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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 ...
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 ...
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.
Entailment; Equisatisfiability; If and only if; Logical biconditional; Logical equality; ≡ the iff symbol (U+2261 IDENTICAL TO) ∷ the a is to b as c is to d symbol (U+2237 PROPORTION) ⇔ the double struck biconditional (U+21D4 LEFT RIGHT DOUBLE ARROW) ↔ the bidirectional arrow (U+2194 LEFT RIGHT ARROW)
Law of noncontradiction – no proposition can be both true and not true; Paraconsistent logic – a family of logics used to address contradictions; Paradox of entailment – a seeming paradox derived from the principle of explosion; Reductio ad absurdum – concluding that a proposition is false because it produces a contradiction
In logic, the law of non-contradiction (LNC; also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "the house is white" and "the house is not white" are mutually exclusive.
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 the following rules, (/) is exactly like except for having the term wherever has the free variable . Universal Generalization (or Universal Introduction) (/) _Restriction 1: is a variable which does not occur in .