64,349 research outputs found
Intensional and Extensional Semantics of Bounded and Unbounded Nondeterminism
We give extensional and intensional characterizations of nondeterministic
functional programs: as structure preserving functions between biorders, and as
nondeterministic sequential algorithms on ordered concrete data structures
which compute them. A fundamental result establishes that the extensional and
intensional representations of non-deterministic programs are equivalent, by
showing how to construct a unique sequential algorithm which computes a given
monotone and stable function, and describing the conditions on sequential
algorithms which correspond to continuity with respect to each order.
We illustrate by defining may and must-testing denotational semantics for a
sequential functional language with bounded and unbounded choice operators. We
prove that these are computationally adequate, despite the non-continuity of
the must-testing semantics of unbounded nondeterminism. In the bounded case, we
prove that our continuous models are fully abstract with respect to may and
must-testing by identifying a simple universal type, which may also form the
basis for models of the untyped lambda-calculus. In the unbounded case we
observe that our model contains computable functions which are not denoted by
terms, by identifying a further "weak continuity" property of the definable
elements, and use this to establish that it is not fully abstract
Effective lambda-models vs recursively enumerable lambda-theories
A longstanding open problem is whether there exists a non syntactical model
of the untyped lambda-calculus whose theory is exactly the least lambda-theory
(l-beta). In this paper we investigate the more general question of whether the
equational/order theory of a model of the (untyped) lambda-calculus can be
recursively enumerable (r.e. for brevity). We introduce a notion of effective
model of lambda-calculus calculus, which covers in particular all the models
individually introduced in the literature. We prove that the order theory of an
effective model is never r.e.; from this it follows that its equational theory
cannot be l-beta or l-beta-eta. We then show that no effective model living in
the stable or strongly stable semantics has an r.e. equational theory.
Concerning Scott's semantics, we investigate the class of graph models and
prove that no order theory of a graph model can be r.e., and that there exists
an effective graph model whose equational/order theory is minimum among all
theories of graph models. Finally, we show that the class of graph models
enjoys a kind of downwards Lowenheim-Skolem theorem.Comment: 34
Probabilistic Argumentation with Epistemic Extensions and Incomplete Information
Abstract argumentation offers an appealing way of representing and evaluating
arguments and counterarguments. This approach can be enhanced by a probability
assignment to each argument. There are various interpretations that can be
ascribed to this assignment. In this paper, we regard the assignment as
denoting the belief that an agent has that an argument is justifiable, i.e.,
that both the premises of the argument and the derivation of the claim of the
argument from its premises are valid. This leads to the notion of an epistemic
extension which is the subset of the arguments in the graph that are believed
to some degree (which we defined as the arguments that have a probability
assignment greater than 0.5). We consider various constraints on the
probability assignment. Some constraints correspond to standard notions of
extensions, such as grounded or stable extensions, and some constraints give us
new kinds of extensions
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