Related papers: Analyzing Individual Proofs as the Basis of Intero…

This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…

Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors initiated in 2004 a study on the computational power of quantum interactive proof systems…

Formal verification tools are often developed by experts for experts; as a result, their usability by programmers with little formal methods experience may be severely limited. In this paper, we discuss this general phenomenon with…

In this article, we present an automated approach that would test for and discover the interoperability of CAD systems based on the approximately-invariant shape properties of their models. We further show that exchanging models in standard…

We define a fragment of propositional logic where isomorphic propositions, such as $A\land B$ and $B\land A$, or $A\Rightarrow (B\land C)$ and $(A\Rightarrow B)\land(A\Rightarrow C)$ are identified. We define System I, a proof language for…

We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…

In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear…

The substitution of a system with another one may occur in several situations like system adaptation, system failure management, system resilience, system reconfiguration, etc. It consists in replacing a running system by another one when…

To refine formal methods for concurrent systems, there are several ways of enriching classical operational semantics of process calculi. One can enable the auditing and undoing of past synchronisations thanks to communication keys, thus…

We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…

We discuss two proof evaluation activities meant to promote the acquisition of learning behaviors of professional mathematics within an introductory undergraduate proof-writing course. These learning behaviors include the ability to read…

There is a lack of formalism for some key foundational concepts in systems engineering. One of the most recently acknowledged deficits is the inadequacy of systems engineering practices for engineering intelligent systems. In our previous…

A scientific reasoning system makes decisions using objective evidence in the form of independent experimental trials, propositional axioms, and constraints on the probabilities of events. As a first step towards this goal, we propose a…

We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded…

In this paper we give an ordinal analysis of the theory of second order arithmetic. We do this by working with proof trees -- that is, "deductions" which may not be well-founded. Working in a suitable theory, we are able to represent…

We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to…

Proof assistants are computer softwares that allow us to write mathematical proofs so as to assess their correctness. In November 2021, I started the project of checking the simplicity of the alternating groups within the Lean theorem…

This paper develops a general methodology to connect propositional and first-order interpolation. In fact, the existence of suitable skolemizations and of Herbrand expansions together with a propositional interpolant suffice to construct a…

Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical…

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…