93,708 research outputs found
On the Satisfiability of Quasi-Classical Description Logics
Though quasi-classical description logic (QCDL) can tolerate the inconsistency of description logic in reasoning, a knowledge base in QCDL possibly has no model. In this paper, we investigate the satisfiability of QCDL, namely, QC-coherency and QC-consistency and develop a tableau calculus, as a formal proof, to determine whether a knowledge base in QCDL is QC-consistent. To do so, we repair the standard tableau for DL by introducing several new expansion rules and defining a new closeness condition. Finally, we prove that this calculus is sound and complete. Based on this calculus, we implement an OWL paraconsistent reasoner called QC-OWL. Preliminary experiments show that QC-OWL is highly efficient in checking QC-consistency
Handling Inconsistency in Knowledge Bases
Real-world automated reasoning systems, based on classical logic, face logically inconsistent information, and they must cope with it. It is onerous to develop such systems because classical logic is explosive. Recently, progress has been made towards semantics that deal with logical inconsistency. However, such semantics was never analyzed in the aspect of inconsistency tolerant relational model.
In our research work, we use an inconsistency and incompleteness tolerant relational model called Paraconsistent Relational Model. The paraconsistent relational model is an extension of the ordinary relational model that can store, not only positive information but also negative information. Therefore, a piece of information in the paraconsistent relational model has four truth values: true, false, both, and unknown.
However, the paraconsistent relational model cannot represent disjunctive information (disjunctive tuples). We then introduce an extended paraconsistent relational model called disjunctive paraconsistent relational model. By using both the models, we handle inconsistency - similar to the notion of quasi-classic logic or four-valued logic -- in deductive databases (logic programs with no functional symbols).
In addition to handling inconsistencies in extended databases, we also apply inconsistent tolerant reasoning technique in semantic web knowledge bases. Specifically, we handle inconsistency assosciated with closed predicates in semantic web. We use again the paraconsistent approach to handle inconsistency.
We further extend the same idea to description logic programs (combination of semantic web and logic programs) and introduce dl-relation to represent inconsistency associated with description logic programs
A topos for algebraic quantum theory
The aim of this paper is to relate algebraic quantum mechanics to topos
theory, so as to construct new foundations for quantum logic and quantum
spaces. Motivated by Bohr's idea that the empirical content of quantum physics
is accessible only through classical physics, we show how a C*-algebra of
observables A induces a topos T(A) in which the amalgamation of all of its
commutative subalgebras comprises a single commutative C*-algebra. According to
the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter
has an internal spectrum S(A) in T(A), which in our approach plays the role of
a quantum phase space of the system. Thus we associate a locale (which is the
topos-theoretical notion of a space and which intrinsically carries the
intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which
is the noncommutative notion of a space). In this setting, states on A become
probability measures (more precisely, valuations) on S(A), and self-adjoint
elements of A define continuous functions (more precisely, locale maps) from
S(A) to Scott's interval domain. Noting that open subsets of S(A) correspond to
propositions about the system, the pairing map that assigns a (generalized)
truth value to a state and a proposition assumes an extremely simple
categorical form. Formulated in this way, the quantum theory defined by A is
essentially turned into a classical theory, internal to the topos T(A).Comment: 52 pages, final version, to appear in Communications in Mathematical
Physic
Probabilities and Quantum Reality: Are There Correlata?
Any attempt to introduce probabilities into quantum mechanics faces
difficulties due to the mathematical structure of Hilbert space, as reflected
in Birkhoff and von Neumann's proposal for a quantum logic. The (consistent or
decoherent) histories solution is provided by its single framework rule, an
approach that includes conventional (Copenhagen) quantum theory as a special
case. Mermin's Ithaca interpretation addresses the same problem by defining
probabilities which make no reference to a sample space or event algebra
(``correlations without correlata''). But this leads to severe conceptual
difficulties, which almost inevitably couple quantum theory to unresolved
problems of human consciousness. Using histories allows a sharper quantum
description than is possible with a density matrix, suggesting that the latter
provides an ensemble rather than an irreducible single-system description as
claimed by Mermin. The histories approach satisfies the first five of Mermin's
desiderata for a good interpretation of quantum mechanics, including Einstein
locality, but the Ithaca interpretation seems to have difficulty with the first
(independence of observers) and the third (describing individual systems).Comment: Latex 31 pages, 3 figures in text using PSTrick
Giant Relaxation Oscillations in a Very Strongly Hysteretic SQUID ring-Tank Circuit System
In this paper we show that the radio frequency (rf) dynamical characteristics
of a very strongly hysteretic SQUID ring, coupled to an rf tank circuit
resonator, display relaxation oscillations. We demonstrate that the the overall
form of these characteristics, together with the relaxation oscillations, can
be modelled accurately by solving the quasi-classical non-linear equations of
motion for the system. We suggest that in these very strongly hysteretic
regimes SQUID ring-resonator systems may find application in novel logic and
memory devices.Comment: 7 pages, 5 figures. Uploaded as implementing a policy of arXiving old
paper
Bohrification
New foundations for quantum logic and quantum spaces are constructed by
merging algebraic quantum theory and topos theory. Interpreting Bohr's
"doctrine of classical concepts" mathematically, given a quantum theory
described by a noncommutative C*-algebra A, we construct a topos T(A), which
contains the "Bohrification" B of A as an internal commutative C*-algebra. Then
B has a spectrum, a locale internal to T(A), the external description S(A) of
which we interpret as the "Bohrified" phase space of the physical system. As in
classical physics, the open subsets of S(A) correspond to (atomic)
propositions, so that the "Bohrified" quantum logic of A is given by the
Heyting algebra structure of S(A). The key difference between this logic and
its classical counterpart is that the former does not satisfy the law of the
excluded middle, and hence is intuitionistic. When A contains sufficiently many
projections (e.g. when A is a von Neumann algebra, or, more generally, a
Rickart C*-algebra), the intuitionistic quantum logic S(A) of A may also be
compared with the traditional quantum logic, i.e. the orthomodular lattice of
projections in A. This time, the main difference is that the former is
distributive (even when A is noncommutative), while the latter is not.
This chapter is a streamlined synthesis of 0709.4364, 0902.3201, 0905.2275.Comment: 44 pages; a chapter of the first author's PhD thesis, to appear in
"Deep Beauty" (ed. H. Halvorson
Is Wave Mechanics consistent with Classical Logic?
Contrary to a wide-spread commonplace, an exact, ray-based treatment holding
for any kind of monochromatic wave-like features (such as diffraction and
interference) is provided by the structure itself of the Helmholtz equation.
This observation allows to dispel - in apparent violation of the Uncertainty
Principle - another commonplace, forbidding an exact, trajectory-based approach
to Wave Mechanics.Comment: 13 pages, 4 figure
- âŠ