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Deductive reasoning. Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and " Socrates is a man" to ...
Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an argument. A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following ...
Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q. Not Q. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument.
A Mastermind player uses abduction to infer the secret colors (top) from summaries (bottom left) of discrepancies in their guesses (bottom right). Abductive reasoning (also called abduction, [1] abductive inference, [1] or retroduction[2]) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations.
Deduction theorem. In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly axiomatize that hypothesis, i.e. to prove an implication A → B, it is sufficient to assume A as a hypothesis and then proceed to derive B. Deduction theorems exist for both ...
Contraposition. 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.
Syllogism. A syllogism (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. "Socrates" at the Louvre. In its earliest form (defined by Aristotle in his 350 BC book Prior ...
Additionally, the term 'inference' has also been applied to the process of generating predictions from trained neural networks. In this context, an 'inference engine' refers to the system or hardware performing these operations. This type of inference is widely used in applications ranging from image recognition to natural language processing.