134 research outputs found
A quantum computational semantics for epistemic logical operators. Part I: epistemic structures
Some critical open problems of epistemic logics can be investigated in the framework
of a quantum computational approach. The basic idea is to interpret sentences like
“Alice knows that Bob does not understand that π is irrational” as pieces of quantum information
(generally represented by density operators of convenient Hilbert spaces). Logical
epistemic operators (to understand, to know. . .) are dealt with as (generally irreversible)
quantum operations, which are, in a sense, similar to measurement-procedures. This approach
permits us to model some characteristic epistemic processes, that concern both human
and artificial intelligence. For instance, the operation of “memorizing and retrieving
information” can be formally represented, in this framework, by using a quantum teleportation
phenomenon
Contextual logic for quantum systems
In this work we build a quantum logic that allows us to refer to physical
magnitudes pertaining to different contexts from a fixed one without the
contradictions with quantum mechanics expressed in no-go theorems. This logic
arises from considering a sheaf over a topological space associated to the
Boolean sublattices of the ortholattice of closed subspaces of the Hilbert
space of the physical system. Differently to standard quantum logics, the
contextual logic maintains a distributive lattice structure and a good
definition of implication as a residue of the conjunction.Comment: 16 pages, no figure
On the nature of continuous physical quantities in classical and quantum mechanics
Within the traditional Hilbert space formalism of quantum mechanics, it is
not possible to describe a particle as possessing, simultaneously, a sharp
position value and a sharp momentum value. Is it possible, though, to describe
a particle as possessing just a sharp position value (or just a sharp momentum
value)? Some, such as Teller (Journal of Philosophy, 1979), have thought that
the answer to this question is No -- that the status of individual continuous
quantities is very different in quantum mechanics than in classical mechanics.
On the contrary, I shall show that the same subtle issues arise with respect to
continuous quantities in classical and quantum mechanics; and that it is, after
all, possible to describe a particle as possessing a sharp position value
without altering the standard formalism of quantum mechanics.Comment: 26 pages, LaTe
Algebras of Measurements: the logical structure of Quantum Mechanics
In Quantum Physics, a measurement is represented by a projection on some
closed subspace of a Hilbert space. We study algebras of operators that
abstract from the algebra of projections on closed subspaces of a Hilbert
space. The properties of such operators are justified on epistemological
grounds. Commutation of measurements is a central topic of interest. Classical
logical systems may be viewed as measurement algebras in which all measurements
commute. Keywords: Quantum measurements, Measurement algebras, Quantum Logic.
PACS: 02.10.-v.Comment: Submitted, 30 page
Extended Representations of Observables and States for a Noncontextual Reinterpretation of QM
A crucial and problematical feature of quantum mechanics (QM) is
nonobjectivity of properties. The ESR model restores objectivity reinterpreting
quantum probabilities as conditional on detection and embodying the
mathematical formalism of QM into a broader noncontextual (hence local)
framework. We propose here an improved presentation of the ESR model containing
a more complete mathematical representation of the basic entities of the model.
We also extend the model to mixtures showing that the mathematical
representations of proper mixtures does not coincide with the mathematical
representation of mixtures provided by QM, while the representation of improper
mixtures does. This feature of the ESR model entails that some interpretative
problems raising in QM when dealing with mixtures are avoided. From an
empirical point of view the predictions of the ESR model depend on some
parameters which may be such that they are very close to the predictions of QM
in most cases. But the nonstandard representation of proper mixtures allows us
to propose the scheme of an experiment that could check whether the predictions
of QM or the predictions of the ESR model are correct.Comment: 17 pages, standard latex. Extensively revised versio
Labels for non-individuals
Quasi-set theory is a first order theory without identity, which allows us to
cope with non-individuals in a sense. A weaker equivalence relation called
``indistinguishability'' is an extension of identity in the sense that if
is identical to then and are indistinguishable, although the
reciprocal is not always valid. The interesting point is that quasi-set theory
provides us a useful mathematical background for dealing with collections of
indistinguishable elementary quantum particles. In the present paper, however,
we show that even in quasi-set theory it is possible to label objects that are
considered as non-individuals. We intend to prove that individuality has
nothing to do with any labelling process at all, as suggested by some authors.
