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Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.
The Markable Mark, an introduction by easy stages to the ideas of Laws of Form; The BF Calculus and the Square Root of Negation by Louis Kauffman and Arthur Collings; it extends the Laws of Form by adding an imaginary logical value. (Imaginary logical values are introduced in chapter 11 of the book Laws of Form.)
The term "Boolean algebra" honors George Boole (1815–1864), a self-educated English mathematician. He introduced the algebraic system initially in a small pamphlet, The Mathematical Analysis of Logic, published in 1847 in response to an ongoing public controversy between Augustus De Morgan and William Hamilton, and later as a more substantial book, The Laws of Thought, published in 1854.
The laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based. The formulation and clarification of such rules have a long tradition in the history of philosophy and logic. Generally they are taken as laws that guide and underlie everyone's thinking, thoughts, expressions, discussions, etc.
The laws listed above define Boolean algebra, in the sense that they entail the rest of the subject. The laws complementation 1 and 2, together with the monotone laws, suffice for this purpose and can therefore be taken as one possible complete set of laws or axiomatization of Boolean algebra. Every law of Boolean algebra follows logically from ...
In logic, a rule of replacement [1] [2] [3] is a transformation rule that may be applied to only a particular segment of an expression. A logical system may be constructed so that it uses either axioms, rules of inference, or both as transformation rules for logical expressions in the system. Whereas a rule of inference is always applied to a ...
Logic studies valid forms of inference like modus ponens. Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and ...
Law of logic may refer to: Basic laws of Propositional Logic or First Order Predicate Logic; Laws of thought, which present first principles (arguably) before reasoning begins; Rules of inference, which dictate the valid use of inferential reasoning