Algebraic logic has at least two meanings:

• the early study of Boolean algebra; and
• abstract algebraic logic, a branch of contemporary mathematical logic.

In its first form it was largely the product of British algebraists of the first half of the nineteenth century, making formal some insights into traditional Aristotelian propositional calculus that had been noted by Leibniz and others. In abstract algebra, a Boolean algebra is an algebraic structure (a collection of elements and operations on them obeying defining axioms) that captures essential properties of both set operations and logic operations. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... In mathematical logic the propositional calculus or sentential calculus is a formal deduction system whose atomic formulas are propositional variables. ... Gottfried Leibniz Gottfried Wilhelm von Leibniz (July 1, 1646 in Leipzig - November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorb descent. ...

The Leibniz influence

What we know on Leibniz's ideas comes from drafts that Louis Couturat found in the Nachlass, and published in 1903. Selections from this volume have been translated into English, mainly by Parkinson (1966) and Loemker (1969). Our present understanding of Leibniz the logician emerges mainly from the work of Wolfgang Lenzen, beginning around 1980; for a summary, see Lenzen (2004). Louis Couturat (January 17, 1868 - August 3, 1914) was a French logician, mathematician, philosopher, and linguist. ... A literary executor is a person with decision-making power in respect of the literary estate of an author who has died. ...

Charles Peirce, Hugh MacColl, Frege, and Bertrand Russell all shared Leibniz's dream of combining symbolic logic, mathematics, and philosophy. The culmination of Leibniz's approach to logic is, arguably, the algebraic logic of Ernst Schröder and the modal logic founded by Clarence Irving Lewis. Charles Sanders Peirce (pronounced purse), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ... Hugh MacColl (1837-1909) was a Scot who trained as a mathematician and evolved into a logician. ... Friedrich Ludwig Gottlob Frege Friedrich Ludwig Gottlob Frege (November 8, 1848 - July 26, 1925) was a German mathematician, logician, and philosopher who is regarded as a founder of both modern mathematical logic and analytic philosophy. ... Bertrand William Russell, 3rd Earl Russell OM FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, and mathematician, working mostly in the 20th century. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... Ernst Schröder Ernst Schröder (25 November 1841 Mannheim, Germany - 16 June 1902 Karlsruhe Germany) was a German mathematician mainly known for his work on algebraic logic. ... A modal logic is any logic for handling modalities: concepts like possibility, impossibility, and necessity. ... Clarence Irving Lewis (April 12, 1883 Stoneham, Massachusetts - February 3, 1964 Cambridge, Massachusetts) was an American academic philosopher. ...

Related to modal logic, Leibniz thus stumbled upon the problem of future contingents concerning the famous "sea battle" example. For an example of how present-day work in logic and metaphysics can draw inspiration from, and shed light on, Leibniz's thought, see Zalta (2000). The problem of the futures contingents designs a logical paradox first posed by Diodorus Cronus from the Megarian school of philosophy, under the name of the dominator, and then reactualized by Aristotle in chapter 9 of De Interpretatione. ...

References

• Loemker, Leroy (1969 (1956)), Leibniz: Philosophical Papers and Letters, Reidel
• Parkinson, G.H.R., 1966. Leibniz: Logical Papers. Oxford Uni. Press.
• Zalta, E. N., 2000, "A (Leibnizian) Theory of Concepts," Philosophiegeschichte und logische Analyse / Logical Analysis and History of Philosophy 3: 137-183.