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R-diagrams can be used to easily simplify complicated logical expressions, using a step-by-step process. Using order of operations, logical operators are applied to R-diagrams in the proper sequence. Finally, the result is an R-diagram that can be converted back into a simpler logical expression. For example, take the following expression:
Because the logical or means a disjunction formula is true when either one or both of its parts are true, it is referred to as an inclusive disjunction. This is in contrast with an exclusive disjunction, which is true when one or the other of the arguments are true, but not both (referred to as exclusive or, or XOR).
Joined points represent an "or" condition, also known as a logical disjunction. A spider diagram is a boolean expression involving unitary spider diagrams and the logical symbols ,,. For example, it may consist of the conjunction of two spider diagrams, the disjunction of two spider diagrams, or the negation of a spider diagram.
An important set of problems in computational complexity involves finding assignments to the variables of a Boolean formula expressed in conjunctive normal form, such that the formula is true. The k -SAT problem is the problem of finding a satisfying assignment to a Boolean formula expressed in CNF in which each disjunction contains at most k ...
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
Weak law of the excluded middle (WLEM) is axiomatised and yields a system where disjunction behaves more like in classical logic than intuitionistic logic, i.e. the disjunction and existence properties don't hold, but where use of non-intuitionistic reasoning is marked by occurrences of double-negation in the conclusion. LEM entails but is not ...