Incompleteness and undecidability have been used for many years as arguments against automatising the practice of mathematics. The advent of powerful computers and proof-assistants – programs that assist the development of formal proofs by human-machine collaboration – has revived the interest in formal proofs and diminished considerably the value of these arguments. In this paper we discuss so...

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...

The recent rise of “computer-assisted” and “experimental” mathematics raises intriguing questions as to the future role of computation in mathematics. These results also draw into question the traditional distinctions that have been drawn between formal proof and computationally-assisted proof. This article explores these questions in the context of the growing consensus among computer technolo...

This paper presents a machine-checked proof of the Basic Theorem on Concept Lattices, which appears in the book ”Formal Concept Analysis” by Ganter and Wille, in the Isabelle/HOL Proof Assistant. As a by-product, the underlying lattice theory by Kammueller has been extended.

We discuss the formal approach to Tarski geometry axioms modelled with the help of the Mizar computerized proof assistant system. We try however to go much further from the use of simple predicates in the direction of the use of structures with their inheritance, attributes as a tool of more human-friendly namespaces for axioms, and registrations of clusters to obtain more automation (with the ...

Building on existing work in proxying interaction with proof assistants, we have previously developed a proof movie. We have now considered the problem of how to augment this movie data structure to support commentary on formal proof development. In this setting, we have studied extracting commentary from an online text by Pierce et al. [11].

Undeniable signature schemes are not publicly verifiable. Therefore, in order to prove the validity/invalidity of a message-signature pair, the signer needs to provide a proof for the rightful verifier. Since the introduction of undeniable signature schemes, various proof systems with different properties and features have been introduced to be incorporated in the structure of such schemes. Amo...

Recent work on the enhancement of typing techniques for multiparty sessions with logical annotations enables, not only the validation of structural properties of the conversations and on the sorts of the messages, but also properties on the actual values exchanged. However, specification and verification of mutual effects of multiple cross-session interactions are still an open problem. We intr...

A novel theoretical model is presented maintaining that consciousness evolved on the basis of time distinctions. Various models of time pertain to the existence of future, present and past. It is proposed that the future represents potentialities, the present the actualization of certain potentialities, and the past a record of actualized potentialities. Actualization of potentialities derives ...

gravitational search algorithm (gsa) is one of the newest swarm based optimization algorithms, which has been inspired by the newtonian laws of gravity and motion. gsa has empirically shown to be an efficient and robust stochastic search algorithm. since introducing gsa a convergence analysis of this algorithm has not yet been developed. this paper introduces the first attempt to a formal conve...