The material conditional, also known as the material implication or truth functional conditional, expresses a property of certain conditionals in logic Logic, from the Greek λογικός is the study of reasoning. Logic is used in most intellectual activity, but is studied primarily in the disciplines of philosophy, mathematics, and computer science. Logic examines general forms which arguments may take, which forms are valid, and which are fallacies. It is one kind of critical thinking. In. In propositional logic In mathematical logic, a propositional calculus or logic is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules and axioms allows certain formulas to be derived, called theorems; which may be interpreted as true propositions. The series of formulas which is constructed, it expresses a binary truth function from truth-values In logic and mathematics, a logical value, also called a truth value, is a value indicating the relation of a proposition to truth to truth-values. In predicate logic In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulas contain variables which can be quantified. Two common quantifiers are the existential ∃ and universal, it can be viewed as a subset relation between the extension of (possibly complex) predicates. Symbolically:
- ,
- , and sometimes
The material conditional is false when X is true and Y is false – otherwise, it is true. X and Y, known respectively as the antecedent and consequent, are variables ranging over formulae In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language of a formal theory. The material conditional is also commonly referred to as material implication with the understanding that the antecedent materially implies the consequent.
Contents |
