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The converse may or may not be true, and even if true, the proof may be difficult. For example, the four-vertex theorem was proved in 1912, but its converse was proved only in 1997. [3] In practice, when determining the converse of a mathematical theorem, aspects of the antecedent may be taken as establishing context.
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 ...
In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent inverted and flipped.
A paradox in logic that arises when considering a statement that asserts its own unprovability, leading to contradictions in certain systems of formal logic. cut In proof theory, a rule or step in a deductive proof that introduces an intermediate conclusion, which is later used to derive further conclusions. cut elimination
Computational logic is the branch of logic and computer science that studies how to implement mathematical reasoning and logical formalisms using computers. This includes, for example, automatic theorem provers , which employ rules of inference to construct a proof step by step from a set of premises to the intended conclusion without human ...
Using minimal logic, a logic with similar axioms to classical logic but without ex falso quodlibet and proof by contradiction, we can investigate the axiomatic strength and properties of various rules that treat contradiction by considering theorems of classical logic that are not theorems of minimal logic. [6]
Logical truths are thought to be the simplest case of statements which are analytically true (or in other words, true by definition). All of philosophical logic can be thought of as providing accounts of the nature of logical truth, as well as logical consequence. [1] Logical truths are generally considered to be necessarily true. This is to ...
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 .