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SPASS FLOTTER Version 0.42
"... t represents the sort restrictions on the variables. There are two extra inference rules which transform the sort constraint into solved form: Sort resolution and empty sort. These rules 1 The name is the result of a lunch break, FLOTTER means "faster", in German. 2 Synergetic Prover Augmenting ..."
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Cited by 54 (3 self)
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t represents the sort restrictions on the variables. There are two extra inference rules which transform the sort constraint into solved form: Sort resolution and empty sort. These rules 1 The name is the result of a lunch break, FLOTTER means "faster", in German. 2 Synergetic Prover Augmenting Superposition with Sorts, SPASS means "fun", in German. implement a specific strategy of the sorted unification algorithm [15] on the sort constraint literals. In addition to these inference rules, SPASS includes a splitting rule. The splitting rule is a variant of the usual firule of tableau. If SPASS splits a clause into two different cases, the two parts will not share variables, i.e. these parts can independently be refuted. For SPASS we implemented powerful reduction rules: tautology deletion, subsumption, condensing, an efficient variant of contextual rewriting,
Tabled HigherOrder Logic Programming
 In 20th International Conference on Automated Deduction
, 2003
"... Elf is a general metalanguage for the specification and implementation of logical systems in the style of the logical framework LF. Based on a logic programming interpretation, it supports executing logical systems and reasoning with and about them, thereby reducing the effort required for each ..."
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Cited by 26 (11 self)
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Elf is a general metalanguage for the specification and implementation of logical systems in the style of the logical framework LF. Based on a logic programming interpretation, it supports executing logical systems and reasoning with and about them, thereby reducing the effort required for each particular logical system. The traditional logic programming paradigm is extended by replacing firstorder terms with dependently typed terms and allowing implication and universal quantification in the bodies of clauses. These higherorder features allow us to model concisely and elegantly conditions on variables and the discharge of assumptions which are prevalent in many logical systems. However, many specifications are not executable under the traditional logic programming semantics and performance may be hampered by redundant computation. To address these problems, I propose a tabled higherorder logic programming interpretation for Elf. Some redundant computation is eliminated by memoizing subcomputation and reusing its result later. If we do not distinguish different proofs for a property, then search based on tabled logic programming is complete and terminates for programs with bounded recursion. In this proposal, I present a prooftheoretical characterization for tabled higherorder logic programming. It is the basis of the implemented prototype for tabled logic programming interpreter for Elf. Preliminary experiments indicate that many more logical specifications are executable under the tabled semantics. In addition, tabled computation leads to more efficient execution of programs. The goal of the thesis is to demonstrate that tabled logic programming allows us to efficiently automate reasoning with and about logical systems in the logical f...
A content based mathematical search engine: whelp
 In: Postproceedings of the Types 2004 International Conference, Vol. 3839 of LNCS
, 2004
"... Abstract. The prototype of a content based search engine for mathematical knowledge supporting a small set of queries requiring matching and/or typing operations is described. The prototype — called Whelp — exploits a metadata approach for indexing the information that looks far more flexible than t ..."
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Cited by 16 (7 self)
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Abstract. The prototype of a content based search engine for mathematical knowledge supporting a small set of queries requiring matching and/or typing operations is described. The prototype — called Whelp — exploits a metadata approach for indexing the information that looks far more flexible than traditional indexing techniques for structured expressions like substitution, discrimination, or context trees. The prototype has been instantiated to the standard library of the Coq proof assistant extended with many user contributions. 1
HigherOrder Substitution Tree Indexing
 19th International Conference on Logic Programming
, 2003
"... We present a higherorder term indexing strategy based on substitution trees. The strategy is based in linear higherorder patterns where computationally expensive parts are delayed. Insertion of terms into the index is based on computing the most specific linear generalization of two linear hig ..."
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Cited by 16 (5 self)
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We present a higherorder term indexing strategy based on substitution trees. The strategy is based in linear higherorder patterns where computationally expensive parts are delayed. Insertion of terms into the index is based on computing the most specific linear generalization of two linear higherorder patterns. Retrieving terms is based on matching two linear higherorder patterns. This indexing structure is implemented as part of the Twelf system to speedup the execution of the tabled higherlogic programming interpreter. Experimental results show substantial performance improvements, between 100% and over 800%.
Recognition and Retrieval of Mathematical Expressions
 INTERNATIONAL JOURNAL ON DOCUMENT ANALYSIS AND RECOGNITION
"... Document recognition and retrieval technologies complement one another, providing improved access to increasingly large document collections. While recognition and retrieval of textual information is fairly mature, with widespread availability of Optical Character Recognition (OCR) and textbased ..."
