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The Polish logician Alfred Tarski identified three features of an adequate characterization of entailment: (1) The logical consequence relation relies on the logical form of the sentences: (2) The relation is a priori, i.e., it can be determined with or without regard to empirical evidence (sense experience); and (3) The logical consequence ...
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.
In propositional logic, material implication [1] [2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- P {\displaystyle P} or Q {\displaystyle Q} and that either form can replace the other in ...
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 ...
An argument is defined as a pair of things, namely a set of sentences, called the premises, [g] and a sentence, called the conclusion. [ 38 ] [ 34 ] [ 37 ] The conclusion is claimed to follow from the premises, [ 37 ] and the premises are claimed to support the conclusion.
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.
Of primary interest in logic is the relation of logical consequence or entailment. This relation holds between the premises of an argument and its conclusion if the argument is governed by a valid rule of inference. It determines what follows logically from what and is present if the truth of the premises ensures the truth of the conclusion.
Grice distinguished conversational implicatures, which arise because speakers are expected to respect general rules of conversation, and conventional ones, which are tied to certain words such as "but" or "therefore". [2] Take for example the following exchange: A (to passerby): I am out of gas. B: There is a gas station 'round the corner.