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2. Three-valued logic - Wikipedia

   en.wikipedia.org/wiki/Three-valued_logic

   In these truth tables, the unknown state can be thought of as neither true nor false in Kleene logic, or thought of as both true and false in Priest logic. The difference lies in the definition of tautologies. Where Kleene logic's only designated truth value is T, Priest logic's designated truth values are both T and U.

3. Validity (logic) - Wikipedia

   en.wikipedia.org/wiki/Validity_(logic)

   Validity of deduction is not affected by the truth of the premise or the truth of the conclusion. The following deduction is perfectly valid: All animals live on Mars. (False) All humans are animals. (True) Therefore, all humans live on Mars. (False) The problem with the argument is that it is not sound.

4. List of valid argument forms - Wikipedia

   en.wikipedia.org/wiki/List_of_valid_argument_forms

   It is, however, slightly more complicated than the first two. In short, it states that if one thing happens, another will as well. If that second thing happens, a third will follow it. Therefore, if the first thing happens, it is inevitable that the third will too. [3] It is shown below in logical form. If A, then B If B, then C Therefore if A ...

5. Truth table - Wikipedia

   en.wikipedia.org/wiki/Truth_table

   A truth table is a structured representation that presents all possible combinations of truth values for the input variables of a Boolean function and their corresponding output values. A function f from A to F is a special relation , a subset of A×F, which simply means that f can be listed as a list of input-output pairs.

6. Tautology (logic) - Wikipedia

   en.wikipedia.org/wiki/Tautology_(logic)

   The method of truth tables illustrated above is provably correct – the truth table for a tautology will end in a column with only T, while the truth table for a sentence that is not a tautology will contain a row whose final column is F, and the valuation corresponding to that row is a valuation that does not satisfy the sentence being tested.

7. Propositional calculus - Wikipedia

   en.wikipedia.org/wiki/Propositional_calculus

   A truth table is a semantic proof method used to determine the truth value of a propositional logic expression in every possible scenario. [93] By exhaustively listing the truth values of its constituent atoms, a truth table can show whether a proposition is true, false, tautological, or contradictory. [94] See § Semantic proof via truth tables.

8. Proof by contradiction - Wikipedia

   en.wikipedia.org/wiki/Proof_by_contradiction

   In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally ...

9. List of rules of inference - Wikipedia

   en.wikipedia.org/wiki/List_of_rules_of_inference

   The column-11 operator (IF/THEN), shows Modus ponens rule: when p→q=T and p=T only one line of the truth table (the first) satisfies these two conditions. On this line, q is also true. Therefore, whenever p → q is true and p is true, q must also be true.