the concept of mathematical proof has been controversial for the past few decades. different philosophers have offered different theories about the nature of mathematical proof, among which theories presented by lakatos and hersh have had significant similarities and differences with each other. it seems that a comparison and critical review of these two theories will lead to a better understan...

D aily, we confront the errors of computers. They crash, hang, succumb to viruses, run buggy software, and harbor spyware. Our tabloids report bizarre computer glitches: the library patron who is fined US$40 trillion for an overdue book, because a barcode is scanned as the size of the fine; or the dentist in San Diego who was delivered over 16,000 tax forms to his doorstep when he abbreviated “...

Increases in the use of automated theorem-provers have renewed focus on the relationship between the informal proofs normally found in mathematical research and fully formalised derivations. Whereas some claim that any correct proof will be underwritten by a fully formal proof, sceptics demur. In this paper I look at the relevance of these issues for formalism, construed as an anti-platonistic ...

We define the notion of formal proof sketch for the mathematical language Mizar. We show by examples that formal proof sketches are very close to informal mathematical proofs. We discuss some ways in which formal proof sketches might be used to improve mathematical proof assistants.

: 1, if n = 1, 0, if p|n for some prime p, (−1), if n = p1p2 · · · pr, where pi are distinct primes. as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function. The second part of the paper is devoted to the notion...

We present the generic system framework of Isabelle/Isar underlying recent versions of Isabelle. Among other things, Isar provides an infrastructure for Isabelle plug-ins, comprising extensible state components and extensible syntax that can be bound to tactical ML programs. Thus the Isabelle/Isar architecture may be understood as an extension and refinement of the traditional “LCF approach”, w...

In this paper we propose a proof format to write formal proofs motivated by a formalisation of floating-point numbers. This proof format aims at being adequate for both proof presentation and mechanised proof checking. We also present a simple graphical interface to support this proof format.