Formal Logical Systems
At its core, mathematical logic deals with mathematical concepts expressed using formal logical systems. These systems, though they differ in many details, share the common property of considering only expressions in a fixed formal language, or signature. The systems of propositional logic and first-order logic are the most widely studied today, because of their applicability to foundations of mathematics and because of their desirable proof-theoretic properties. Stronger classical logics such as second-order logic or infinitary logic are also studied, along with nonclassical logics such as intuitionistic logic.
Read more about this topic: Mathematical Logic
Famous quotes containing the words formal, logical and/or systems:
“Two clergymen disputing whether ordination would be valid without the imposition of both hands, the more formal one said, “Do you think the Holy Dove could fly down with only one wing?””
—Horace Walpole (1717–1797)
“There is no logical reason why the camel of great art should pass through the needle of mob intelligence.”
—Rebecca West (1892–1983)
“Our little systems have their day;
They have their day and cease to be:
They are but broken lights of thee,
And thou, O Lord, art more than they.”
—Alfred Tennyson (1809–1892)