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Using LATEX as a semantic markup format
 Mathematics in Computer Science
"... Abstract. One of the great problems of Mathematical Knowledge Management (MKM) systems is to obtain access to a sufficiently large corpus of mathematical knowledge to allow the management/search/navigation techniques developed by the community to display their strength. Such systems usually expect ..."
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Abstract. One of the great problems of Mathematical Knowledge Management (MKM) systems is to obtain access to a sufficiently large corpus of mathematical knowledge to allow the management/search/navigation techniques developed by the community to display their strength. Such systems usually expect the mathematical knowledge they operate on in the form of semantically enhanced documents, but mathematicians and publishers in Mathematics have heavily invested into the TEX/LATEX format and workflow. We analyze the current practice of semisemantic markup in LATEX documents and extend it by a markup infrastructure that allows to embed semantic annotations into LATEX documents without changing their visual appearance. This collection of TEX macro packages is called sTEX (semantic TEX) as it allows to markup LATEX documents semantically without leaving the timetried TEX/LATEX workflow, essentially turning LATEX into an MKM format. At the heart of sTEX is a definition mechanism for semantic macros for mathematical objects and a nonstandard scoping construct for them, which is oriented at the semantic dependency relation rather than the document structure. We evaluate the sTEX macro collection on a large case study: the course materials of a twosemester course in Computer Science was annotated semantically and converted to the OMDoc MKM format by Bruce Miller’s LaTeXML system. 1.
Modularization of Ontologies  WonderWeb: Ontology Infrastructure for the Semantic Web
, 2001
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A mathematical approach to ontology authoring and documentation. https://svn.omdoc.org/repos/ omdoc/trunk/doc/blue/foaf/note.pdf
, 2008
"... Abstract. The semantic web ontology languages RDFS and OWL are widely used but limited in both their expressivity and their support for modularity and integrated documentation. Expressivity, modularity, and documentation of formal knowledge have always been important issues in the MKM community. The ..."
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Cited by 8 (7 self)
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Abstract. The semantic web ontology languages RDFS and OWL are widely used but limited in both their expressivity and their support for modularity and integrated documentation. Expressivity, modularity, and documentation of formal knowledge have always been important issues in the MKM community. Therefore, we try to improve these ontology languages by welltried MKM techniques. Concretely, we propose OMDoc as an alternative. We show how OMDoc can be made compatible with semantic web ontology languages, focusing on knowledge representation, modular design, documentation, and metadata. We evaluate our technology by reimplementing the Friendofafriend (FOAF) ontology and applying it in a novel metadata framework for technical documents (including ontologies). 1 EdNote(1) 1
Structuring Metatheory on Inductive Definitions
, 2000
"... We examine a problem for machine supported metatheory. There are statements true about a theory that are true of some (but only some) extensions; however standard theorystructuring facilities do not support selective inheritance. We use the example of the deduction theorem for modal logic and s ..."
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We examine a problem for machine supported metatheory. There are statements true about a theory that are true of some (but only some) extensions; however standard theorystructuring facilities do not support selective inheritance. We use the example of the deduction theorem for modal logic and show how a statement about a theory can explicitly formalize the closure conditions extensions should satisfy for it to remain true. We show how metatheories based on inductive denitions allow theories and general metatheorems to be organized this way, and report on a case study using the theory FS0 . 1 Introduction Hierarchical theory structuring plays an important role in the application of theorem provers to nontrivial problems, and many systems provide support for it. For example HOL [6], Isabelle [13] and their predecessor LCF [7] support simple theory hierarchies. In these systems a theory is a specication of a language, using types and typed constants, and a collection of rules...
Chiron: A set theory with types, undefinedness, quotation, and evaluation
, 2007
"... Chiron is a derivative of vonNeumannBernaysGödel (nbg) set theory that is intended to be a practical, generalpurpose logic for mechanizing mathematics. Unlike traditional set theories such as ZermeloFraenkel (zf) and nbg, Chiron is equipped with a type system, lambda notation, and definite and ..."
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Chiron is a derivative of vonNeumannBernaysGödel (nbg) set theory that is intended to be a practical, generalpurpose logic for mechanizing mathematics. Unlike traditional set theories such as ZermeloFraenkel (zf) and nbg, Chiron is equipped with a type system, lambda notation, and definite and indefinite description. The type system includes a universal type, dependent types, dependent function types, subtypes, and possibly empty types. Unlike traditional logics such as firstorder logic and simple type theory, Chiron admits undefined terms that result, for example, from a function applied to an argument outside its domain or from an improper definite or indefinite description. The most noteworthy part of Chiron is its facility for reasoning about the syntax of expressions. Quotation is used to refer to a set called a construction that represents the syntactic structure of an expression, and evaluation is used to refer to the value of the expression that a construction
Locales: a Module System for Mathematical Theories
"... Locales are a module system for managing theory hierarchies in a theorem prover through theory interpretation. They are available for the theorem prover Isabelle. In this paper, their semantics is defined in terms of local theories and morphisms. Locales aim at providing flexible means of extension ..."
