Karl Popper thought he had solved the problem through his method of falsification, a method that relies on the valid deductive inference-form of modus tollens.

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The inferred conclusion of a valid deductive inference is necessarily true if the premises it is based on are true.

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A relation of inference is monotonic if the addition of premises does not undermine previously reached conclusions; otherwise the relation is nonmonotonic.

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That is, a valid inference does not depend on the truth of the premises and conclusion, but on the formal rules of inference being used.

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Several techniques can be used by that system to extend KB by means of valid inferences.

Inference is the act or process of deriving a conclusion based on what one already knows or on what one assumes.

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John Stuart Mill produced a set of criteria known as "Mill's Methods" for distinguishing between strong and weak inductive inferences.

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The problem of the invalidity of all inductive inferences—often known as the "problem of induction," and also as "Hume's problem"—was first presented in detail by philosopher David Hume (1711-1776).

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A central rule of Bayesian inference is Bayes' theorem, which gave its name to the field.

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By contrast with induction and abduction, a valid deductive inference cannot lead to a false conclusion if the premises are true.

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Greek philosophers defined a number of syllogisms, correct three-part inferences, that can be used as building blocks for more complex reasoning.

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A valid deductive inference (or argument) is one that fits or exhibits a valid argument form.

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Various kinds of defeasible but remarkably successful inference have traditionally captured the attention of philosophers (theories of induction, Peirce’s theory of abduction, inference to the best explanation, etc.).

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The inference is valid because it follows the form of a correct or valid inference, but the inference is unsound—even though the conclusion is true—because at least one of the premises is false.

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Philosophical logic has attempted to define the rules of proper inference, i.e., the formal rules that, when correctly applied to true premises, lead to true conclusions.

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Philosophers and scientists who follow the Bayesian framework for inference use the mathematical rules of probability to find this best explanation.

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