This is a report about formalising a maths proof with the theorem prover Isabelle/HOL. The proof was for the completeness theorem of first order logic. The informal proof used symmetry arguments (duality) and also gave the cut elimination theorem as a corollary. Both these aspects were preserved formally. The paper outlines this formalisation. It notes that parts of the proof can be viewed as a...

Previous research demonstrated an antiprimacy effect in conversational arguments (Bailenson & Rips, 1996; Rips, 1998). In those studies, participants perceived the speaker presenting the 1st proposition in the dialogue as having more burden of proof than the 2nd speaker. In this article, I demonstrate that antiprimacy occurs because the 1st speaker tends to proportionally have fewer contrasts t...

Lockless concurrent programming brings new challenges to the field of program verification. These lockless programs require methods such as compare-and-swap and memory fences to ensure correctness. However, their unpredictable behaviour in combination with these methods complicates verifying such algorithms. We use linearisation points[3], i.e. the points in time when the state of the system ch...

In the paper by Grando et al. [1], the authors use formal methods to prove whether a computer-interpretable guideline modeling language satisfies a set of control-flow workflow patterns [2]. They contrast the formal proof with an earlier informal analysis [3] in which we had compared different guideline modeling languages according to workflow patterns that they supported. Grando et al. find di...

We describe a new approach to interface design called algebraic semiotics, combining semiotics with algebraic speciication to give a rigorous theory of representation quality, and we apply it to the tatami distributed cooperative proving project. This project uses standard html, Java, etc. for remote proof browsing, servers for remote proof execution, a protocol to maintain truth of distributed...

Both female and male elementary school students have difficulty doing action proof by using manipulative objects to provide conjectures of the truth a mathematical statement. Counter-examples can help build informal stages propose statement more precisely. This study analyzes through counter-examples stimulation for in schools. The stage this focuses on three stages: proved their primitive conj...

It is a pleasure to dedicate this article to Dov Gabbay on the occasion of his sixtieth birthday. I still have fond memories of him as a very young person, when I met him for the first time four decades ago at Stanford. That discovering or finding proofs is essentially a psychological process is widely recognized. Distinguished mathematicians such as Poincare and Hadamard have written very pers...

This paper is an informal (and nonexhaustive) overview over some existing notions of proof nets for classical logic, and gives some hints why they might be considered to be unsatisfactory.

Proofs, both formal and informal, are documents that circulate within societies of human and machine agents distributed across time and space in order to provide trust. Such trust might lead one mathematician to accept a certain statement as true or it might help convince a consumer of the quality and reliability of a safety-critical computer system. By exploiting recent results about focused p...

This technical report contains the full type-safety proof for the language presented in the paper Existential Types for Imperative Languages, originally submitted for publication in October 2001. Because this report should be read only after the paper, effectively as an appendix, we do not repeat the motivation, examples, and informal presentation contained there. Also refer to the paper for re...