2,310 research outputs found
Predicativity, the Russell-Myhill Paradox, and Church's Intensional Logic
This paper sets out a predicative response to the Russell-Myhill paradox of
propositions within the framework of Church's intensional logic. A predicative
response places restrictions on the full comprehension schema, which asserts
that every formula determines a higher-order entity. In addition to motivating
the restriction on the comprehension schema from intuitions about the stability
of reference, this paper contains a consistency proof for the predicative
response to the Russell-Myhill paradox. The models used to establish this
consistency also model other axioms of Church's intensional logic that have
been criticized by Parsons and Klement: this, it turns out, is due to resources
which also permit an interpretation of a fragment of Gallin's intensional
logic. Finally, the relation between the predicative response to the
Russell-Myhill paradox of propositions and the Russell paradox of sets is
discussed, and it is shown that the predicative conception of set induced by
this predicative intensional logic allows one to respond to the Wehmeier
problem of many non-extensions.Comment: Forthcoming in The Journal of Philosophical Logi
super-Charging Object-Oriented Programming Through Precise Typing of Open Recursion
We present a new variation of object-oriented programming built around three simple and orthogonal constructs: classes for storing object state, interfaces for expressing object types, and mixins for reusing and overriding implementations. We show that the latter can be made uniquely expressive by leveraging a novel feature that we call precisely-typed open recursion. This features uses "this" and "super" annotations to express the requirements of any given partial method implementation on the types of respectively the current object and the inherited definitions. Crucially, the fact that mixins do not introduce types nor subtyping relationships means they can be composed even when the overriding and overridden methods have incomparable types. Together with advanced type inference and structural typing support provided by the MLscript programming language, we show that this enables an elegant and powerful solution to the Expression Problem
Challenges in Bridging Social Semantics and Formal Semantics on the Web
This paper describes several results of Wimmics, a research lab which names
stands for: web-instrumented man-machine interactions, communities, and
semantics. The approaches introduced here rely on graph-oriented knowledge
representation, reasoning and operationalization to model and support actors,
actions and interactions in web-based epistemic communities. The re-search
results are applied to support and foster interactions in online communities
and manage their resources
Inductive-data-type Systems
In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the last
two authors presented a combined language made of a (strongly normalizing)
algebraic rewrite system and a typed lambda-calculus enriched by
pattern-matching definitions following a certain format, called the "General
Schema", which generalizes the usual recursor definitions for natural numbers
and similar "basic inductive types". This combined language was shown to be
strongly normalizing. The purpose of this paper is to reformulate and extend
the General Schema in order to make it easily extensible, to capture a more
general class of inductive types, called "strictly positive", and to ease the
strong normalization proof of the resulting system. This result provides a
computation model for the combination of an algebraic specification language
based on abstract data types and of a strongly typed functional language with
strictly positive inductive types.Comment: Theoretical Computer Science (2002
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