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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.
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.
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.
Textual entailment measures natural language understanding as it asks for a semantic interpretation of the text, and due to its generality remains an active area of research. Many approaches and refinements of approaches have been considered, such as word embedding , logical models, graphical models, rule systems, contextual focusing, and ...
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.
Dec. 26: United States 10, Germany 4. James Hagens had two goals and two assists and Cole Hutson had five assists. Hagens opened the scoring in the first period and put the USA back ahead by two ...
President-elect Donald Trump was sentenced Friday in his New York criminal hush money case. But he has already pledged to appeal.
A system is complete when its proof system can derive every conclusion that is semantically entailed by its premises. In other words, its proof system can lead to any true conclusion, as defined by the semantics. Thus, soundness and completeness together describe a system whose notions of validity and entailment line up perfectly. [103]