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Lecture

Theorem Proving and Vampire

Related concepts (26)

Sound Blaster

Sound Blaster is a family of sound cards and audio peripherals designed by Singaporean technology company Creative Technology (known in the US as Creative Labs). The first Sound Blaster card was introduced in 1989, and since then, the Sound Blaster brand has become synonymous with high-quality computer audio.

Proof assistant

In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics.

Sound card

A sound card (also known as an audio card) is an internal expansion card that provides input and output of audio signals to and from a computer under the control of computer programs. The term sound card is also applied to external audio interfaces used for professional audio applications. Sound functionality can also be integrated onto the motherboard, using components similar to those found on plug-in cards. The integrated sound system is often still referred to as a sound card.

Vampire (theorem prover)

Vampire is an automatic theorem prover for first-order classical logic developed in the Department of Computer Science at the University of Manchester. Up to Version 3, it was developed by Andrei Voronkov together with Kryštof Hoder and previously with Alexandre Riazanov. Since Version 4, the development has involved a wider international team including Laura Kovacs, Giles Reger, and Martin Suda. Since 1999 it has won at least 53 trophies in the CADE ATP System Competition, the "world cup for theorem provers", including the most prestigious FOF division and the theory-reasoning TFA division.

Set theory

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.

Empty set

In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called non-empty. In some textbooks and popularizations, the empty set is referred to as the "null set".