Related papers: Formal Mathematics on Display: A Wiki for Flyspeck
Libraries of formal proofs are an important part of our mathematical heritage, but their usability and sustainability is poor. Indeed, each library is specific to a proof system, sometimes even to some version of this system. Thus, a…
Tabular data is difficult to analyze and to search through, yielding for new tools and interfaces that would allow even non tech-savvy users to gain insights from open datasets without resorting to specialized data analysis tools or even…
The formalisation of mathematics is continuing rapidly, however combinatorics continues to present challenges to formalisation efforts, such as its reliance on techniques from a wide range of other fields in mathematics. This paper presents…
Gappa uses interval arithmetic to certify bounds on mathematical expressions that involve rounded as well as exact operators. Gappa generates a theorem with its proof for each bound treated. The proof can be checked with a higher order…
Optical systems are becoming increasingly important by resolving many bottlenecks in today's communication, electronics, and biomedical systems. However, given the continuous nature of optics, the inability to efficiently analyze optical…
Monte Carlo (MC) simulations, particularly using FLUKA, are essential for replicating real-world scenarios across scientific and engineering fields. Despite the robustness and versatility, FLUKA faces significant limitations in automation…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
Ackermann's function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of…
Formal software specification is known to enable early error detection and explicit invariants, yet it has seen limited industrial adoption due to its high notation overhead and the expertise required to use traditional formal languages.…
Formal verification of floating-point arithmetic remains challenging due to non-linear arithmetic behavior and the tight coupling between control and datapath logic. Existing approaches often rely on high-level C models for equivalence…
The aim of the FESCA workshop is to bring together junior researchers from formal methods, software engineering, and industry interested in the development and application of formal modelling approaches as well as associated analysis and…
Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…
Despite the considerable interest in new dependent type theories, simple type theory (which dates from 1940) is sufficient to formalise serious topics in mathematics. This point is seen by examining formal proofs of a theorem about…
This work presents the system ANITA (Analytic Tableau Proof Assistant) developed for teaching analytic tableaux to computer science students. The tool is written in Python and can be used as a desktop application, or in a web platform. This…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
Answer Set Programming (ASP) with stable model semantics has proven highly effective for knowledge representation and reasoning. However, the minimality requirement of stable models can be restrictive for applications requiring exploration…
Open Learning Analytics (OLA) is an emerging research area that aims at improving learning efficiency and effectiveness in lifelong learning environments. OLA employs multiple methods to draw value from a wide range of educational data…
We present a tool called Hoax for the execution of {\omega}-automata expressed in the popular HOA format. The tool leverages the notion of trap sets to enable runtime monitoring of any (non-parity) acceptance condition supported by the…