en Carew Arthur Meredith

C. A. Meredith
C. A. Meredith
Born	28 June 1904; Dublin, Ireland
Died	31 March 1976 (aged 71); Dublin, Ireland
Nationality	Irish
Education	Trinity College, Cambridge
Alma mater	Trinity College, Cambridge
Known for	condensed detachment
	Scientific career
Fields	Logic, Mathematics
Institutions	Trinity College Dublin

Carew Arthur Meredith (28 July 1904 – 31 March 1976), usually cited as C. A. Meredith, was an influential Irish logician, who worked in Trinity College, Dublin from 1943 to 1964.^[1] His work on condensed detachment (inspired by the work of Łukasiewicz) is influential in modern research.^[2]^[3]^[4]^[5]^[6]

Biography

Born 28 July 1904 into a distinguished Dublin family, he was the son of barrister Arthur Francis Carew Meredith K.C., whose opinions were sought by Éamon de Valera in drafting the constitution of the Irish Republic (1919–22). Educated in England at Winchester College, he went on to read mathematics at Trinity College, Cambridge, in 1922 becoming the first mathematical student to take a double first and 'B star' in two years. He worked in England until 1939 as a private tutor for university students, when he moved to Ireland, as he was a committed pacifist. In 1943 he became a lecturer in mathematics in Trinity College Dublin.

Łukasiewicz was appointed professor at the Royal Irish Academy, where he lectured on mathematical logic. Meredith attended these lectures from 1947 on, and became keenly interested in the Lukasiewicz's detachment operation, for which—as he himself once phrased it—he "seemed to have some aptitude."^[1]

Meredith was the cousin of David Meredith.^[5] He was also related to another mathematician, Thomas Meredith. He was a nephew of Richard Edmund Meredith and a cousin of Monk Gibbon, Judge James Creed Meredith and Ralph Creed Meredith. His old school friend from Winchester, William Empson, described him as "a small, gnomelike figure with a grin like a Cheshire cat and a pronounced Dublin accent (good for reading aloud from Joyce)".

He did logic whenever time and opportunity presented themselves, and he did it on whatever materials came to hand: in a pub, his favored pint of porter within reach, he would use the inside of cigarette packs to write proofs for logical colleagues.^[1]

Work

He proved the shortest known axiomatic bases for a number of logic systems, such as this one-axiom basis for propositional calculus:^[7]

$(((((\phi \to \psi )\to (\neg \chi \to \neg \theta ))\to \chi )\to \tau )\to ((\tau \to \phi )\to (\theta \to \phi )))$

His achievements in that area were unsurpassed until automated theorem provers in the last few years, which build on his work, proved some shorter ones for some systems and proved his shortest for others. Notably, Stephen Wolfram, William McCune and others built on Meredith's work to produce the shortest known single axiom equivalent to the axioms of propositional calculus.^[8]^[9]

Selected publications

C.A. Meredith (1953). "Single axioms for the systems (C,N), (C,0), and (A,N) of the two-valued propositional calculus". Journal of Computing Systems. 1: 155–164.
E.J. Lemmon and C.A. Meredith and D. Meredith and A.N. Prior and I. Thomas (1957). Calculi of pure strict implication (Technical Report). Canterbury University College, Christchurch. (Reprinted in Philosophical Logic, Reidel, 1970 doi:10.1007/978-94-010-9614-0_17)
C. Meredith and A. Prior (1963). "Notes on the axiomatics of the propositional calculus". Notre Dame Journal of Formal Logic. 4 (3): 171–187. doi:10.1305/ndjfl/1093957574.
C.A. Meredith and A.N. Prior (1968). "Equational logic". Notre Dame Journal of Formal Logic. 9 (3): 212–226. doi:10.1305/ndjfl/1093893457.

References

^ ^a ^b ^c Meredith, David (October 1977). "In memoriam: Carew Arthur Meredith (1904—1976)". Notre Dame Journal of Formal Logic. 18 (4): 513–516. doi:10.1305/ndjfl/1093888116. ISSN 0029-4527.
^ Wernhard, Christoph; Bibel, Wolfgang (2021). "Learning from Łukasiewicz and Meredith: Investigations into proof structures". In Platzer, André; Sutcliffe, Geoff (eds.). Automated Deduction – CADE 28 – 28th International Conference on Automated Deduction, Virtual Event, July 12–15, 2021, Proceedings. Lecture Notes in Computer Science. Vol. 12699. Springer. pp. 58–75. arXiv:2104.13645. doi:10.1007/978-3-030-79876-5_4.
^ Kalman, J.A. (1983). "Condensed detachment as a rule of inference". Studia Logica. 42 (4): 443–451. doi:10.1007/BF01371632. JSTOR 20015133. S2CID 121221548. Retrieved 30 December 2021.
^ McCune, William; Woa, Larry (2000). "Experiments in Automated Deduction with Condensed Detachment". The Collected Works of Larry Wos. World Scientific. pp. 1193–1210. doi:10.1142/9789812813411_0053. ISBN 9789810240011. Retrieved 30 December 2021.
^ ^a ^b Rybaříková, Zuzana; Hasle, Per (2018). "CA Meredith, AN Prior, and Possible Worlds" (PDF). Logic and Philosophy of Time. 1: 42–61. Retrieved 31 December 2021.
^ Copeland, B. Jack (2006). "Meredith, Prior, and the history of possible worlds semantics". Synthese. 150 (3): 373–397. doi:10.1007/s11229-005-5514-9. S2CID 44556747. Retrieved 31 December 2021.
^ "meredith – Metamath Proof Explorer". us.metamath.org. Retrieved 22 May 2019.
^ History of logic axioms Stephen Wolfram, A New Kind of Science, 2002, p. 1175.
^ McCune, William; Veroff, Robert; Fitelson, Branden; Harris, Kenneth; Feist, Andrew; Wos, Larry (2002), "Short single axioms for Boolean algebra", Journal of Automated Reasoning, 29 (1): 1–16, doi:10.1023/A:1020542009983, MR 1940227, S2CID 207582048