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A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises ...
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
Linguistic entailments are entailments which arise in natural language.If a sentence A entails a sentence B, sentence A cannot be true without B being true as well. [1] For instance, the English sentence "Pat is a fluffy cat" entails the sentence "Pat is a cat" since one cannot be a fluffy cat without being a cat.
The comma can be left out without changing the meaning. There are several variations of this sentence pattern, although they do not work as smoothly as the original. Dutch language shares this same example, with the noticeable difference of not capitalising the initials of nouns, making it " Als achter vliegen vliegen vliegen, vliegen vliegen ...
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.
The task of paraphrasing involves recognizing when two texts have the same meaning and creating a similar or shorter text that conveys almost the same information. Textual entailment is similar [6] but weakens the relationship to be unidirectional. Mathematical solutions to establish textual entailment can be based on the directional property ...
Some logicians define valid inference or entailment in terms of logical necessity: the premises entail the conclusion if it is impossible for the premises to be true and the conclusion to be false. [17] This can also be expressed by saying that the conjunction of the premises and the negation of the conclusion is logically impossible.
In this case, the conclusion contradicts the deductive logic of the preceding premises, rather than deriving from it. Therefore, the argument is logically 'invalid', even though the conclusion could be considered 'true' in general terms. The premise 'All men are immortal' would likewise be deemed false outside of the framework of classical logic.