Logical consequence  

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Logical consequence is a fundamental concept in logic. It is the relation that holds between a set of sentences (or propositions) and a sentence (proposition) when the former "entails" the latter. For example, 'Kermit is green' is said to be a logical consequence of 'All frogs are green' and 'Kermit is a frog', because it would be "self-contradictory" to affirm the latter and deny the former. Logical consequence is the relationship between the premises and the conclusion of a valid argument. These explanations and definitions tend to be circular; the provision of a satisfactory account of logical consequence and entailment is an important topic of philosophy of logic.

The truth of the above consequence depends on both the truth of the antecedents and the relationship of logical consequence between the antecedents and the consequence. The consequence might NOT be true if not all frogs were green. Logical consequences or inferences by deductive reasoning are a major aspect of epistemology that communicates to the general public hypotheses about causality of risk factors.

A formally specified logical consequence relation may be characterized model-theoretically or proof-theoretically (or both).

Logical consequence can also be expressed as a function from sets of sentences to sets of sentences (Tarski's preferred formulation), or as a relation between two sets of sentences (multiple-conclusion logic).

See also

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