Automated theorem proving

Automated theorem proving refers to the process of using computer programs to independently prove mathematical theorems. This technique involves checking whether a statement is a logical consequence of a set of axioms and hypotheses, and is performed entirely by the computer program.From: The Cognitive Early Warning Predictive System Using the Smart Vaccine [2019], Foundations of mathematics under neuroscience conditions of lateral inhibition and lateral activation [2018]

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Published in Jay Liebowitz, The Handbook of Applied Expert Systems, 2019

Randy G. Goebel

The resolution procedure was first proposed by Robinson (Robinson). It is a simple yet extremely powerful rule of inference that has been shown sound and complete, and the associated proof procedure is very amenable to machine implementation. Resolution stimulated research and development in automatic theorem proving and found many applications in natural language understanding, planning, database systems, and logic programming, among other areas.

Foundations of mathematics under neuroscience conditions of lateral inhibition and lateral activation

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Published in International Journal of Parallel, Emergent and Distributed Systems, 2018

Andrew Schumann, Alexander V. Kuznetsov

The subject of our paper is related to the automated theorem proving (ATP) – a technique which allows us to check by means of a computer program that a statement is a logical consequence obtained from a set of statements (axioms and hypotheses) mechanically. However, using ATP in a real process of mathematical reasoning is not so easy. For example, in functional analysis a completely formal exposition of a theory is extremely difficult. The point is that a huge number of axioms and already proven theorems, as well as a complexity of all the connections among them, makes ATP almost impossible. Therefore, ATP systems are used more often in an interactive way, when a user can guide some inferences made by the system or look at intermediate lemmas to be proved on the way of proving the whole theorem. As we see, the process of automatic proof of mathematical theorems requires a kind of heuristics to be more successful in interactions with ATP.

Automated theorem proving

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Logic

Foundations of mathematics under neuroscience conditions of lateral inhibition and lateral activation