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Integrated Semantic Browsing of the Mizar Mathematical Library for Authoring Mizar Articles
 Proceeding of the Third International Conference on Mathematical Knowledge Management
, 2004
"... articles ..."
Information retrieval and rendering with MML Query
 Proc. of MKM 2006, Lecture Notes in Artificial Intelligence 4108
, 2006
"... Abstract. Mizar, a proofchecking system, is used to build the Mizar Mathematical Library (MML). MML Query is a semanticsbased tool for searching, browsing and presentation of the evolving MML content. The tool is becoming widely used as an aid for Mizar authors and plays an essential role in the o ..."
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Abstract. Mizar, a proofchecking system, is used to build the Mizar Mathematical Library (MML). MML Query is a semanticsbased tool for searching, browsing and presentation of the evolving MML content. The tool is becoming widely used as an aid for Mizar authors and plays an essential role in the ongoing reorganization of MML. We present new features of MML Query implemented in the third release and describe the possibilities offered by them. 1
Semantic Selection of Premisses for Automated Theorem Proving
"... We develop and implement a novel algorithm for discovering the optimal sets of premisses for proving and disproving conjectures in firstorder logic. The algorithm uses interpretations to semantically analyze the conjectures and the set of premisses of the given theory to find the optimal subsets of ..."
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We develop and implement a novel algorithm for discovering the optimal sets of premisses for proving and disproving conjectures in firstorder logic. The algorithm uses interpretations to semantically analyze the conjectures and the set of premisses of the given theory to find the optimal subsets of the premisses. For each given conjecture the algorithm repeatedly constructs interpretations using an automated model finder, uses the interpretations to compute the optimal subset of premisses (based on the knowledge it has at the point) and tries to prove the conjecture using an automated theorem prover. 1 Importance of selecting appropriate premisses in automated theorem proving A proper set of premisses 1 can be essential for proving a conjecture by an automated theorem prover. Clearly, the larger the number of the initial premisses the larger the number of the inferred formulae. And as for the most proving techniques the number of inferred formulae is in general superexponential in the number of input formulae,
Escape to ATP for Mizar
 PxTP2011 (2011
"... An interactive ATP service is a new feature in the Mizar proof assistant. The functionality of the service is in many respects analogous to the Sledgehammer subsystem of Isabelle/HOL. The ATP service requires minimal user configuration and is accessible via a few keystrokes from within Mizar mode in ..."
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An interactive ATP service is a new feature in the Mizar proof assistant. The functionality of the service is in many respects analogous to the Sledgehammer subsystem of Isabelle/HOL. The ATP service requires minimal user configuration and is accessible via a few keystrokes from within Mizar mode in Emacs. In return, for a given goal formula, the ATP service, when it succeeds, finds premises sufficient to prove the goal. The “escape ” to ATP uses a sound translation from Mizar’s language to that of firstorder provers, the same translation that has been used in the more batch oriented Automated Reasoning for Mizar (MizAR) web services presented in [16]. We briefly present the interactive ATP service followed by an account of initial experiments with the tool. We claim with some confidence that the tool will substantially ease the process of preparing new Mizar articles. 1
Automated Reasoning for Mizar: Artificial Intelligence through Knowledge Exchange
"... This paper gives an overview of the existing link between the Mizar project for formalization of mathematics and Automated Reasoning tools (mainly the Automated Theorem Provers (ATPs)). It explains the motivation for this work, gives an overview of the translation method, discusses the projects and ..."
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This paper gives an overview of the existing link between the Mizar project for formalization of mathematics and Automated Reasoning tools (mainly the Automated Theorem Provers (ATPs)). It explains the motivation for this work, gives an overview of the translation method, discusses the projects and works that are based on it, and possible future projects and directions. 1
Mizar’s Soft Type System
"... Abstract. In Mizar, unlike in most other proof assistants, the types are not part of the foundations of the system. Mizar is based on untyped set theory, which means that in Mizar expressions are typed but the values of those expressions are not. In this paper we present the Mizar type system as a c ..."
