1997
DOI: 10.1007/bfb0052165
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Semilinearity as a syntactic invariant

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Cited by 47 publications
(29 citation statements)
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“…On the complexity side, we expect that, using techniques similar to those in [37], it might be possible to prove that verifying whether the value of a λY +Ω-term is greater than a hereditary prime element of a monotone model is of the same complexity as the emptiness and membership problems for the safe OI hierarchy, which is (n − 2)-Exptime-complete for order n-grammars (see [12]; with Huet's convention, the order of a grammar is one more than the order of its corresponding higher-order pushdown automaton). While most string sets corresponding to natural languages seem to be describable using simple (first order) macro grammars [17] (although some data suggests that this is not enough [24,20]), it is common to find proposals about syntactic mechanisms which ultimately involve higher order types [21], which are needed to associate the desired semantic representation with the derived string. In the domain of semantics, where higher types are commonplace, least fixed point computations have been proposed by [26] (and are a natural way to understand certain prominent proposals about ellipsis resolution [38]) and non-determinism has been (implicitly) used to model pronoun resolution [11].…”
Section: Resultsmentioning
confidence: 99%
“…On the complexity side, we expect that, using techniques similar to those in [37], it might be possible to prove that verifying whether the value of a λY +Ω-term is greater than a hereditary prime element of a monotone model is of the same complexity as the emptiness and membership problems for the safe OI hierarchy, which is (n − 2)-Exptime-complete for order n-grammars (see [12]; with Huet's convention, the order of a grammar is one more than the order of its corresponding higher-order pushdown automaton). While most string sets corresponding to natural languages seem to be describable using simple (first order) macro grammars [17] (although some data suggests that this is not enough [24,20]), it is common to find proposals about syntactic mechanisms which ultimately involve higher order types [21], which are needed to associate the desired semantic representation with the derived string. In the domain of semantics, where higher types are commonplace, least fixed point computations have been proposed by [26] (and are a natural way to understand certain prominent proposals about ellipsis resolution [38]) and non-determinism has been (implicitly) used to model pronoun resolution [11].…”
Section: Resultsmentioning
confidence: 99%
“…While most string sets corresponding to natural languages seem to be describable using simple (first order) macro grammars [17] (although some data suggests that this is not enough [24,20]), it is common to find proposals about syntactic mechanisms which ultimately involve higher order types [21], which are needed to associate the desired semantic representation with the derived string. In the domain of semantics, where higher types are commonplace, least fixed point computations have been proposed by [26] (and are a natural way to understand certain prominent proposals about ellipsis resolution [38]) and nondeterminism has been (implicitly) used to model pronoun resolution [11].…”
Section: Resultsmentioning
confidence: 99%
“…7. The analysis of Chinese number names in Radzinski (1991) poses a problem for the MCS hypothesis, as does the analysis of the case marking system of Old Georgian in Michaelis and Kracht (1997). These constructions are peripheral in Chinese and Georgian, and the linguistic status of the data in these examples is debated, and so we will leave them aside here in favor of several other much more common constructions: A-not-A questions in Mandarin Chinese and VP-ellipsis in English.…”
Section: Discussionmentioning
confidence: 99%