Information Retrieval in MML

Bancerek, Grzegorz; Rudnicki, Piotr

doi:10.1007/3-540-36469-2_10

Cited by 33 publications

(22 citation statements)

References 3 publications

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“…Custom exports of MML have been developed by Urban and Bancerek for semantic searching tools such as MoMM [56] and MML Query [10] and their integration in the MizarMode Emacs interface [11,71].…”

Section: Exports Between Mizar and Other Systemsmentioning

confidence: 99%

A Goal-Directed Decision Procedure for Hybrid PDL

Kaminski

Smolka

2013

J Autom Reasoning

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We formally define the foundations of the Mizar system as an object logic in the Isabelle logical framework. For this, we propose adequate mechanisms to represent the various components of Mizar. We express Mizar types in a uniform way, provide a common type intersection operation, allow reasoning about type inhabitation, and develop a type inference mechanism. We provide Mizar-like definition mechanisms which require the same proof obligations and provide same derived properties. Structures and set comprehension operators can be defined as definitional extensions. Re-formalized proofs from various parts of the Mizar Library show the practical usability of the specified foundations.

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Section: Exports Between Mizar and Other Systemsmentioning

confidence: 99%

A Goal-Directed Decision Procedure for Hybrid PDL

Kaminski

Smolka

2013

J Autom Reasoning

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“…The second important number was that in about 35% of these cases (i.e., about every seventh MML theorem), relevant Mizar theorems and definitions sufficient for a feasible ATP proof could be selected fully automatically by an independent Bayesian advisor [6] trained on previous MML proofs. 3 The primary goal of the first MPTP version was to make these initial measurements possible in order to get some real feedback about the feasibility of (inductively assisted) ATP over a very large body of formalized mathematics. No such hard evidence had been previously known, which sometimes led to overly pessimistic views of such a project.…”

Section: First Mptp Versionmentioning

confidence: 99%

MPTP 0.2: Design, Implementation, and Initial Experiments

Urban

2006

J Autom Reasoning

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This paper describes the second version of the Mizar Problems for Theorem Proving (MPTP) system and first experimental results obtained with it. The goal of the MPTP project is to make the large formal Mizar Mathematical Library (MML) available to current first-order automated theorem provers (ATPs) (and vice versa) and to boost the development of domain-based, knowledge-based, and generally AIbased ATP methods. This version of MPTP switches to a generic extended TPTP syntax that adds term-dependent sorts and abstract (Fraenkel) terms to the TPTP syntax. We describe these extensions and explain how they are transformed by MPTP to standard TPTP syntax using relativization of sorts and deanonymization of abstract terms. Full Mizar proofs are now exported and also encoded in the extended TPTP syntax, allowing a number of ATP experiments. This covers, for example, consistent handling of proof-local constants and proof-local lemmas and translating of a number of Mizar proof constructs into the TPTP formalism. The proofs using second-order Mizar schemes are now handled by the system, too, by remembering (and, if necessary, abstracting from the proof context) the first-order instances that were actually used. These features necessitated changes in Mizar, in the Mizar-to-TPTP exporter, and in the problem-creating tools. Mizar has been reimplemented to produce and use natively a detailed XML format, suitable for communication with other tools. The Mizar-to-TPTP exporter is now just a XSLT stylesheet translating the XML tree to the TPTP syntax. The problem creation and other MPTP processing tasks are now implemented in about 1,300 lines of Prolog. All these changes have made MPTP more generic, more complete, and more correct. The largest remaining issue is the handling of the Mizar arithmetical evaluations. We describe several initial ATP experiments, both on the easy and on the hard MML problems, sometimes assisted by machine learning. It is shown that on the nonarithmetical problems, countersatisfiability (completions) is no longer detected 22 J Autom Reasoning (2006) 37:21-43 by the ATP systems, suggesting that the 'Mizar deconstruction' done by MPTP is in this case already complete. About every fifth nonarithmetical theorem is proved in a fully autonomous mode, in which the premises are selected by a machine-learning system trained on previous proofs. In 329 of these cases, the newly discovered proofs are shorter than the MML originals and therefore are likely to be used for MML refactoring. This situation suggests that even a simple inductive or deductive system trained on formal mathematics can be sometimes smarter than MML authors and usable for general discovery in mathematics.

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“…The parser needs to retrieve for each identifier the list of all the objects whose name is equal to the identifier. The task can easily be performed making the parser consult a search engine for mathematical formulae as the one developed in the MoWGLI project [5] or the similar, but less generic one, developed by the Mizar group [2].…”

Section: Analysis and Future Improvementsmentioning

confidence: 99%

Efficient Ambiguous Parsing of Mathematical Formulae

Coen

Zacchiroli

2004

Lecture Notes in Computer Science

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Abstract. Mathematical notation has the characteristic of being ambiguous: operators can be overloaded and information that can be deduced is often omitted. Mathematicians are used to this ambiguity and can easily disambiguate a formula making use of the context and of their ability to find the right interpretation. Software applications that have to deal with formulae usually avoid these issues by fixing an unambiguous input notation. This solution is annoying for mathematicians because of the resulting tricky syntaxes and becomes a show stopper to the simultaneous adoption of tools characterized by different input languages. In this paper we present an efficient algorithm suitable for ambiguous parsing of mathematical formulae. The only requirement of the algorithm is the existence of a "validity" predicate over abstract syntax trees of incomplete formulae with placeholders. This requirement can be easily fulfilled in the applicative area of interactive proof assistants, and in several other areas of Mathematical Knowledge Management.

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Information Retrieval in MML

Cited by 33 publications

References 3 publications

A Goal-Directed Decision Procedure for Hybrid PDL

A Goal-Directed Decision Procedure for Hybrid PDL

MPTP 0.2: Design, Implementation, and Initial Experiments

Efficient Ambiguous Parsing of Mathematical Formulae

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