13,182 research outputs found
Explicit Substitutions for Contextual Type Theory
In this paper, we present an explicit substitution calculus which
distinguishes between ordinary bound variables and meta-variables. Its typing
discipline is derived from contextual modal type theory. We first present a
dependently typed lambda calculus with explicit substitutions for ordinary
variables and explicit meta-substitutions for meta-variables. We then present a
weak head normalization procedure which performs both substitutions lazily and
in a single pass thereby combining substitution walks for the two different
classes of variables. Finally, we describe a bidirectional type checking
algorithm which uses weak head normalization and prove soundness.Comment: In Proceedings LFMTP 2010, arXiv:1009.218
Laws, Causation and Dynamics at Different Levels
I have two main aims. The first is general, and more philosophical (Section 2). The second is specific, and more closely related to physics (Sections 3 and 4).
The first aim is to state my general views about laws and causation at different `levels'. The main task is to understand how the higher levels sustain notions of law and causation that `ride free' of reductions to the lower level or levels. I endeavour to relate my views to those of other symposiasts.
The second aim is to give a framework for describing dynamics at different levels, emphasising how the various levels' dynamics can mesh or fail to mesh. This framework is essentially that of elementary dynamical systems theory. The main idea will be, for simplicity, to work with just two levels, dubbed `micro' and `macro' which are related by coarse-graining. I use this framework to describe, in part, the first four of Ellis' five types of top-down causation
Mechanized semantics
The goal of this lecture is to show how modern theorem provers---in this
case, the Coq proof assistant---can be used to mechanize the specification of
programming languages and their semantics, and to reason over individual
programs and over generic program transformations, as typically found in
compilers. The topics covered include: operational semantics (small-step,
big-step, definitional interpreters); a simple form of denotational semantics;
axiomatic semantics and Hoare logic; generation of verification conditions,
with application to program proof; compilation to virtual machine code and its
proof of correctness; an example of an optimizing program transformation (dead
code elimination) and its proof of correctness
An Empirical Examination of Symptom Substitution Associated with Behavior Therapy for Tourette\u27s Disorder
Over the past six decades, behavior therapy has been a major contributor to the development of evidence-based psychotherapy treatments. However, a long-standing concern with behavior therapy among many nonbehavioral clinicians has been the potential risk for symptom substitution. Few studies have been conducted to evaluate symptom substitution in response to behavioral treatments, largely due to measurement and definitional challenges associated with treated psychiatric symptoms. Given the overt motor and vocal tics associated with Touretteās disorder, it presents an excellent opportunity to empirically evaluate the potential risk for symptom substitution associated with behavior therapy. The present study examined the possible presence of symptom substitution using four methods: (a) the onset of new tic symptoms, (b) the occurrence of adverse events, (c) change in tic medications, and (d) worsening of co-occurring psychiatric symptoms. Two hundred twenty-eight participants with Touretteās disorder or persistent motor or vocal tic disorders were randomly assigned to receive behavioral therapy or supportive therapy for tics. Both therapies consisted of eight sessions over 10 weeks. Results indicated that participants treated with behavior therapy were not more likely to have an onset of new tic symptoms, experience adverse events, increase tic medications, or have an exacerbation in co-occurring psychiatric symptoms relative to participants treated with supportive therapy. Further analysis suggested that the emergence of new tics was attributed with the normal waxing and waning nature of Touretteās disorder. Findings provide empirical support to counter the long-standing concern of symptom substitution in response to behavior therapy for individuals with Tourette\u27s disorder
On the Emergence of Time in Quantum Gravity
We discuss from a philosophical perspective the way in which the normal
concept of time might be said to `emerge' in a quantum theory of gravity. After
an introduction, we briefly discuss the notion of emergence, without regard to
time (Section 2). We then introduce the search for a quantum theory of gravity
(Section 3); and review some general interpretative issues about space, time
and matter Section 4). We then discuss the emergence of time in simple quantum
geometrodynamics, and in the Euclidean approach (Section 5). Section 6
concludes.Comment: To appear in ``The Arguments of Time'', ed. J. Butterfield, Oxford
University Press, 199
FO(FD): Extending classical logic with rule-based fixpoint definitions
We introduce fixpoint definitions, a rule-based reformulation of fixpoint
constructs. The logic FO(FD), an extension of classical logic with fixpoint
definitions, is defined. We illustrate the relation between FO(FD) and FO(ID),
which is developed as an integration of two knowledge representation paradigms.
The satisfiability problem for FO(FD) is investigated by first reducing FO(FD)
to difference logic and then using solvers for difference logic. These
reductions are evaluated in the computation of models for FO(FD) theories
representing fairness conditions and we provide potential applications of
FO(FD).Comment: Presented at ICLP 2010. 16 pages, 1 figur
On Irrelevance and Algorithmic Equality in Predicative Type Theory
Dependently typed programs contain an excessive amount of static terms which
are necessary to please the type checker but irrelevant for computation. To
separate static and dynamic code, several static analyses and type systems have
been put forward. We consider Pfenning's type theory with irrelevant
quantification which is compatible with a type-based notion of equality that
respects eta-laws. We extend Pfenning's theory to universes and large
eliminations and develop its meta-theory. Subject reduction, normalization and
consistency are obtained by a Kripke model over the typed equality judgement.
Finally, a type-directed equality algorithm is described whose completeness is
proven by a second Kripke model.Comment: 36 pages, superseds the FoSSaCS 2011 paper of the first author,
titled "Irrelevance in Type Theory with a Heterogeneous Equality Judgement
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