Related papers: Introducing H, an institution-based formal specifi…
We propose an epistemic approach to formalizing statistical properties of machine learning. Specifically, we introduce a formal model for supervised learning based on a Kripke model where each possible world corresponds to a possible…
This set of theories presents a formalisation in Isabelle/HOL+Isar of data dependencies between components. The approach allows to analyse system structure oriented towards efficient checking of system: it aims at elaborating for a concrete…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
The development and application of formal methods is a long standing research topic within the field of computer science. One particular challenge that remains is the uptake of formal methods into industrial practices. This paper introduces…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
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…
Many project-specific languages, including in particular filtering languages, are defined using non-formal specifications written in natural languages. This leads to ambiguities and errors in the specification of those languages. This paper…
We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification…
We present a formalization of basics related to infinite words in the generic proof assistant Isabelle/HOL. Furthermore, we present a formalization of purely morphic and morphic languages. Finally, we present a formalized definition of…
We propose stratified institutions (a decade old generalised version of the theory of institutions of Goguen and Burstall) as a fully abstract model theoretic approach to modal logic. This allows for a uniform treatment of model theoretic…
The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…
We discuss a formal system of mathematics. We use it to construct the natural numbers.
A major determinant of the quality of software systems is the quality of their requirements, which should be both understandable and precise. Most requirements are written in natural language, good for understandability but lacking in…
We present a simple and concise semantics for temporal planning. Our semantics are developed and formalised in the logic of the interactive theorem prover Isabelle/HOL. We derive from those semantics a validation algorithm for temporal…
The validation of requirements is a fundamental step in the development process of safety-critical systems. In safety critical applications such as aerospace, avionics and railways, the use of formal methods is of paramount importance both…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…
This report introduces and investigates a family of metrics on sets of pointed Kripke models. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or…
Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model-theoretic structures; the latter represents meaning as vectors in high-dimensional spaces shaped…
We develop an extension of institution theory that accommodates implicitly the partiality of the signature morphisms and its syntactic and semantic effects. This is driven primarily by applications to conceptual blending, but other…