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{{Normal forms in logic | state = collapsed}} will show the template collapsed, i.e. hidden apart from its title bar. {{Normal forms in logic | state = expanded}} will show the template expanded, i.e. fully visible. This template organizes various normal forms used in logic, split into three categories: propositional logic, predicate logic, and ...
In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or — in philosophical logic — a cluster concept. [1] As a normal form, it is useful in automated theorem proving.
[8] [9] This provides a procedure for converting between conjunctive normal form and disjunctive normal form. [10] Since the Disjunctive Normal Form Theorem shows that every formula of propositional logic is expressible in disjunctive normal form, every formula is also expressible in conjunctive normal form by means of effecting the conversion ...
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
The De Morgan dual is the canonical conjunctive normal form , maxterm canonical form, or Product of Sums (PoS or POS) which is a conjunction (AND) of maxterms. These forms can be useful for the simplification of Boolean functions, which is of great importance in the optimization of Boolean formulas in general and digital circuits in particular.
A graphical representation of a partially built propositional tableau. In proof theory, the semantic tableau [1] (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux), also called an analytic tableau, [2] truth tree, [1] or simply tree, [2] is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. [1]
Another form of argument is known as modus tollens (commonly abbreviated MT). In this form, you start with the same first premise as with modus ponens. However, the second part of the premise is denied, leading to the conclusion that the first part of the premise should be denied as well. It is shown below in logical form. If A, then B Not B
Venn diagram, depicting the truth table values as a colouring of regions of the plane; Algebraically, as a propositional formula using rudimentary Boolean functions: Negation normal form, an arbitrary mix of AND and ORs of the arguments and their complements; Disjunctive normal form, as an OR of ANDs of the arguments and their complements