We discuss the physical interpretation of our results.Comment: 11 pages, no figure
Day and night closed-loop control in adults with type 1 diabetes: a comparison of two closed-loop algorithms driving continuous subcutaneous insulin infusion versus patient self-management.
OBJECTIVE: To compare two validated closed-loop (CL) algorithms versus patient self-control with CSII in terms of glycemic control. RESEARCH DESIGN AND METHODS: This study was a multicenter, randomized, three-way crossover, open-label trial in 48 patients with type 1 diabetes mellitus for at least 6 months, treated with continuous subcutaneous insulin infusion. Blood glucose was controlled for 23 h by the algorithm of the Universities of Pavia and Padova with a Safety Supervision Module developed at the Universities of Virginia and California at Santa Barbara (international artificial pancreas [iAP]), by the algorithm of University of Cambridge (CAM), or by patients themselves in open loop (OL) during three hospital admissions including meals and exercise. The main analysis was on an intention-to-treat basis. Main outcome measures included time spent in target (glucose levels between 3.9 and 8.0 mmol/L or between 3.9 and 10.0 mmol/L after meals). RESULTS: Time spent in the target range was similar in CL and OL: 62.6% for OL, 59.2% for iAP, and 58.3% for CAM. While mean glucose level was significantly lower in OL (7.19, 8.15, and 8.26 mmol/L, respectively) (overall P = 0.001), percentage of time spent in hypoglycemia (<3.9 mmol/L) was almost threefold reduced during CL (6.4%, 2.1%, and 2.0%) (overall P = 0.001) with less time ≤2.8 mmol/L (overall P = 0.038). There were no significant differences in outcomes between algorithms. CONCLUSIONS: Both CAM and iAP algorithms provide safe glycemic control
`What is a Thing?': Topos Theory in the Foundations of Physics
The goal of this paper is to summarise the first steps in developing a
fundamentally new way of constructing theories of physics. The motivation comes
from a desire to address certain deep issues that arise when contemplating
quantum theories of space and time. In doing so we provide a new answer to
Heidegger's timeless question ``What is a thing?''.
Our basic contention is that constructing a theory of physics is equivalent
to finding a representation in a topos of a certain formal language that is
attached to the system. Classical physics uses the topos of sets. Other
theories involve a different topos. For the types of theory discussed in this
paper, a key goal is to represent any physical quantity with an arrow
\breve{A}_\phi:\Si_\phi\map\R_\phi where \Si_\phi and are two
special objects (the `state-object' and `quantity-value object') in the
appropriate topos, .
We discuss two different types of language that can be attached to a system,
. The first, \PL{S}, is a propositional language; the second, \L{S}, is
a higher-order, typed language. Both languages provide deductive systems with
an intuitionistic logic. With the aid of \PL{S} we expand and develop some of
the earlier work (By CJI and collaborators.) on topos theory and quantum
physics. A key step is a process we term `daseinisation' by which a projection
operator is mapped to a sub-object of the spectral presheaf \Sig--the topos
quantum analogue of a classical state space. The topos concerned is \SetH{}:
the category of contravariant set-valued functors on the category (partially
ordered set) \V{} of commutative sub-algebras of the algebra of bounded
operators on the quantum Hilbert space \Hi.Comment: To appear in ``New Structures in Physics'' ed R. Coeck
Noncomparabilities & Non Standard Logics
Many normative theories set forth in the welfare economics, distributive justice and cognate literatures posit noncomparabilities or incommensurabilities between magnitudes of various kinds. In some cases these gaps are predicated on metaphysical claims, in others upon epistemic claims, and in still others upon political-moral claims. I show that in all such cases they are best given formal expression in nonstandard logics that reject bivalence, excluded middle, or both. I do so by reference to an illustrative case study: a contradiction known to beset John Rawls\u27s selection and characterization of primary goods as the proper distribuendum in any distributively just society. The contradiction is avoided only by reformulating Rawls\u27s claims in a nonstandard form, which form happens also to cohere quite attractively with Rawls\u27s intuitive argumentation on behalf of his claims
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