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Conditional disjunction information


In logic, the term conditional disjunction can refer to:

  • conditioned disjunction, a ternary logical connective introduced by Alonzo Church
  • a rule in classical logic that the material conditional ¬pq is equivalent to the disjunction pq, so that these two formulae are interchangeable - see Negation

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Conditional disjunction

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In logic, the term conditional disjunction can refer to: conditioned disjunction, a ternary logical connective introduced by Alonzo Church a rule in classical...

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Logical connective

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negation and contradiction for more). Neither conjunction, disjunction, nor material conditional has an equivalent form constructed from the other four logical...

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Ternary conditional operator

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computer programming, the ternary conditional operator is a ternary operator that is part of the syntax for basic conditional expressions in several programming...

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Material conditional

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propositional theorem, but the material conditional is used to define negation.[clarification needed] When disjunction, conjunction and negation are classical...

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Exclusive or

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biconditional, by the rules of material implication (a material conditional is equivalent to the disjunction of the negation of its antecedent and its consequence)...

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Conditional proof

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A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to...

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Conditioned disjunction

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In logic, conditioned disjunction (sometimes called conditional disjunction) is a ternary logical connective introduced by Church. Given operands p, q...

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Stoic logic

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dispute. [c] These five indemonstrable arguments are made up of conditional, disjunction, and negation conjunction connectives, and all other arguments...

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Hypothetical syllogism

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hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises. Ancient references point to...

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Index of logic articles

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Conceptualism -- Condensed detachment -- Conditional disjunction -- Conditional probability -- Conditional proof -- Conditional quantifier -- Confirmation bias...

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Paul Grice

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might appear one could make these deductions by contraposition and conditional disjunction: ([a] from [ii]) If Yog was white, then 1/2 of the time Yog won...

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Conditional event algebra

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operations and, or, and not. A conditional event algebra (CEA) contains not just ordinary events but also conditional events, which have the form "if...

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Truth table

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addition, and as logically equivalent to the exclusive-or (exclusive disjunction) binary logic operation. In this case it can be used for only very simple...

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Relevance logic

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negation, this section will consider only languages with a conditional, conjunction, and disjunction. An operational frame F {\displaystyle F} is a triple...

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Simplification of disjunctive antecedents

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(SDA) is the phenomenon whereby a disjunction in the antecedent of a conditional appears to distribute over the conditional as a whole. This inference is...

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Necessity and sufficiency

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terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If P then Q",...

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XOR gate

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The two leftmost transistors mentioned above, perform an optimized conditional inversion of A when B is at a logic high using pass transistor logic...

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Boolean algebra

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algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and the negation (not) denoted as ¬. Elementary algebra...

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Paraconsistent logic

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disjunction introduction but keep disjunctive syllogism and transitivity. In this approach, rules of natural deduction hold, except for disjunction introduction...

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List of rules of inference

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11, if/then, Material conditional; 12, p, Projection function; 13, then/if, Converse implication; 14, OR, Logical disjunction; 15, true, Tautology. Each...

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Modus tollens

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premise is a conditional ("if-then") claim, such as P implies Q. The second premise is an assertion that Q, the consequent of the conditional claim, is not...

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List of Boolean algebra topics

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Conditioned disjunction Evasive Boolean function Exclusive or Functional completeness Logical biconditional Logical conjunction Logical disjunction Logical...

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Barbershop paradox

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.." entirely (reducing to disjunctions), so no protasis and apodosis exist and no counter-argument is needed. Conditional sentences in English Crocodile...

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Disjunctive syllogism

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three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q" is a disjunction, where P and Q are called the statement's...

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Functional completeness

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{\displaystyle \land } ); disjunction ( ∨ {\displaystyle \lor } ); negation ( ¬ {\displaystyle \neg } ); material conditional ( → {\displaystyle \to }...

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Modus ponens

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premise is a conditional ("if–then") claim, namely that P implies Q. The second premise is an assertion that P, the antecedent of the conditional claim, is...

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