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A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises ...
Logical reasoning happens by inferring a conclusion from a set of premises. [3] Premises and conclusions are normally seen as propositions . A proposition is a statement that makes a claim about what is the case.
In logical argument and mathematical proof, the therefore sign, ∴, is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read therefore. While it is not generally used in formal writing, it is used in mathematics and shorthand.
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
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 ...
A way of writing mathematical and logical expressions where the operator precedes its operands, facilitating unambiguous interpretation without parentheses. prelinearity axiom The formula (P → Q) ∨ (Q → P). [237] [238] premise A statement in an argument that provides support or evidence for the conclusion. prenex normal form
It is possible for deductive reasoning conclusions to be inaccurate or incorrect entirely, but the reasoning and premise is logical. For example, ‘All bald men are grandfathers. Harold is bald. Therefore, Harold is a grandfather.’ is a valid and logical conclusion but it is not true as the original assumption is incorrect. [12]
Argumentation theory is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning. With historical origins in logic , dialectic , and rhetoric , argumentation theory includes the arts and sciences of civil debate, dialogue , conversation , and persuasion .