Despite the science of modern formal reasoning being more than a century old, mechanized formal reasoning is nowhere near what expert human reasoners (formal and informal) can achieve. Meanwhile, there is a steadily increasing need for automated theorem proving in various fields of science and engineering. Proof discovery and verification in science and mathematics [2,3,4,5], formal verificatio...

A Clifford algebra has three major multiplications: inner product, outer product and geometric product. Accordingly, the same Clifford algebra has three versions: Clifford vector algebra, which features on inner products and outer products of multivectors; Clifford bracket algebra, which features on pseudoscalars and inner products of vectors; Clifford geometric algebra, which features on geome...

We present a combination of raising, explicit variable dependency representation, the liberalized δrule, and preservation of solutions for first-order deductive theorem proving. Our main motivation is to provide the foundation for our work on inductive theorem proving.

We present a combination of raising, explicit variable dependency representation, the liberalized δrule, and preservation of solutions for first-order deductive theorem proving. Our main motivation is to provide the foundation for our work on inductive theorem proving.

In this contribution I advocate an open system for formalised mathematical reasoning that is able to capture diierent mathematical formalisms as well as a wide variety of proof formats. This is assumed to be much more adequate since it more closely reeects the situation in mathematics as a whole. In particular I try to classify diierent dimension according to which proofs can be classiied.

We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational semantics, axiomatic semantics, and abstract interpretation. Descriptions as recursive functions are also provided whenever suitable, thus yielding a a verifica...

Accessing knowledge of a single knowledge source with different client applications often requires the help of mediator systems as middleware components. In the domain of theorem proving large efforts have been made to formalize knowledge for mathematics and verification issues, and to structure it in databases. But these databases are either specialized for a single client, or if the knowledge...