On Correctness of Mathematical Texts from a Logical and Practical Point of View

Verchinine, Konstantin; Lyaletski, Alexander V.; Paskevich, Andrei; Anisimov, A. V.

doi:10.1007/978-3-540-85110-3_47

Cited by 12 publications

(9 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The need for natural interfaces (both superficial and functional) in automated verification has been recognized to varying degrees by the designers of the Tutch proof checker [1], the Scunak mathematical assistant system [9], the ForTheL language and SAD proof assistant [31], the EPGY Theorem-Proving Environment [21], the ΩMEGA proof verifier [28], and in the work of Sieg and Cittadini [27]. The ontology-oriented, lightweight verification capabilities of the automated assistant are inspired by work in the assembly of large-scale formal and semi-formal ontologies [24].…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Safe compositional network sketches

Bestavros

Kfoury

Lapets

et al. 2010

Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control

View full text Add to dashboard Cite

NetSketch is a tool for the specification of constrained-flow networks (CFNs) and the certification of desirable safety properties imposed thereon, conceived to assist system integrators in modeling and design. It provides compositional analysis capabilities based on a strongly-typed domain-specific language (DSL) for describing and reasoning about CFNs and relevant invariants. Users can model or design individual network components and perform manual or automated whole-system analysis of the properties thereof. Users can also assemble many instances of these components into larger networks, relying on NetSketch's less precise but more tractable compositional analysis capabilities. This ability to trade "precision of analysis" for "feasibility of analysis" according to available resources is among the novel features of NetSketch. In earlier work we illustrated how NetSketch is applied to actual domains [6], and provided a formal definition of its underlying formalism [7].While the NetSketch DSL provides automatic compositional analysis capabilities for modeling and designing entire networks, users may need to employ a wider variety of tools and techniques when modeling and designing individual network components. These can include common tools for reasoning about systems of constraints of various classes (such as linear constraints, quadratic constraints, and so on), as well as logical systems and ontologies that deal with concepts relevant to the application domain. We integrate the AARTIFACT [14] lightweight automated assistant for formal reasoning (which has also been applied in proving the soundness of the NetSketch formalism [15]) as a tool for modeling and designing individual network components. We present use cases within the context of an example application of the NetSketch DSL that demonstrate how the automated assistant provides NetSketch users with both an interface for reasoning formally about constraints, and a straightforward way to implicitly employ a rich domain-specific ontology of logical propositions. This allows users to verify common properties of constraints and constraint sets, and to reason about constraint relationships using automatically verifiable algebraic manipulations.

show abstract

Section: Related Work and Conclusionmentioning

confidence: 99%

Safe compositional network sketches

Bestavros

Kfoury

Lapets

et al. 2010

Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control

View full text Add to dashboard Cite

show abstract

“…The EA project seems to have run since the beginning of the 1970s, but it hasn't become known outside of Russia and Ukraine and publications about the project are all in Russian. The project has evolved into a system SAD (System for Automated Deduction) [45], which checks mathematical texts written in the language ForTheL (FORmal THEory Language) [67]. The latter is a declarative formal language for writing definitions, lemmas and proofs, very much in the spirit of Mizar, but developed independently from it.…”

Section: Evidence Algorithmmentioning

confidence: 99%

Proof assistants: History, ideas and future

Geuvers

2009

Sadhana

View full text Add to dashboard Cite

In this paper we will discuss the fundamental ideas behind proof assistants: What are they and what is a proof anyway? We give a short history of the main ideas, emphasizing the way they ensure the correctness of the mathematics formalized. We will also briefly discuss the places where proof assistants are used and how we envision their extended use in the future. While being an introduction into the world of proof assistants and the main issues behind them, this paper is also a position paper that pushes the further use of proof assistants. We believe that these systems will become the future of mathematics, where definitions, statements, computations and proofs are all available in a computerized form. An important application is and will be in computer supported modelling and verification of systems. But their is still along road ahead and we will indicate what we believe is needed for the further proliferation of proof assistants.

show abstract

“…Some examples are articles in journals, hypertext documents on the web, and theory files produced using theorem provers. An example of a recent MKM 2008 paper written from the document view is "On Correctness of Mathematical Texts from a Logical and Practical Point of View" by K. Verchinine et al [30]. It is concerned with formalized mathematical documents.…”

Section: Viewsmentioning

confidence: 99%

A Review of Mathematical Knowledge Management

Carette

Farmer

2009

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Mathematical Knowledge Management (MKM), as a field, has seen tremendous growth in the last few years. This period was one where many research threads were started, and the field was defining itself. We believe that we are now in a position to use the MKM body of knowledge as a means to define what MKM is, what it worries about, etc. In this paper, we review the literature of MKM and gather various metadata from these papers. After offering some definitions surrounding MKM, we analyse the metadata we have gathered from these papers, in an effort to cast more light on the field of MKM and its evolution.

show abstract

On Correctness of Mathematical Texts from a Logical and Practical Point of View

Cited by 12 publications

References 18 publications

Safe compositional network sketches

Safe compositional network sketches

Proof assistants: History, ideas and future

A Review of Mathematical Knowledge Management

Contact Info

Product

Resources

About