104,171 research outputs found
A Nominal Theory of Objects with Dependent Types
We design and study newObj, a calculus and dependent type system forobjects and classes which can have types as members. Type members canbe aliases, abstract types, or new types. The type system can modelthe essential concepts of Java's inner classes as well as virtual typesand family polymorphism found in BETA or gbeta. It can also model mostconcepts of SML-style module systems, including sharing constraintsand higher-order functors, but excluding applicative functors.The type system can thus be used as a basis for unifying conceptsthat so far existed in parallel in advanced object systems and inmodule systems. The technical report presents results on confluenceof the calculus, soundness of the type system, and undecidability oftype checking
A dependent nominal type theory
Nominal abstract syntax is an approach to representing names and binding
pioneered by Gabbay and Pitts. So far nominal techniques have mostly been
studied using classical logic or model theory, not type theory. Nominal
extensions to simple, dependent and ML-like polymorphic languages have been
studied, but decidability and normalization results have only been established
for simple nominal type theories. We present a LF-style dependent type theory
extended with name-abstraction types, prove soundness and decidability of
beta-eta-equivalence checking, discuss adequacy and canonical forms via an
example, and discuss extensions such as dependently-typed recursion and
induction principles
Token-based typology and word order entropy: A study based on universal dependencies
The present paper discusses the benefits and challenges of token-based typology, which takes into account the frequencies of words and constructions in language use. This approach makes it possible to introduce new criteria for language classification, which would be difficult or impossible to achieve with the traditional, type-based approach. This point is illustrated by several quantitative studies of word order variation, which can be measured as entropy at different levels of granularity. I argue that this variation can be explained by general functional mechanisms and pressures, which manifest themselves in language use, such as optimization of processing (including avoidance of ambiguity) and grammaticalization of predictable units occurring in chunks. The case studies are based on multilingual corpora, which have been parsed using the Universal Dependencies annotation scheme
Metaphoric coherence: Distinguishing verbal metaphor from `anomaly\u27
Theories and computational models of metaphor comprehension generally circumvent the question of metaphor versus “anomaly” in favor of a treatment of metaphor versus literal language. Making the distinction between metaphoric and “anomalous” expressions is subject to wide variation in judgment, yet humans agree that some potentially metaphoric expressions are much more comprehensible than others. In the context of a program which interprets simple isolated sentences that are potential instances of cross‐modal and other verbal metaphor, I consider some possible coherence criteria which must be satisfied for an expression to be “conceivable” metaphorically. Metaphoric constraints on object nominals are represented as abstracted or extended along with the invariant structural components of the verb meaning in a metaphor. This approach distinguishes what is preserved in metaphoric extension from that which is “violated”, thus referring to both “similarity” and “dissimilarity” views of metaphor. The role and potential limits of represented abstracted properties and constraints is discussed as they relate to the recognition of incoherent semantic combinations and the rejection or adjustment of metaphoric interpretations
An Algebraic Weak Factorisation System on 01-Substitution Sets: A Constructive Proof
We will construct an algebraic weak factorisation system on the category of
01 substitution sets such that the R-algebras are precisely the Kan fibrations
together with a choice of Kan filling operation. The proof is based on Garner's
small object argument for algebraic weak factorization systems. In order to
ensure the proof is valid constructively, rather than applying the general
small object argument, we give a direct proof based on the same ideas. We use
this us to give an explanation why the J computation rule is absent from the
original cubical set model and suggest a way to fix this
Formal foundations for semantic theories of nominalisation
This paper develops the formal foundations of semantic theories dealing with various kinds of nominalisations. It introduces a combination of an event-calculus with a type-free theory which allows a compositional description to be given of such phenomena like Vendler's distinction between perfect and imperfect nominals, iteration of gerunds and Cresswell's notorious non-urrival of'the train examples. Moreover, the approach argued for in this paper allows a semantic explanation to be given for a wide range of grammatical observations such as the behaviour of certain tpes of nominals with respect to their verbal contexts or the distribution of negation in nominals
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