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Abstract. In Mizar, unlike in most other proof assistants, the types are not part of the foundations of the system. Mizar is based on untyped set theory, which means that in Mizar expressions are typed but the values of those expressions are not. In this paper we present the Mizar type system as a collection of type inference rules. We will interpret Mizar types as soft types, by translating Mizar’s type judgments into sequents of untyped first order predicate logic. We will then prove that the Mizar type system is correct with respect to this translation in the sense that each derivable type judgment translates to a provable sequent.
Combining Mizar and TPTP Semantic Presentation and Verification Tools
"... This paper describes a combination of several Mizarbased tools (the MPTP translator, XSL style sheets for Mizar), and TPTPbased tools (IDV, AGInT, SystemOnTPTP, GDV) used for visualizing, analyzing, and independent verification of Mizar proofs. The combination delivers to the readers of the Mizar M ..."
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This paper describes a combination of several Mizarbased tools (the MPTP translator, XSL style sheets for Mizar), and TPTPbased tools (IDV, AGInT, SystemOnTPTP, GDV) used for visualizing, analyzing, and independent verification of Mizar proofs. The combination delivers to the readers of the Mizar Mathematical Library (MML) an easy, powerful, and almost playful way of exploring the semantics and the structure of the library. The key factors for the relative easiness of having these functionalities are the choice of XML as both internal and external interface of Mizar, and the existence of a TPTP representation of MML articles. This shows the great added value that can be obtained by cooperation of several quite diverse (and quite often separately developed) projects, provided that they are based on the same communication standards.
Dependencies in formal mathematics: Applications and extraction for Coq and Mizar (2011), arxiv.org preprint abs/1109.3687
"... Abstract. Two methods for extracting detailed formal dependencies from the Coq and Mizar system are presented and compared. The methods are used for dependency extraction from two large mathematical repositories: the Coq Repository at Nijmegen and the Mizar Mathematical Library. Several applications ..."
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Abstract. Two methods for extracting detailed formal dependencies from the Coq and Mizar system are presented and compared. The methods are used for dependency extraction from two large mathematical repositories: the Coq Repository at Nijmegen and the Mizar Mathematical Library. Several applications of the detailed dependency analysis are described and proposed. Motivated by the different applications, we discuss the various kinds of dependencies that we are interested in, and the suitability of various dependency extraction methods. 1
Managing mathematical texts with OWL and their graphical representation
"... Mathematical knowledge contained in scientific digital publications poses a challenge for intelligent retrieval mechanisms. Many current approaches use statistical (e.g. Google) or natural language processing methods to find correlations in texts and annotate texts semantically. However both kinds o ..."
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Mathematical knowledge contained in scientific digital publications poses a challenge for intelligent retrieval mechanisms. Many current approaches use statistical (e.g. Google) or natural language processing methods to find correlations in texts and annotate texts semantically. However both kinds of approaches face the problem of extracting and processing knowledge from mathematical equations. The presented system is based on natural language processing techniques, and benefits from characteristic linguistic structures defined by the language used in mathematical texts. It accumulates extracted information snippets from texts, symbols, and equations in knowledge bases. These knowledge bases provide the foundation for the information retrieval. This article describes the concepts and the prototypical technical implementation.
mArachna – Ontology Engineering for Mathematical Natural Language Texts
"... The knowledge contained in the growing number of scientific digital publications, particularly over the internet creates new demands for intelligent retrieval mechanisms. One basic approach in support of such retrieval mechanisms is the generation of semantic annotation, based on ontologies describi ..."
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The knowledge contained in the growing number of scientific digital publications, particularly over the internet creates new demands for intelligent retrieval mechanisms. One basic approach in support of such retrieval mechanisms is the generation of semantic annotation, based on ontologies describing both the field and the structure of the texts themselves. Many current approaches use statistical methods similar to the ones employed by Google to find correlations within the texts. This approach neglects the additional information provided in the upper ontology used by the author. mArachna, however, is based on natural language processing techniques, taking advantage of characteristic linguistic structures defined by the language used in mathematical texts. It stores the extracted knowledge in a knowledge base, creating a lowlevel ontology of mathematics and mapping this ontology onto the structure of the knowledge base. The following article gives an overview over the concepts and technical implementation of the mArachna prototype. 1