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Cited by 12 (3 self)
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Document recognition and retrieval technologies complement one another, providing improved access to increasingly large document collections. While recognition and retrieval of textual information is fairly mature, with widespread availability of Optical Character Recognition (OCR) and textbased search engines, recognition and retrieval of graphics such as images, figures, tables, diagrams, and mathematical expressions are in comparatively early stages of research. This paper surveys the state of the art in recognition and retrieval of mathematical expressions, organized around four key problems in math retrieval (query construction, normalization, indexing, and relevance feedback), and four key problems in math recognition (detecting expressions, detecting and classifying symbols, analyzing symbol layout, and constructing a representation of meaning). Of special interest is the machine learning problem of jointly optimizing the component algorithms in a math recognition system, and developing effective indexing, retrieval and relevance feedback algorithms for math retrieval. Another important open problem is developing user interfaces that seamlessly integrate recognition and retrieval. Activity in these important research areas is increasing, in part because math notation provides an excellent domain for studying problems common to many document and graphics recognition and retrieval applications, and also because mature applications will likely provide substantial benefits for education, research, and mathematical literacy.
Efficient Retrieval of Mathematical Statements
 In Proceeding of the Third International Conference on Mathematical Knowledge Management, MKM 2004. Bialowieza, Poland. LNCS 3119
, 2004
"... Abstract. The paper describes an innovative technique for efficient retrieval of mathematical statements from large repositories, developing and substantially improving the metadatabased approach introduced in [13]. 1 ..."
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Cited by 8 (2 self)
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Abstract. The paper describes an innovative technique for efficient retrieval of mathematical statements from large repositories, developing and substantially improving the metadatabased approach introduced in [13]. 1
Equational Prover of Theorema
, 2003
"... The equational prover of the Theorema system is described. It is implemented on Mathematica and is designed for unit equalities in the first order or in the applicative higher order form. A (restricted) usage of sequence variables and Mathematica builtin functions is allowed. ..."
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Cited by 7 (6 self)
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The equational prover of the Theorema system is described. It is implemented on Mathematica and is designed for unit equalities in the first order or in the applicative higher order form. A (restricted) usage of sequence variables and Mathematica builtin functions is allowed.
FirstOrder Term Compression: Techniques and Applications
, 1998
"... Lossless sequential data compression techniques are wellknown. ..."
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Cited by 6 (1 self)
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Lossless sequential data compression techniques are wellknown.
Context Trees
 In Proceedings of the First Int. Conf. on Automated Reasoning (IJCAR 2001), volume 2083 of LNCS
, 2001
"... Indexing data structures have a crucial impact on the performance of automated theorem provers. Examples are discrimination trees, which are like tries where terms are seen as strings and common prefixes are shared, and substitution trees, where terms keep their tree structure and all common con ..."
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Cited by 6 (1 self)
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Indexing data structures have a crucial impact on the performance of automated theorem provers. Examples are discrimination trees, which are like tries where terms are seen as strings and common prefixes are shared, and substitution trees, where terms keep their tree structure and all common contexts can be shared. Here we describe a new indexing data structure, called context trees, where, by means of a limited kind of context variables, also common subterms can be shared, even if they occur below di#erent function symbols. Apart from introducing the concept, we also provide evidence for its practical value. We describe an implementation of context trees based on Curry terms and on an extension of substitution trees with equality constraints, where one also does not distinguish between internal and external variables.
Efficient Instance Retrieval with Standard and Relational Path Indexing
 PROC. OF THE 19TH CADE, MIAMI, LNAI 2741
, 2003
"... Backward demodulation is a simpli cation technique used in saturationbased theorem proving with superposition and ordered paramodulation. It requires instance retrieval, i.e., search for instances of some term in a typically large set of terms. Path indexing is a family of indexing techniques that ..."
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Cited by 5 (1 self)
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Backward demodulation is a simpli cation technique used in saturationbased theorem proving with superposition and ordered paramodulation. It requires instance retrieval, i.e., search for instances of some term in a typically large set of terms. Path indexing is a family of indexing techniques that can be used to solve this problem efficiently. We propose a number of powerful optimisations to standard path indexing. We also describe a novel framework that combines path indexing with relational joins. The main advantage of the proposed scheme is exibility, which we illustrate by sketching how to adapt the scheme to instance retrieval modulo commutativity and backward subsumption on multiliteral clauses.