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  2. Logical consequence - Wikipedia

    en.wikipedia.org/wiki/Logical_consequence

    Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. [1] A sentence is said to be a logical consequence of a set of sentences, for a given language , if and only if , using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must ...

  3. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    material conditional (material implication) implies, if P then Q, it is not the case that P and not Q propositional logic, Boolean algebra, Heyting algebra: is false when A is true and B is false but true otherwise. may mean the same as

  4. 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 ...

  5. List of rules of inference - Wikipedia

    en.wikipedia.org/wiki/List_of_rules_of_inference

    13, then/if, Converse implication; 14, OR, Logical disjunction; 15, true, Tautology. Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples:

  6. Paradoxes of material implication - Wikipedia

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

    In this example there is no possible situation in which the premises are true while the conclusion is false. Since there is no counterexample, the argument is valid. But one could construct an argument in which the premises are inconsistent.

  7. Material conditional - Wikipedia

    en.wikipedia.org/wiki/Material_conditional

    Material implication does not closely match the usage of conditional sentences in natural language. For example, even though material conditionals with false antecedents are vacuously true, the natural language statement "If 8 is odd, then 3 is prime" is typically judged false. Similarly, any material conditional with a true consequent is ...

  8. Implicature - Wikipedia

    en.wikipedia.org/wiki/Implicature

    An example of a conventional implicature is "Donovan is poor but happy", where the word "but" implicates a sense of contrast between being poor and being happy. [ 7 ] Later linguists introduced refined and different definitions of the term, leading to somewhat different ideas about which parts of the information conveyed by an utterance are ...

  9. Modus tollens - Wikipedia

    en.wikipedia.org/wiki/Modus_tollens

    Every use of modus tollens can be converted to a use of modus ponens and one use of transposition to the premise which is a material implication. For example: If P, then Q. (premise – material implication) If not Q, then not P. (derived by transposition) Not Q. (premise) Therefore, not P. (derived by modus ponens)

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