imps, an Interactive Mathematical Proof System, is intended to provide mechanical support for traditional mathematical techniques and styles of practice. The system consists of a library of axiomatic theories and a collection of tools for exploring and extending the mathematics embodied in the theory library. One of the chief tools is a facility for developing formal proofs. imps is equally wel...

‎A universal schema for diagonalization was popularized by N.S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fi...

the discourse of the :union: of the intellect and the intelligible is one of the important philosophical issues and porphyrius and aristotle can be mentioned as among the early advocates of it, which has been common among the peripatetics. however, kandī and fārābi can be mentioned among the early muslims who brought up the issue of the :union: of the intellect and the intelligible, but ibn sīn...

the problem of the knowledge of human soul and its correlation to god's knowledge have been introduced between muslims of the beginning of islamic age and thought, using at correct traditions for ahl ul-bayt. muslim philosophers' affected by islamic teachings have studied in this respect and raised its problem as an islamic philosophical problem. they discussed this problem from two a...

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

It is frequently claimed (see e.g. [Rav]) that the formalization of a mathematical proof requires a quality of understanding that subsumes all necessary acts for checking the proof and that, consequently, automatic proof checking cannot lead to an epistemic gain about a proof. We present a project developing what is sometimes called a ’fortified formalism’ and argue taking a phenomenological lo...

Up-to techniques have been introduced to enhance the bisimulation proof method for establishing bisimilarity results. While up-to techniques for strong bisimilarity are well understood, the irregularities that appear in the weak case make it difficult to give a unified presentation. We propose a uniform and modular theory of up-to techniques for weak bisimulation that captures most of the exist...

We present a recent application area of the proof assistant Ωmega, the teaching of mathematical proofs within an environment for tutorial dialog. We discuss the design of our dialog system prototype for proof tutoring in the light of the requirements imposed by its potential users. Empirical studies investigating those requirements guide the development of the system.

The generic proof assistant Isabelle provides a landscape of specification contexts that is considerably richer than that of most other provers. Theories are the level of specification where object-logics are axiomatised. Isabelle’s proof language Isar enables local exploration in contexts generated in the course of natural deduction proofs. Finally, locales, which may be seen as detached proof...