98,816 research outputs found
Reflection in conditional rewriting logic
AbstractWe recall general metalogical axioms for a reflective logic based on the notion of a universal theory, that is, a theory that can simulate the deductions of all other theories in a class of theories of interest, including itself. We then show that conditional rewriting logic is reflective, generalizing in two stages: first to the unsorted conditional case, and then to the many-sorted conditional case, the already known result for unconditional and unsorted rewriting logic (Reflection in Rewriting Logic: Metalogical Foundations and Metaprogramming Applications. CSLI Publications, 2000). This work should be seen as providing foundations for many useful applications of rewriting logic reflection. The results presented here have greatly influenced the design of the Maude language, which implements rewriting logic and supports its reflective capabilities, and have been used as a theoretical foundation for applications such as internal rewrite strategies, reflective design of theorem proving tools, module algebra and metaprogramming, and metareasoning in metalogical frameworks
The semantics of fuzzy logic
Summarized here are the results of recent research on the conceptual foundations of fuzzy logic. The focus is primarily on the principle characteristics of a model that quantifies resemblance between possible worlds by means of a similarity function that assigns a number between 0 and 1 to every pair of possible worlds. Introduction of such a function permits one to interpret the major constructs and methods of fuzzy logic: conditional and unconditional possibility and necessity distributions and the generalized modus ponens of Zadeh on the basis of related metric relationships between subsets of possible worlds
Quantum key distribution without the wavefunction
A well-known feature of quantum mechanics is the secure exchange of secret
bit strings which can then be used as keys to encrypt messages transmitted over
any classical communication channel. It is demonstrated that this quantum key
distribution allows a much more general and abstract access than commonly
thought. The results include some generalizations for the Hilbert space version
of quantum key distribution,but base upon a general non-classical extension of
conditional probability. A special state-independent conditional probability is
identified as origin of the superior security of quantum key distribution and
may have more profound implications for the foundations and interpretation of
quantum mechanics,quantum information theory, and the philosophical question
what actually constitutes physical reality.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1502.0215
Logic Programming as Constructivism
The features of logic programming that
seem unconventional from the viewpoint of classical logic
can be explained in terms of constructivistic logic. We
motivate and propose a constructivistic proof theory of
non-Horn logic programming. Then, we apply this formalization
for establishing results of practical interest.
First, we show that 'stratification can be motivated in a
simple and intuitive way. Relying on similar motivations,
we introduce the larger classes of 'loosely stratified' and
'constructively consistent' programs. Second, we give a
formal basis for introducing quantifiers into queries and
logic programs by defining 'constructively domain
independent* formulas. Third, we extend the Generalized
Magic Sets procedure to loosely stratified and constructively
consistent programs, by relying on a 'conditional
fixpoini procedure
Non-classical conditional probability and the quantum no-cloning theorem
The quantum mechanical no-cloning theorem for pure states is generalized and
transfered to the quantum logics with a conditional probability calculus in a
rather abstract, though simple and basic fashion without relying on a tensor
product construction or finite dimension as required in other generalizations.Comment: 6 page
A simple and quantum-mechanically motivated characterization of the formally real Jordan algebras
Quantum theory's Hilbert space apparatus in its finite-dimensional version is
nearly reconstructed from four simple and quantum-mechanically motivated
postulates for a quantum logic. The reconstruction process is not complete,
since it excludes the two-dimensional Hilbert space and still includes the
exceptional Jordan algebras, which are not part of the Hilbert space apparatus.
Options for physically meaningful potential generalizations of the apparatus
are discussed.Comment: 19 page
Quantum teleportation and Grover's algorithm without the wavefunction
In the same way as the quantum no-cloning theorem and quantum key
distribution in two preceding papers, entanglement-assisted quantum
teleportation and Grover's search algorithm are generalized by transferring
them to an abstract setting, including usual quantum mechanics as a special
case. This again shows that a much more general and abstract access to these
quantum mechanical features is possible than commonly thought. A non-classical
extension of conditional probability and, particularly, a very special type of
state-independent conditional probability are used instead of Hilbert spaces
and wavefunctions.Comment: 21 pages, including annex, important typo in annex corrected in v2,
Found Phys (2017
- …