Computational logic: its origins and applications

• Published in: Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 474; no. 2210; p. 20170872
• Main Author: Paulson, Lawrence C.
• Format: Journal Article
• Language: English
• Published: England The Royal Society Publishing 01.02.2018
• Edition: Royal Society (Great Britain)
• Subjects: Computation; Formal Verification; Formalism; Isabelle; Logic; Logic For Computable Functions; Logic programming; Low cycle fatigue; Perspective; Proof Assistants; Theorem Proving; logic for computable functions; proof assistants; formal verification; theorem proving; Isabelle
• ISSN: 1364-5021; 1471-2946; 1471-2946
• DOI: 10.1098/rspa.2017.0872

Computational logic is the use of computers to establish facts in a logical formalism. Originating in nineteenth century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms, techniques and technologies. One strand of work follows the ‘logic for computable functions (LCF) approach’ pioneered by Robin Milner, where proofs can be constructed interactively or with the help of users’ code (which does not compromise correctness). A refinement of LCF, called Isabelle, retains these advantages while providing flexibility in the choice of logical formalism and much stronger automation. The main application of these techniques has been to prove the correctness of hardware and software systems, but increasingly researchers have been applying them to mathematics itself.