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A rule of inference is a way or schema of drawing a conclusion from a set of premises. [17] This happens usually based only on the logical form of the premises. A rule of inference is valid if, when applied to true premises, the conclusion cannot be false. A particular argument is valid if it follows a valid rule of inference.
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.
Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BCE). Deduction is inference deriving logical conclusions from premises known or assumed to be true , with the laws of valid inference being studied in logic .
An argument map with 'modus ponens' in the inference box. An inference can be the target of an objection. Such inference objections highlight invalid or weak inferences. [12] [13] In the diagram below, B is the premise, A is the conclusion, and C is an objection to the inference from A to B. Argument map of an inference objection.
In a Hilbert system, the premises and conclusion of the inference rules are simply formulae of some language, usually employing metavariables.For graphical compactness of the presentation and to emphasize the distinction between axioms and rules of inference, this section uses the sequent notation instead of a vertical presentation of rules.
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.
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Most experimentation on deduction has been carried out on hypothetical thought, in particular, examining how people reason about conditionals, e.g., If A then B. [3] Participants in experiments make the modus ponens inference, given the indicative conditional If A then B, and given the premise A, they conclude B.