185 research outputs found
A continuation semantics of interrogatives that accounts for Baker's ambiguity
Wh-phrases in English can appear both raised and in-situ. However, only
in-situ wh-phrases can take semantic scope beyond the immediately enclosing
clause. I present a denotational semantics of interrogatives that naturally
accounts for these two properties. It neither invokes movement or economy, nor
posits lexical ambiguity between raised and in-situ occurrences of the same
wh-phrase. My analysis is based on the concept of continuations. It uses a
novel type system for higher-order continuations to handle wide-scope
wh-phrases while remaining strictly compositional. This treatment sheds light
on the combinatorics of interrogatives as well as other kinds of so-called
A'-movement.Comment: 20 pages; typo fixe
The partition semantics of questions, syntactically
Groenendijk and Stokhof (1984, 1996; Groenendijk 1999) provide a logically
attractive theory of the semantics of natural language questions, commonly
referred to as the partition theory. Two central notions in this theory are
entailment between questions and answerhood. For example, the question "Who is
going to the party?" entails the question "Is John going to the party?", and
"John is going to the party" counts as an answer to both. Groenendijk and
Stokhof define these two notions in terms of partitions of a set of possible
worlds.
We provide a syntactic characterization of entailment between questions and
answerhood . We show that answers are, in some sense, exactly those formulas
that are built up from instances of the question. This result lets us compare
the partition theory with other approaches to interrogation -- both linguistic
analyses, such as Hamblin's and Karttunen's semantics, and computational
systems, such as Prolog. Our comparison separates a notion of answerhood into
three aspects: equivalence (when two questions or answers are interchangeable),
atomic answers (what instances of a question count as answers), and compound
answers (how answers compose).Comment: 14 page
Exact Recursive Probabilistic Programming
Recursive calls over recursive data are widely useful for generating
probability distributions, and probabilistic programming allows computations
over these distributions to be expressed in a modular and intuitive way. Exact
inference is also useful, but unfortunately, existing probabilistic programming
languages do not perform exact inference on recursive calls over recursive
data, forcing programmers to code many applications manually. We introduce a
probabilistic language in which a wide variety of recursion can be expressed
naturally, and inference carried out exactly. For instance, probabilistic
pushdown automata and their generalizations are easy to express, and
polynomial-time parsing algorithms for them are derived automatically. We
eliminate recursive data types using program transformations related to
defunctionalization and refunctionalization. These transformations are assured
correct by a linear type system, and a successful choice of transformations, if
there is one, is guaranteed to be found by a greedy algorithm
On the Static and Dynamic Extents of Delimited Continuations
We show that breadth-first traversal exploits the difference between the static delimited-control operator shift (alias S) and the dynamic delimited-control operator control (alias F). For the last 15 years, this difference has been repeatedly mentioned in the literature but it has only been illustrated with one-line toy examples. Breadth-first traversal fills this vacuum. We also point out where static delimited continuations naturally give rise to the notion of control stack whereas dynamic delimited continuations can be made to account for a notion of `control queue.'
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