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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.
A logical operator that specifies the quantity of specimens in the domain of discourse that satisfy an open formula, such as "all", "some", or "exists". quantifier shift fallacy A logical fallacy involving the incorrect interchange of the position of two quantifiers, or a quantifier and a modal operator, leading to invalid conclusions.
"Logical" refers to the Boolean logical operations of disjunction, conjunction, and negation between two sequences of bits, in which each bit in one sequence is simply compared to its counterpart in the other sequence. Programmers therefore have the option of working in and applying the rules of either numeric algebra or Boolean algebra as needed.
Some languages, e.g., Perl and Ruby, have two sets of Boolean operators, with identical functions but different precedence. Typically these languages use and, or and not for the lower precedence operators. Some programming languages derived from PL/I have a bit string type and use BIT(1) rather than a separate Boolean type. In those languages ...
Logical connectives can be used to link zero or more statements, so one can speak about n-ary logical connectives. The boolean constants True and False can be thought of as zero-ary operators. Negation is a unary connective, and so on.
Propositional logic, as currently studied in universities, is a specification of a standard of logical consequence in which only the meanings of propositional connectives are considered in evaluating the conditions for the truth of a sentence, or whether a sentence logically follows from some other sentence or group of sentences.
The ternary operator (,,) = is one such operator which is actually a unary operator applied to one input, and ignoring the other two inputs. "Not" is a unary operator, it takes a single term (¬P). The rest are binary operators, taking two terms to make a compound statement (P ∧ Q, P ∨ Q, P → Q, P ↔ Q).
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science.Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language.