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  2. Material conditional - Wikipedia

    en.wikipedia.org/wiki/Material_conditional

    The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol → {\displaystyle \rightarrow } is interpreted as material implication, a formula P → Q {\displaystyle P\rightarrow Q} is true unless P {\displaystyle P} is true and Q {\displaystyle Q} is false.

  3. Material implication (rule of inference) - Wikipedia

    en.wikipedia.org/wiki/Material_implication_(rule...

    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 ...

  4. Paradoxes of material implication - Wikipedia

    en.wikipedia.org/wiki/Paradoxes_of_material...

    A material conditional formula is true unless is true and is false. If natural language conditionals were understood in the same way, that would mean that the sentence "If the Nazis had won World War Two, everybody would be happy" is vacuously true .

  5. Material implication - Wikipedia

    en.wikipedia.org/wiki/Material_implication

    Material implication may refer to: Material conditional , a logical connective Material implication (rule of inference) , a rule of replacement for some propositional logic

  6. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    Corner quotes, also called “Quine quotes”; for quasi-quotation, i.e. quoting specific context of unspecified (“variable”) expressions; [4] also used for denoting Gödel number; [5] for example “⌜G⌝” denotes the Gödel number of G. (Typographical note: although the quotes appears as a “pair” in unicode (231C and 231D), they ...

  7. Strict conditional - Wikipedia

    en.wikipedia.org/wiki/Strict_conditional

    In logic, a strict conditional (symbol: , or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic , combined with the necessity operator from modal logic .

  8. Material inference - Wikipedia

    en.wikipedia.org/wiki/Material_inference

    Material inference should not be confused with the following concepts, which refer to formal, not material validity: Material conditional — the logical connective "→" (i.e. "formally implies") Material implication (rule of inference) — a rule for formally replacing "→" by "¬" (negation) and "∨" (disjunction)

  9. Logical connective - Wikipedia

    en.wikipedia.org/wiki/Logical_connective

    One approach is to choose a minimal set, and define other connectives by some logical form, as in the example with the material conditional above. The following are the minimal functionally complete sets of operators in classical logic whose arities do not exceed 2: