 179–98. https://doi.org/10.1007/3-540-45738-0_11.

Michaelis, Jens. 2001b. “Transforming Linear Context-Free Rewriting Systems into Minimalist Grammars.” Logical Aspects of Computational Linguistics, LNCS, vol. 2099: 228–44. https://doi.org/10.1007/3-540-48199-0_14.

Stabler, Edward P. 1997. “Derivational Minimalism.” In Logical Aspects of Computational Linguistics, vol. 1328. LNCS. Springer.

--- title: Minimalist grammars bibliography: ../../references.bib --- MCFG rules describe directly how string tuples concatenate. What would a grammar look like if lexical features instead determined the available syntactic operations? Minimalist grammars (MGs) formalize a feature-driven system of Merge and Move [@stabler1997derivational]. An MG lexical item describes which of those operations it can trigger or satisfy. ::: {.callout-note title="Reading"} Read @stabler1997derivational on lexical feature sequences, Merge, and Move. ::: ## Feature sequences An MG lexicon pairs a phonological form with a finite sequence of features. Four common feature shapes are: - $=x$: select an expression of category $x$; - $x$: project or satisfy category $x$; - $+f$: trigger movement associated with feature $f$; and - $-f$: mark an expression that must undergo that movement. For instance, a transitive verb might have the sequence $=d\;=d\;v$: it selects two determiner phrases and then behaves as a verbal expression. The order and interpretation of the two selectors depend on the chosen MG definition. ## Merge and Move *Merge* applies when a selector $=x$ matches category $x$. It combines the two expressions and removes the matched features. *Move* applies when a licensor $+f$ in an expression matches a licensee $-f$ contained within it. It reorders the licensed subexpression and removes the matched movement features. These are formal operations over feature-bearing expressions. Calling an operation *Move* does not by itself determine its linguistic analysis; the lexicon determines which dependencies the grammar derives. ::: {.callout-note collapse="true" title="Question"} What prevents Merge from combining any two lexical items? ::: {.callout-tip collapse="true" title="Answer"} Merge requires a matching selector and category. An expression with initial feature $=d$ can select an expression whose relevant category feature is $d$, but it cannot select an arbitrary $n$ or $v$ expression. ::: ::: ## Compilation to string-tuple grammars Formal versions of MGs and MCFGs or LCFRSs are weakly equivalent: each system can be translated into the other while preserving the generated strings [@michaelis1998derivational; @michaelis2001transforming; @harkema2001parsing]. This is a statement about *weak* generative capacity. It does not identify MG derivation trees with MCFG derivation trees, nor does it imply that every linguistic analysis transfers unchanged. The equivalence supplies a computational route from feature-driven grammars to tuple-based recognition. An MG can be compiled into an MCFG and then recognized with an MCFG parsing algorithm [@kobele2007parsing]. The compiled grammar records the string components needed to track expressions whose surface material is discontinuous. Research on subregular constraints over MG derivation trees asks a different question: how complex are the well-formed sets of derivations once those derivations are represented as trees [@graf2013local]? That connection returns to the subregular perspective from phonology, but it changes the objects under study from surface strings to derivation structures. The [next section](proving-equivalences.qmd) demonstrates both directions of this equivalence slowly. It first identifies the tuple of string pieces associated with a partial MG expression, then shows how Merge and Move preserve that tuple invariant, and finally reverses the construction for a normalized LCFRS. The five formalisms in this unit thus should not be collapsed into one class. TAG and suitably restricted CCG are weakly equivalent; MG and general MCFG or LCFRS are weakly equivalent under the cited formal definitions; and the general MCFG family properly contains the TAG language class. The final project works at the MCFG level because tuple-valued rules expose the information a recognizer must store.