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Logical consequence (also entailment or implication) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
Entailment contrasts with the pragmatic notion of implicature. While implicatures are fallible inferences, entailments are enforced by lexical meanings plus the laws of logic. [ 3 ] Entailments also differ from presuppositions , whose truth is taken for granted.
An informal fallacy in which a conclusion is not logically justified by sufficient or unbiased evidence; drawing a general conclusion from a too-small sample size. Henkin semantics A generalization of standard first-order semantics that allows for models where the range of quantifiers can be restricted, named after Leon Henkin.
The entailment relation in full CLL is undecidable. [8] When considering fragments of CLL, the decision problem has varying complexity: Multiplicative linear logic (MLL): only the multiplicative connectives. MLL entailment is NP-complete, even restricting to Horn clauses in the purely implicative fragment, [9] or to atom-free formulas. [10]
Logical consequence (or entailment), the relationship between statements that holds true when one logically "follows from" one or more others; Result (or upshot), the final consequence of a sequence of actions or events; Affirmative conclusion from a negative premise, a logical fallacy
Deductive reasoning is the psychological process of drawing deductive inferences.An inference is a set of premises together with a conclusion. This psychological process starts from the premises and reasons to a conclusion based on and supported by these premises.
In natural language, an instance of the paradox of entailment arises: It is raining. And It is not raining. Therefore George Washington is made of rakes. This arises from the principle of explosion, a law of classical logic stating that inconsistent premises always make an argument valid; that is, inconsistent premises imply any conclusion at all.
Conclusion: It's cloudy. The logical form of this argument is known as modus ponens , [ 39 ] which is a classically valid form. [ 40 ] So, in classical logic, the argument is valid , although it may or may not be sound , depending on the meteorological facts in a given context.