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In propositional logic, tautology is either of two commonly used rules of replacement. [1] [2] [3] The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are: The principle of idempotency of disjunction:
In mathematical logic, the rules of passage govern how quantifiers distribute over the basic logical connectives of first-order logic.The rules of passage govern the "passage" (translation) from any formula of first-order logic to the equivalent formula in prenex normal form, and vice versa.
[1] [48] [49] [6] Many-valued logic is a logic that allows for additional truth values besides true and false in classical logic. [1] [50] [2] In this sense, it rejects the principle of the bivalence of truth. [8] [4] In a simple form of three-valued logic, for example, a third truth value is introduced: undefined. [51]
A four-valued logic was established by IEEE with the standard IEEE 1364: It models signal values in digital circuits. The four values are 1, 0, Z and X. 1 and 0 stand for Boolean true and false, Z stands for high impedance or open circuit and X stands for don't care (e.g., the value has no effect).
Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the nineteenth century with the aid of an artificial notation and a rigorously deductive method. [5]
The exportation rule may be written in sequent notation: (()) (())where is a metalogical symbol meaning that (()) is a syntactic equivalent of (()) in some logical system; . or in rule form:
In modern logic, this is not assumed so the faded ones do not hold. (There can be no element in the faded red areas in the modern logic.) Depiction from the 15th century. In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions.
Science of Logic (SL; German: Wissenschaft der Logik, WdL), first published between 1812 and 1816, is the work in which Georg Wilhelm Friedrich Hegel outlined his vision of logic. Hegel's logic is a system of dialectics , i.e., a dialectical metaphysics : it is a development of the principle that thought and being constitute a single and active ...