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  2. Corollary - Wikipedia

    en.wikipedia.org/wiki/Corollary

    In mathematics, a corollary is a theorem connected by a short proof to an existing theorem. The use of the term corollary, rather than proposition or theorem, is intrinsically subjective. More formally, proposition B is a corollary of proposition A, if B can be readily deduced from A or is self-evident from its proof.

  3. Proposition - Wikipedia

    en.wikipedia.org/wiki/Proposition

    Two meaningful declarative sentences express the same proposition, if and only if they mean the same thing. [citation needed] which defines proposition in terms of synonymity. For example, "Snow is white" (in English) and "Schnee ist weiß" (in German) are different sentences, but they say the same thing, so they express the same proposition.

  4. Logical reasoning - Wikipedia

    en.wikipedia.org/wiki/Logical_reasoning

    A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water is boiling." expresses a proposition since it can be true or false. The sentences "Is the water boiling?"

  5. Entailment (linguistics) - Wikipedia

    en.wikipedia.org/wiki/Entailment_(linguistics)

    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. On the other hand, this sentence does not entail "Pat chases mice" since it is possible (if unlikely ...

  6. Sentence function - Wikipedia

    en.wikipedia.org/wiki/Sentence_function

    The declarative sentence is the most common kind of sentence in language, in most situations, and in a way can be considered the default function of a sentence. What this means essentially is that when a language modifies a sentence in order to form a question or give a command, the base form will always be the declarative.

  7. Glossary of logic - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_logic

    corollary A proposition that follows directly from another proposition or theorem with little or no additional proof. correspondence theory of truth The philosophical doctrine that the truth or falsity of a statement is determined by how it relates to the world and whether it accurately describes (corresponds with) that world. counterexample 1.

  8. Propositional formula - Wikipedia

    en.wikipedia.org/wiki/Propositional_formula

    The predicate calculus goes a step further than the propositional calculus to an "analysis of the inner structure of propositions" [4] It breaks a simple sentence down into two parts (i) its subject (the object (singular or plural) of discourse) and (ii) a predicate (a verb or possibly verb-clause that asserts a quality or attribute of the object(s)).

  9. Square of opposition - Wikipedia

    en.wikipedia.org/wiki/Square_of_opposition

    A categorical proposition is a simple proposition containing two terms, subject (S) and predicate (P), in which the predicate is either asserted or denied of the subject. Every categorical proposition can be reduced to one of four logical forms , named A , E , I , and O based on the Latin a ff i rmo (I affirm), for the affirmative propositions ...