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An Algebraic Perspective on the Person Case Constraint

Graf, Thomas

Abstract Graf (2011) and Kobele (2011) proved independently that Minimalist grammars can express all constraints that are definable in weak monadic second-order logic (MSO), i.e. the extension of first-order logic with quantification over finite sets. The proof takes as its vantage point the well-known equivalence between MSO and finite-state tree automata and then shows how such automata can be emulated in the Minimalist feature calculus. On the one hand this is a welcome result, as numerous phenomena that seem bewildering to linguists can now be understood as merely arising from the unexpected MSO-like power of the feature calculus. On the other hand, it also exacerbates the overgeneration problem —- there are infinitely many patterns that are MSO-definable yet are not realized in any known language. For example, it is a relatively easy exercise to write an MSO-formula that is satisfied in a tree only if assigning each leaf $l$ the value $0$ or $1$ depending on whether the length of the shortest path from the root to $l$ is even or odd yields a string that is the binary encoding of the longest sentence in Hermann Broch’s The Death of Virgil (which allegedly contains over a thousand words). Seeing how the feature calculus is the essential component in capturing the expressivity of MSO, it is a natural idea to look for empirically motivated restrictions that might curtail its excessive power.

As a first step in this direction, I show here how the attested variants of the Person Case Constraint can be treated with MSO in a unified fashion if one posits certain plausible restrictions on the algebra of person features. The general upshot is that the different Person Case Constraints correspond to specific preorders over the set of person features, and that these preorders form a particular class of presemilattices.

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  author    = {Graf, Thomas},
  title     = {An Algebraic Perspective on the {P}erson {C}ase {C}onstraint},
  year      = {2012},
  editor    = {Graf, Thomas and Paperno, Denis and Szabolcsi, Anna and
          Tellings, Jos},
  booktitle = {Theories of Everything. {I}n Honor of {E}d {K}eenan},
  pages     = {85--90},
  volume    = {17},
  series    = {UCLA Working Papers in Linguistics}