Abstract Semantic automata theory studies the complexity of generalized quantifiers in terms of the string languages that describe their truth conditions. An important point has gone unnoticed so far: for most quantifiers that are determiners, these string languages are subregular. Whereas quantifier phrases such as an even number of correspond to specific regular languages, every, no, some and not all stay within the much weaker class of tier-based strictly local languages (TSL). In addition, it seems to hold crosslinguistically that a TSL quantifier may be expressed by a single lexical item only if its tier projection is monotonic. This constitutes a novel typological universal that limits how complex a meaning may be stored in a single lexical item. TSL is also known to play a central role in phonology, morphology, and syntax, which suggests that subregularity in general and tier-based strict locality in particular may be a computational universal of natural language that surfaces across all its submodules, including semantics.

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A Subregular Bound on the Complexity of Lexical Quantifiers

Sun 15 December 2019 | in Papers |
| subregular | semantics | generalized quantifiers | typology |

Graf, Thomas

Abstract Semantic automata theory studies the complexity of generalized quantifiers in terms of the string languages that describe their truth conditions. An important point has gone unnoticed so far: for most quantifiers that are determiners, these string languages are subregular. Whereas quantifier phrases …
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Subregular Morpho-Semantics: The Expressive Limits of Monomorphemic Quantifiers

Fri 15 December 2017 | in Presentations |
| subregular hierarchy | semantics | typology | tiers | monotonicity |

Graf, Thomas

Abstract Even though languages are capable of expressing very complex generalized quantifiers such as all but seven and an even number of, the range of possible meanings for monomorphemic determiners seems to be limited to every, no, some, and numerals. In this talk …
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Evaluating Subregular Distinctions in the Complexity of Generalized Quantifiers

Sat 22 July 2017 | in Presentations |
| subregular hierarchy | semantics | quantifiers | typology | tiers |

De Santo, Aniello, Thomas Graf, and John E. Drury

Abstract Semantic automata were developed to compare the complexity of generalized quantifiers based on the complexity of the string languages that describe their truth conditions. An important point that has gone unnoticed so far is that …
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Fragments of First-Order Logic for Linguistic Structures

Mon 24 April 2017 | in Presentations |
| phonology | morphology | syntax | semantics | morphosemantics | subregular hierarchy | logic | tiers |

Graf, Thomas

Abstract Logic has always played a central role in the study of natural language meaning. But logic can also be used to describe the structure of words and sentences. Recent research has revealed that these structures are so simple that they can be …
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Adjuncts, Islands, Algebra (with a Sprinkling of Semantics)

Graf, Thomas

Files [pdf] [code]

@Misc{Graf14CUNYtalk,
  author    = {Graf, Thomas},
  title     = {Adjuncts, Islands, Algebra (With a Sprinkling of
          Semantics)},
  year      = {2014},
  note      = {Invited talk, November 4, CUNY Graduate Center, New York,
          NY}
}

Optimality Is Not a Race: Against a Performance-Based View of Reference-Set Computation

Fri 29 April 2011 | in Presentations |
| transderivationality | reference-set computation | constraints | syntax | semantics | transducers |

Graf, Thomas

Abstract Reference-set constraints (RCs; also known as transderivational constraints) differ from standard well-formedness conditions in that for every tree, they compute a set of output candidates called its reference set and pick from said set the optimal candidate(s) according to some economy …
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Syntax, Semantics, Pragmatics: Where Do We Find Optimality?

Graf, Thomas

Files [pdf] [code]

@Misc{Graf10Goettingentalk,
  author    = {Graf, Thomas},
  title     = {Syntax, Semantics, Pragmatics: {W}here do we Find
          Optimality?},
  year      = {2010},
  note      = {Invited talk, December 15, Institut für Anglistik,
          Universität Göttingen, Göttingen, Germany}
}

Optimality Conditions Could Care Less About Optimality

Graf, Thomas

Files [pdf] [code]

@Misc{Graf10ZAStalk,
  author    = {Graf, Thomas},
  title     = {Optimality Conditions Could Care Less About Optimality},
  year      = {2010},
  note      = {Invited talk, December 10, Zentrum für Allgemeine
          Sprachwissenschaft (ZAS), Berlin, Germany}
}

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