Related papers: The Foundation of a Generic Theorem Prover
First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an…
Evidential reasoning is cast as the problem of simplifying the evidence-hypothesis relation and constructing combination formulas that possess certain testable properties. Important classes of evidence as identifiers, annihilators, and…
Consensus protocols are crucial for a blockchain system as they are what allow agreement between the system's nodes in a potentially adversarial environment. For this reason, it is paramount to ensure their correct design and implementation…
Automated theorem provers are now commonly used within interactive theorem provers to discharge an increasingly large number of proof obligations. To maintain the trustworthiness of a proof, the automatically found proof must be verified…
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…
We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal)…
The paper gives a detailed presentation of a framework, embedded into the simply typed higher-order logic and aimed at the support of sound and structured reasoning about various properties of models of imperative programs with interleaved…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
In this article we present an ongoing effort to formalise quantum algorithms and results in quantum information theory using the proof assistant Isabelle/HOL. Formal methods being critical for the safety and security of algorithms and…
Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is…
We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to 'recover' the properties of classical…
Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…
Our goal is a modern approach to answering questions via systematic reasoning where answers are supported by human interpretable proof trees grounded in an NL corpus of authoritative facts. Such a system would help alleviate the challenges…
We generalize several propositional preprocessing techniques to higher-order logic, building on existing first-order generalizations. These techniques eliminate literals, clauses, or predicate symbols from the problem, with the aim of…
Logic is a foundation for many modern areas of computer science. In artificial intelligence, as a basis of database query languages, as well as in formal software and hardware verification --- modelling scenarios using logical formalisms…
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…
We present a categorical framework for formal systems in which inference rules with $m$ metavariables over a category of syntax $\mathscr{S}$, taken to be a cartesian PROP, are represented by operations of arity $k \to n$ equipped with…
Argumentation is the process of constructing arguments about propositions, and the assignment of statements of confidence to those propositions based on the nature and relative strength of their supporting arguments. The process is modelled…
We present a proof procedure for univariate real polynomial problems in Isabelle/HOL. The core mathematics of our procedure is based on univariate cylindrical algebraic decomposition. We follow the approach of untrusted certificates,…
Induction lies at the heart of mathematics and computer science. However, automated theorem proving of inductive problems is still limited in its power. In this abstract, we first summarize our progress in automating inductive theorem…