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DynGenPar – A Dynamic Generalized Parser for Common Mathematical Language ⋆
"... Abstract. This paper introduces a dynamic generalized parser aimed primarily at common natural mathematical language. Our algorithm combines the efficiency of GLR parsing, the dynamic extensibility of tableless approaches and the expressiveness of extended contextfree grammars such as parallel mult ..."
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Abstract. This paper introduces a dynamic generalized parser aimed primarily at common natural mathematical language. Our algorithm combines the efficiency of GLR parsing, the dynamic extensibility of tableless approaches and the expressiveness of extended contextfree grammars such as parallel multiple contextfree grammars (PMCFGs). In particular, it supports efficient dynamic rule additions to the grammar at any moment. The algorithm is designed in a fully incremental way, allowing to resume parsing with additional tokens without restarting the parse process, and can predict possible next tokens. Additionally, we handle constraints on the token following a rule. This allows for grammatically correct English indefinite articles when working with word tokens. It can also represent typical operations for scannerless parsing such as maximal matches when working with character tokens. Our longterm goal is to computerize a large library of existing mathematical knowledge using the new parser, starting from natural language input as found in textbooks or in the papers collected by the digital mathematical library (DML) projects around the world. In this paper, we present the algorithmic ideas behind our approach, give a short overview of the implementation, and present some efficiency results. The new parser is available at
Premise Selection in the Naproche System
"... Abstract. Automated theorem provers (ATPs) struggle to solve problems with large sets of possibly superfluous axiom. Several algorithms have been developed to reduce the number of axioms, optimally only selecting the necessary axioms. However, most of these algorithms consider only single problems. ..."
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Abstract. Automated theorem provers (ATPs) struggle to solve problems with large sets of possibly superfluous axiom. Several algorithms have been developed to reduce the number of axioms, optimally only selecting the necessary axioms. However, most of these algorithms consider only single problems. In this paper, we describe an axiom selection method for series of related problems that is based on logical and textual proximity and tries to mimic a human way of understanding mathematical texts. We present first results that indicate that this approach is indeed useful. Key words: formal mathematics, automated theorem proving, axiom selection 1
Implicit dynamic function introduction and its connections to the foundations of mathematics
"... Abstract: We discuss a feature of the natural language of mathematics – the implicit dynamic introduction of functions – that has, to our knowledge, not been captured in any formal system so far. If this feature is used without limitations, it yields a paradox analogous to Russell’s paradox. Hence a ..."
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Abstract: We discuss a feature of the natural language of mathematics – the implicit dynamic introduction of functions – that has, to our knowledge, not been captured in any formal system so far. If this feature is used without limitations, it yields a paradox analogous to Russell’s paradox. Hence any formalism capturing it has to impose some limitations on it. We sketch two formalisms, both extensions of Dynamic Predicate Logic, that innovatively do capture this feature, and that differ only in the limitations they impose onto it. One of these systems is based on a novel theory of functions that interprets ZFC, and thus exhibits interesting connections to the foundations of mathematics.