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Mechanizing set theory: Cardinal arithmetic and the axiom of choice
 Journal of Automated Reasoning
, 1996
"... Abstract. Fairly deep results of ZermeloFrænkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is κ ⊗ κ = κ, where κ is any infinite cardinal. Proving this resu ..."
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Cited by 16 (9 self)
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Abstract. Fairly deep results of ZermeloFrænkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is κ ⊗ κ = κ, where κ is any infinite cardinal. Proving
Fast Binary Feature Selection with Conditional Mutual Information
 Journal of Machine Learning Research
, 2004
"... We propose in this paper a very fast feature selection technique based on conditional mutual information. ..."
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Cited by 171 (1 self)
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We propose in this paper a very fast feature selection technique based on conditional mutual information.
Mechanising Set Theory: Cardinal Arithmetic and the Axiom of Choice
, 1995
"... A growing corpus of mathematics has been checked by machine. Researchers have constructed computer proofs of results in logic [23], number theory [22], group theory [25],calculus [9], etc. An especially wide variety of results have been mechanised using the Mizar Proof Checker and published in the ..."
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A growing corpus of mathematics has been checked by machine. Researchers have constructed computer proofs of results in logic [23], number theory [22], group theory [25],calculus [9], etc. An especially wide variety of results have been mechanised using the Mizar Proof Checker and published in the Mizar journal [6]. However,
Hidden Field Equations (HFE) and Isomorphisms of Polynomials (IP): two new Families of Asymmetric Algorithms
, 1996
"... In [11] T. Matsumoto and H. Imai described a new asymmetric algorithm based on multivariate polynomials of degree twoo ver a finite field. Then in [14] this algorithm was broken. The aim of this paper is to show that despite this result it is probably possible to use multivariate polynomials of degr ..."
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Cited by 148 (9 self)
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In [11] T. Matsumoto and H. Imai described a new asymmetric algorithm based on multivariate polynomials of degree twoo ver a finite field. Then in [14] this algorithm was broken. The aim of this paper is to show that despite this result it is probably possible to use multivariate polynomials of degree two in carefully designed algorithms for asymmetric cryptography. In this paper we will give some examples of suchschemes. All the examples that we will give, belong to two large family of schemes: HFE and IP. With HFE we will be able to do encryption, signatures or authentication in an asymmetric way. Moreover HFE (with properly chosen parameters) resist to all known attacks and can be used in order to givevery short asymmetric signatures or very short encrypted messages (of length 128 bits or 64 bits for example). IP can be used for asymmetric authentications or signatures. IP authentications are zero knowledge.
A Logic MetaProgramming Approach to Support the CoEvolution of ObjectOriented Design and Implementation
, 2001
"... this documentation uptodate. This problem is clearly visible in objectoriented frameworks. An objectoriented framework is defined as a set of classes which embody an abstract design for solutions to a family of related problems [JF88]. It can be seen as a skeleton that implements an abstract app ..."
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Cited by 128 (13 self)
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this documentation uptodate. This problem is clearly visible in objectoriented frameworks. An objectoriented framework is defined as a set of classes which embody an abstract design for solutions to a family of related problems [JF88]. It can be seen as a skeleton that implements an abstract application for some specific domain. In order to get a working application, this skeleton then has to be fitted with the specific outward appearance. This is called instantiating the framework
Ontological Semantics
, 2004
"... This book introduces ontological semantics, a comprehensive approach to the treatment of text meaning by computer. Ontological semantics is an integrated complex of theories, methodologies, descriptions and implementations. In ontological semantics, a theory is viewed as a set of statements determin ..."
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Cited by 126 (37 self)
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This book introduces ontological semantics, a comprehensive approach to the treatment of text meaning by computer. Ontological semantics is an integrated complex of theories, methodologies, descriptions and implementations. In ontological semantics, a theory is viewed as a set of statements determining the format of descriptions of the phenomena with which the theory deals. A theory is associated with a methodology used to obtain the descriptions. Implementations are computer systems that use the descriptions to solve specific problems in text processing. Implementations of ontological semantics are combined with other processing systems to produce applications, such as information extraction or machine translation. The theory of ontological semantics is built as a society of microtheories covering such diverse ground as specific language phenomena, world knowledge organization, processing heuristics and issues relating to knowledge representation and implementation system architecture. The theory briefly sketched above is a toplevel microtheory, the ontological semantics theory per se. Descriptions in ontological semantics include text meaning representations, lexical entries, ontological concepts and instances as well as procedures for manipulating texts and their meanings. Methodologies in ontological semantics are sets of techniques and instructions for acquiring and
Theorem Proving with the Real Numbers
, 1996
"... This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification ..."
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Cited by 116 (14 self)
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This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of floating point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We describe the rigorous definitional construction of the real numbers, using a new version of Cantor's method, and the formalization of a significant portion of real analysis. We also describe an advanced derived decision procedure for the `Tarski subset' of real algebra as well as some more modest but practically useful tools for automating explicit calculations and routine linear arithmetic reasoning. Finally,...
Results 11  20
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2,841