2,452 research outputs found
Extensional and Intensional Strategies
This paper is a contribution to the theoretical foundations of strategies. We
first present a general definition of abstract strategies which is extensional
in the sense that a strategy is defined explicitly as a set of derivations of
an abstract reduction system. We then move to a more intensional definition
supporting the abstract view but more operational in the sense that it
describes a means for determining such a set. We characterize the class of
extensional strategies that can be defined intensionally. We also give some
hints towards a logical characterization of intensional strategies and propose
a few challenging perspectives
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
Resolving the Quantitative-Qualitative Dilemma: A Critical Realist Approach
The philosophical issues underpinning the quantitative–qualitative divide in educational research are examined. Three types of argument which support a resolution are considered: pragmatism, false duality and warranty through triangulation. In addition a number of proposed strategies—alignment, sequencing, translation and triangulation—are critically assessed. The article concludes by suggesting that many of these ways of reconciling quantitative and qualitative methods and approaches are still deficient in relation to the development of an overarching and correct view of ontological and epistemological matters, and that critical realism offers a more coherent solution, where the reconciliation occurs at the ontological level
Defining Law Terms: A Cross-Cultural Perspective
The translation practice trends towards legal definitions seem to be more and more informed by the globalization and ‘Europeanisation’ processes now constituting a still broader context of legal communication rather than confined to the text of a legal instrument itself
The Broadest Necessity
In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language. This relates more generally to a conjecture that it is not possible to define intensional connectives from extensional notions. This conjecture is formulated precisely in higher-order logic, and concrete cases in which it fails are examined. The paper ends with a discussion of the logic of broad necessity. It is shown that the logic of broad necessity is a normal modal logic between S4 and Triv, and that it is consistent with a natural axiomatic system of higher-order logic that it is exactly S4. Some philosophical reasons to think that the logic of broad necessity does not include the S5 principle are given
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