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Locales are a module system for managing theory hierarchies in a theorem prover through theory interpretation. They are available for the theorem prover Isabelle. In this paper, their semantics is defined in terms of local theories and morphisms. Locales aim at providing flexible means of extension and reuse. Theory modules (which are called locales) may be extended by definitions and theorems. Interpretation to Isabelle’s global theories and proof contexts is possible via morphisms. Even the locale hierarchy may be changed if declared relations between locales do not adequately reflect logical relations, which are implied by the locales’ specifications. By discussing their design and relating it to more commonly known structuring mechanisms of programming languages and provers, locales are made accessible to a wider audience beyond the users of Isabelle. The discussed mechanisms include MLstyle functors, type classes and mixins (the latter are found in modern objectoriented languages). 1
A tough nut for mathematical knowledge management
 Mathematical Knowledge Management – 4th International Conference, MKM 2005
, 2006
"... Abstract. In this contribution we address two related questions. Firstly, we want to shed light on the question how to use a representation formalism to represent a given problem. Secondly, we want to find out how different formalizations are related and in particular how it is possible to check tha ..."
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Abstract. In this contribution we address two related questions. Firstly, we want to shed light on the question how to use a representation formalism to represent a given problem. Secondly, we want to find out how different formalizations are related and in particular how it is possible to check that one formalization entails another. The latter question is a tough nut for mathematical knowledge management systems, since it amounts to the question, how a system can recognize that a solution to a problem is already available, although possibly in disguise. As our starting point we take McCarthy’s 1964 mutilated checkerboard challenge problem for proof procedures and compare some of its different formalizations. 1
Interpretation and Instantiation of Theories for Reasoning about Formal Specifications
 QUEENSLAND UNIVERSITY OF TECHNOLOGY
, 1997
"... In this paper an outline is given of an approach to formally reasoning about importation, parameterisation and instantiation of specifications written in a modular extension of the Z language (called Sum). Interpretation and instantiation of theories in first order logic are well understood. We illu ..."
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In this paper an outline is given of an approach to formally reasoning about importation, parameterisation and instantiation of specifications written in a modular extension of the Z language (called Sum). Interpretation and instantiation of theories in first order logic are well understood. We illustrate how to use these results directly to provide a framework within which we can soundly and efficiently reason about modular specifications. A reasoning environment within the Ergo 4:1 theorem prover has been constructed that provides the theory management, construction and extension facilities needed to support such a reasoning process. Sum specifications are mapped to the appropriate Ergo structures by a straightforward translation process. A simple example in Sum is presented to demonstrate the use of these theory extension mechanisms. As far as the authors are aware, no other system offers interpreted automated support for reasoning about parameterisation and instantiation of modular...
Proof Script Pragmatics in IMPS
 Automated Deduction CADE12, volume 814 of Lecture Notes in Computer Science
, 1994
"... . This paper introduces the imps proof script mechanism and some practical methods for exploiting it. 1 Introduction imps, an Interactive Mathematical Proof System [4, 2], is intended to serve three ultimate purposes: { To provide mathematics education with a mathematics laboratory for students ..."
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. This paper introduces the imps proof script mechanism and some practical methods for exploiting it. 1 Introduction imps, an Interactive Mathematical Proof System [4, 2], is intended to serve three ultimate purposes: { To provide mathematics education with a mathematics laboratory for students to develop axiomatic theories, proofs, and rigorous methods of symbolic computation. { To provide mathematical research with mechanized support covering a range of concrete and abstract mathematics, eventually with the help of a large theory library of formal mathematics. { To allow applied formal methods to use exible approaches to formalizing problem domains and proof techniques, in showing software or hardware correctness. Thus, the goal of imps is to provide mechanical support for traditional methods and activities of mathematics, and for traditional styles of mathematical proof. Other automated theorem provers may be intended for quite dierent sorts of problems, and they can theref...
Spreadsheet interaction with frames: Exploring a mathematical practice. This Volume
"... Abstract. Since Mathematics really is about what mathematicians do, in this paper, we will look at the mathematical practice of framing, in which an object of interest is viewed in terms of wellunderstood mathematical structures. The new perspective not only allows to deepen the understanding of a ..."
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Abstract. Since Mathematics really is about what mathematicians do, in this paper, we will look at the mathematical practice of framing, in which an object of interest is viewed in terms of wellunderstood mathematical structures. The new perspective not only allows to deepen the understanding of a resp. object, it also facilitates new insights. We propose a model for framing in the context of theory graphs, and show how framing can be exploited to enhance the interaction with MKM systems. We use the framing extension of our SACHS system — a semantic help system for MS Excel — as a concrete example. 1