The phrase "modern logic" is correct and usable in written English.
It can be used when discussing contemporary approaches or systems of reasoning in philosophy, mathematics, or computer science.
Example: "The principles of modern logic have significantly influenced the development of artificial intelligence."
Alternatives: "contemporary logic" or "current logic".
It is an important question in the historiography of modern logic whether Leibniz's logical calculi influenced logic in its present state or whether they were only ingenious anticipations.
Since the development of modern logic, important concepts, e.g., syntax, semantics, inference, logical consequence, validity, and completeness, have been applied to sentential representation systems only.
What characterizes analytic philosophy as it was founded by Frege and Russell is the role played by logical analysis, which depended on the development of modern logic.
("Who Invented Cantor's Back-and-Forth Argument?" Modern Logic, Vol 4, No. 1, January 1994).
Thereafter, second-order functions became a ubiquitous feature of modern logic and semantic analysis.
Using tools of modern logic, the definition may be made as follows: I.
Frege's work represents the beginning of modern logic because of his invention of the notation of quantifiers and variables.
Sibajiban and Matilal have made important contributions toward rendering the concepts of Navya-Nyaya logic into the language of modern logic.
Lewis's theory of "conceptualistic pragmatism" was derived partly from his study of modern logic and partly from the influence of Royce and the classic pragmatists.
Because Aristotle's handling of these verbs differs from contemporary treatments, his discussion of this fallacy has no direct counterpart in modern logic.
His treatise, Das Wesen der Wahrheit nach der modernen Logik (1910; "The Nature of Truth According to Modern Logic"), reflected his scientific training and helped him obtain a teaching post at the University of Rostock in 1911.
