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An Environment for Building Mathematical Knowledge Libraries
 Proc. of the 3rd Int. Conference on Mathematical Knowledge Management, MKM’04
, 2004
"... Proving is an activity that makes use of mathematical knowledge. ..."
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Proving is an activity that makes use of mathematical knowledge.
The theorema environment for interactive proof development. Contributed talk at
 12th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR’05
, 2005
"... Abstract. We describe an environment that allows the users of the Theorema system to flexibly control aspects of computersupported proof development. The environment supports the display and manipulation of proof trees and proof situations, logs the user activities (commands communicated with the s ..."
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Abstract. We describe an environment that allows the users of the Theorema system to flexibly control aspects of computersupported proof development. The environment supports the display and manipulation of proof trees and proof situations, logs the user activities (commands communicated with the system during the proving session), and presents (also unfinished) proofs in a humanoriented style. In particular, the user can navigate through the proof object, expand/remove proof branches, provide witness terms, develop several proofs concurrently, proceed step by step or automatically and so on. The environment enhances the effectiveness and flexibility of the reasoners of the Theorema system. 1
User interface features in Theorema: A summary
 In Mathematical UserInterfaces Workshop
, 2004
"... Abstract. This paper presents the main features of Theorema’s user interface. We briefly describe how mathematical knowledge can be expressed in the Theorema Formal Text Language and how the knowledge can be used for proving, solving, computing. We illustrate how the system presents the proofs it ge ..."
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Abstract. This paper presents the main features of Theorema’s user interface. We briefly describe how mathematical knowledge can be expressed in the Theorema Formal Text Language and how the knowledge can be used for proving, solving, computing. We illustrate how the system presents the proofs it generated and how the user can influence the proof search process interactively. 1
Knowledge Archives in Theorema: A LogicInternal Approach
"... Abstract. Archives are implemented as an extension of Theorema for representing mathematical repositories in a natural way. An archive can be conceived as one large formula in a language consisting of higherorder predicate logic together with a few constructs for structuring knowledge: attaching la ..."
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Abstract. Archives are implemented as an extension of Theorema for representing mathematical repositories in a natural way. An archive can be conceived as one large formula in a language consisting of higherorder predicate logic together with a few constructs for structuring knowledge: attaching labels to subhierarchies, disambiguating symbols by the use of namespaces, importing symbols from other namespaces and specifying the domains of categories and functors as namespaces with variable operations. All these constructs are logicinternal in the sense that they have a natural translation to higherorder logic so that certain aspects of Mathematical Knowledge Management can be realized in the object logic itself. There are a variety of operations on archives, though in this paper we can only sketch a few of them: knowledge retrieval and theory exploration, merging and splitting, insertion and translation to predicate logic.
An Automated Prover for ZermeloFraenkel Set Theory in Theorema
 JOURNAL OF SYMBOLIC COMPUTATION
"... This paper presents some fundamental aspects of the design and the implementation of an automated prover for ZermeloFraenkel set theory within the Theorema system. The method applies the “ProveComputeSolve”paradigm as its major strategy for generating proofs in a natural style for statements inv ..."
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This paper presents some fundamental aspects of the design and the implementation of an automated prover for ZermeloFraenkel set theory within the Theorema system. The method applies the “ProveComputeSolve”paradigm as its major strategy for generating proofs in a natural style for statements involving constructs from set theory.
Mathematical Knowledge Archives in Theorema
"... Archives are implemented as an extension of Theorema for representing large bodies of mathematics. They provide various constructs for organizing knowledge bases in a natural way: breaking formulae across cells, grouping them in a hierarchical structure, attaching labels to subhierarchies, disambigu ..."
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Archives are implemented as an extension of Theorema for representing large bodies of mathematics. They provide various constructs for organizing knowledge bases in a natural way: breaking formulae across cells, grouping them in a hierarchical structure, attaching labels to subhierarchies, disambiguating symbols by the use of namespaces, importing symbols from other namespaces, addressing the domains of categories and functors as namespaces with variable opera− tions. All constructs are logic–internal in the sense that they have a natural translation to higher–order logic so that �mathematical knowledge management � can be treated by the object logic itself. 1
zur Erlangung des akademischen Grades
"... Ich erkläre an Eides statt, dass ich die vorliegende Dissertation selbstständig und ohne fremde ..."
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Ich erkläre an Eides statt, dass ich die vorliegende Dissertation selbstständig und ohne fremde
INFORMATICS: ENGINEERING & MANAGEMENT∗ and OPEN INFORMATICS† Submitted by:
, 2011
"... in the master’s study programs ..."