2014/12/09 by Stanley Burris, Burris, Stanley, H. P. Sankappanavar +1
Computer Science · #Advanced Algebra and Logic #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.1412.2953
openalex publication_date 2014/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In modern algebra it is well-known that one cannot, in general, apply ordinary equational reasoning when dealing with partial algebras. However Boole did not know this, and he took the opposite to be a fundamental truth, which he called the Principles of Symbolical Reasoning in his 1854 book \em Laws of Thought. Although Boole made no mention of it, his Principles were clearly a generalization of the earlier publications on algebra by the Cambridge mathematician Peacock. After a detailed examination of Boole's presentation of his Principles, we give a correct version that is applicable to his algebra of logic for classes.