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Then the converse of S is the statement Q implies P (Q → P). In general, the truth of S says nothing about the truth of its converse, [2] unless the antecedent P and the consequent Q are logically equivalent. For example, consider the true statement "If I am a human, then I am mortal."
In the monoid of binary endorelations on a set (with the binary operation on relations being the composition of relations), the converse relation does not satisfy the definition of an inverse from group theory, that is, if is an arbitrary relation on , then does not equal the identity relation on in general.
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the ...
For example, Aristotelian logic restricts itself to propositions in a subject-predicate form in which the predicate expresses qualities or attributes of a single entity in the subject position. [131] Modern logic, by contrast, also allows reasoning with relations to express how several entities stand to each other. [ 132 ]
In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. [1] The logical equivalence of p {\displaystyle p} and q {\displaystyle q} is sometimes expressed as p ≡ q {\displaystyle p\equiv q} , p :: q {\displaystyle p::q} , E p q {\displaystyle {\textsf {E}}pq} , or p q ...
A model of a theory that satisfies the axioms of the theory but has properties not intended by the original formulation, often revealing the theory's consistency or independence results. normal form In logic, a standardized way of expressing logical formulas, such as conjunctive normal form (CNF) or disjunctive normal form (DNF), to facilitate ...
In logic, converse nonimplication [1] is a logical connective which is the negation of converse implication (equivalently, the negation of the converse of implication). Definition [ edit ]
Semantic completeness is the converse of soundness for formal systems. A formal system is complete with respect to tautologousness or "semantically complete" when all its tautologies are theorems, whereas a formal system is "sound" when all theorems are tautologies (that is, they are semantically valid formulas: formulas that are true under every interpretation of the language of the system ...