1. revised and extended axiomatic theory and proof development. 2. a new curriculum with extensive questions, intuitive illustrations of key concepts, exercises in formal proofs, and an emphasis on the use of mathematical logic as a formal tool for the analysis of informal concept". 3. parallel languages-a completely new formal language containing concise formulas for use in proofs together wit...

This paper presents an analysis of the concept of burden of proof in argument. Relationship of burden of proof to three traditional informal fallacies is considered: (i) argumentum ad hominem (ii) petitio principii and (iii) argumentum ad ignorantiam. Other topics discussed include persuasive dialogue, pragmatic reasoning, legal burden of proof, plausible reasoning in regulated disputes, rules ...

We present ‘Ribbon Proofs’, a graphical proof system for the Logic of Bunched Implications (BI). We give the informal, graphical, notation, we formalise the system algebraically and sketch the proof of its soundness and completeness. We discuss the spatial and geometrical nature of the proof system and its relation to BI’s spatial model theory.

We describe a mechanically-checked proof of the optimality of earliest-deadline-rst (EDF) schedulers on periodic tasks accomplished using the Nqthm theorem prover. We present a formalization of the theorem and discuss why the machine-checked proof is both more complex and more reliable than a corresponding informal proof.

The Milner-Damas typing algorithm W is one of the classic algorithms in Computer Science. In this paper we describe a formalised soundness and completeness proof for this algorithm. Our formalisation is based on names for both term and type variables, and is carried out in Isabelle/HOL using the Nominal Datatype Package. It turns out that in our formalisation we have to deal with a number of is...

We introduce a platform for presenting and cross-linking formal and informal proof developments together. The platform supports writing natural language ‘narratives’ that include islands of formal text. The formal text contains hyperlinks and gives on-demand state information for each proof step. We argue that such a system significantly lowers the threshold for understanding formal development...

A widely circulated list of spurious proof types may help to clarify our understanding of informal mathematical reasoning. An account in terms of argumentation schemes is proposed.

CERES, HLK and ProofTool form together a system for the computer-aided analysis of mathematical proofs. This analysis is based on a proof transformation known as cut-elimination, which corresponds to the elimination of lemmas in the corresponding informal proofs. Consequently, the resulting formal proof in atomic-cut normal form corresponds to a direct, i.e. without lemmas, informal mathematica...

Proof lies at the heart of mathematics yet we know from research in mathematics education that proof is an elusive concept for many mathematics students. The question that we are now asking is whether the introduction of dynamic geometry systems will improve the situation – or will it make the transition from informal to formal proof in mathematics even harder? How far will innovative teaching ...

This paper presents a new proof language for the Coq proof assistant. This language uses the declarative style. It aims at providing a simple, natural and robust alternative to the existing Ltac tactic language. We give the syntax of our language, an informal description of its commands and its operational semantics. We explain how this language can be used to implement formal proof sketches. F...