145,365 research outputs found
A Survey of Languages for Specifying Dynamics: A Knowledge Engineering Perspective
A number of formal specification languages for knowledge-based systems has been developed. Characteristics for knowledge-based systems are a complex knowledge base and an inference engine which uses this knowledge to solve a given problem. Specification languages for knowledge-based systems have to cover both aspects. They have to provide the means to specify a complex and large amount of knowledge and they have to provide the means to specify the dynamic reasoning behavior of a knowledge-based system. We focus on the second aspect. For this purpose, we survey existing approaches for specifying dynamic behavior in related areas of research. In fact, we have taken approaches for the specification of information systems (Language for Conceptual Modeling and TROLL), approaches for the specification of database updates and logic programming (Transaction Logic and Dynamic Database Logic) and the generic specification framework of abstract state machine
A formally verified proof of the prime number theorem
The prime number theorem, established by Hadamard and de la Vall'ee Poussin
independently in 1896, asserts that the density of primes in the positive
integers is asymptotic to 1 / ln x. Whereas their proofs made serious use of
the methods of complex analysis, elementary proofs were provided by Selberg and
Erd"os in 1948. We describe a formally verified version of Selberg's proof,
obtained using the Isabelle proof assistant.Comment: 23 page
Finite Rank Bargmann-Toeplitz Operators with Non-Compactly Supported Symbols
Theorems about characterization of finite rank Toeplitz operators in
Fock-Segal-Bargmann spaces, known previously only for symbols with compact
support, are carried over to symbols without that restriction, however with a
rather rapid decay at infinity. The proof is based upon a new version of the
Stone-Weierstrass approximation theorem
Speakable in Quantum Mechanics
At the 1927 Como conference Bohr spoke the now famous words "It is wrong to
think that the task of physics is to find out how nature is. Physics concerns
what we can say about nature." However, if the Copenhagen interpretation really
holds on to this motto, why then is there this feeling of conflict when
comparing it with realist interpretations? Surely what one can say about nature
should in a certain sense be interpretation independent. In this paper I take
Bohr's motto seriously and develop a quantum logic that avoids assuming any
form of realism as much as possible. To illustrate the non-triviality of this
motto a similar result is first derived for classical mechanics. It turns out
that the logic for classical mechanics is a special case of the derived quantum
logic. Finally, some hints are provided in how these logics are to be used in
practical situations and I discuss how some realist interpretations relate to
these logics
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