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62
systems using Mizar
"... definition of probability on finite and discrete sample space for proving security of cryptographic ..."
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definition of probability on finite and discrete sample space for proving security of cryptographic
An Outline of PC Mizar
, 1993
"... this article, ffl the library reference TARSKI:2 indicates the second theorem in the article TARSKI, ffl the library reference BOOLE:def 1 indicates the first definitional theorem in the article BOOLE. 2. When referring to a schema we write from identifierofschema (% 1 , ... , %n ); where % 1 , ..."
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Cited by 7 (0 self)
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this article, ffl the library reference TARSKI:2 indicates the second theorem in the article TARSKI, ffl the library reference BOOLE:def 1 indicates the first definitional theorem in the article BOOLE. 2. When referring to a schema we write from identifierofschema (% 1 , ... , %n ); where % 1
The Lattice of Topological Domains: An Example of Mizar Development
"... We present the complete development of the theory of topological domains (regular sets) in the Mizar formalism. It enveloped the latticetheoretic foundations of the theory of domains that was given in [23] and in [12]. The aim is to present the main result in [11] concerning certain characteriza ..."
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characterizations of an extremally disconnected topological space by means of properties of the lattice of domains and the main result in [12] concerning completeness of the lattice of domains of a topological space. Beforehand in comparison with a mathematical vernacular we present the mizared definitions
Development of the theory of continuous lattices in mizar
 In Kerber and Kohlhase
, 2001
"... Abstract. This paper reports on Mizar formalization of the theory of continuous lattices included in the A Compendium of Continuous Lattices, [7]. Mizar formalization means a formalization of theorems, definitions, and proofs in the Mizar language such that it is accepted by the Mizar system. This e ..."
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Abstract. This paper reports on Mizar formalization of the theory of continuous lattices included in the A Compendium of Continuous Lattices, [7]. Mizar formalization means a formalization of theorems, definitions, and proofs in the Mizar language such that it is accepted by the Mizar system
The Mutilated Chessboard Problem  checked by Mizar
"... The problem presented by John McCarthy during his lecture "Heavy duty set theory" 1 has been resolved here. The final version of that article has been made with the commitment of Andrzej Trybulec. Proofs have been written in Mizar language and were checked by PC Mizar system. In this pap ..."
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. In this paper only definitions and theorems are published apart from proofs (this is the so called `mizar abstract'). Then it has been automatically translated into English. The format of this article is exactly the same as in journal Formalized Mathematics. MML Identifier: M BOARD. The articles [10], [12
Automated reasoning and presentation support for formalizing mathematics in Mizar
 In Autexier et al
"... Abstract. This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for firstorder automated reasoning. The main di ..."
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Cited by 15 (10 self)
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differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure firstorder logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems, definitions, and proofs (rather than
Rough Concept Analysis – theory development in the Mizar system
 Proc. of MKM 2004, Lecture Notes in Computer Science 3119
, 2004
"... Abstract. Theories play an important role in building mathematical knowledge repositories. Organizing knowledge in theories is an obvious approach to cope with the growing number of definitions, theorems, and proofs. However, they are also a matter of subject on their own: developing a new piece of ..."
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Cited by 3 (0 self)
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of mathematics often relies on extending or combining already developed theories in this way reusing definitions as well as theorems. We believe that this aspect of theory development is crucial for mathematical knowledge management. In this paper we investigate the facilities of the Mizar system concerning
Gröbner Bases — Theory Refinement in the Mizar System
"... Abstract. We argue that for building mathematical knowledge repositories a broad development of theories is of major importance. Organizing mathematical knowledge in theories is an obvious approach to cope with the immense number of topics, definitions, theorems, and proofs in a general repository t ..."
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Abstract. We argue that for building mathematical knowledge repositories a broad development of theories is of major importance. Organizing mathematical knowledge in theories is an obvious approach to cope with the immense number of topics, definitions, theorems, and proofs in a general repository
Preprint submitted to CPP 2016 Towards a Mizar Environment for Isabelle: Foundations and Language
"... In this paper we explore the possibility of emulating the Mizar environment as close as possible inside the Isabelle logical framework. We introduce adaptations to the Isabelle/FOL object logic that correspond to the logic of Mizar, as well as Isar inner syntax notations that correspond to these ..."
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definitions and provide simple abbreviations that allow the introduction of Mizar predicates, functions, attributes and modes using the Isabelle/Pure language elements for introducing definitions and theorems. We finally consider the definite and indefinite description operators in Mizar and their use
First Order Proof Problems Extracted from an Article in the Mizar Mathematical Library
 in the MIZAR Mathematical Library. In Proceedings of the 1st FTP
, 1997
"... this article, set is the only type which is used, hence the resulting proof problems can be considered as first order problems by ignoring the type information. This article contains 97 theorems. The Boolean operators on sets are defined and their basic properties are proved. The proofs use axioms o ..."
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of GrothendieckTarski set theory and other theorems proved in this article. For each of these 97 theorems in the article a theory was built consisting of the definitions and theorems which have been referenced in its proof. When a functor or predicate is defined in a Mizar article, it is checked whether some
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