Related papers: Point-and-write --- Documenting Formal Mathematics…
This paper presents inference rules for Resource Description Framework (RDF), RDF Schema (RDFS) and Web Ontology Language (OWL). Our formalization is based on Notation 3 Logic, which extended RDF by logical symbols and created Semantic Web…
For many decades, formal methods are considered to be the way forward to help the software industry to make more reliable and trustworthy software. However, despite this strong belief and many individual success stories, no real change in…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
We propose a formal treatment of scenarios in the context of a dialectical argumentation formalism for qualitative reasoning about uncertain propositions. Our formalism extends prior work in which arguments for and against uncertain…
This paper is devoted to the problems of ontology-based mathematical knowledge management and representation. The main attention is paid to the development of a formal model for the representation of mathematical statements in the Open…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization techniques. I mean the (informal) notion of axiomatic theory according to which a…
We introduce a new technique for constructing a finite state deterministic automaton from a regular expression, based on the idea of marking a suitable set of positions inside the expression, intuitively representing the possible points…
The use of lightweight formal methods (LFM) for the development of industrial applications has become a major trend. Although the term "lightweight formal methods" has been used for over ten years now, there seems to be no common agreement…
Artificial intelligence systems have achieved remarkable capability in natural language processing, perception and decision-making tasks. However, their behaviour often remains opaque and difficult to verify, limiting their applicability in…
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
In this paper we propose an interpretation for self-referential propositions in a "meta-model" N* of ZF. This meta-model N* is considered as an informal model of arithmetic that mathematicians often use when working with number theory.…
ALEXANDRIA is an ERC-funded project that started in 2017, with the aim of bringing formal verification to mathematics. The past six years have seen great strides in the formalisation of mathematics and also in some relevant technologies,…
This article focuses on the application of model development and opening the source code available and implemented by the Free Software and Open Source FLOSS to the instructional and teaching has both mathematics and computer by the…
Formal methods were frequently shown to be effective and, perhaps because of that, practitioners are interested in using them more often. Still, these methods are far less applied than expected, particularly, in critical domains where they…
We introduce MLFMF, a collection of data sets for benchmarking recommendation systems used to support formalization of mathematics with proof assistants. These systems help humans identify which previous entries (theorems, constructions,…
We introduce ProofNet, a benchmark for autoformalization and formal proving of undergraduate-level mathematics. The ProofNet benchmarks consists of 371 examples, each consisting of a formal theorem statement in Lean 3, a natural language…
Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant…
To analyse and verify the safety and security properties of interactive systems, a formal specification might be necessary. There are many types of formal languages and frameworks. The decision regarding what type of formal specification…