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  2. Truth table - Wikipedia

    en.wikipedia.org/wiki/Truth_table

    Then move left to the next column and alternate pairs of T's and F's until you run out of lines. Then continue to the next left-hand column and double the numbers of T's and F's until completed. [5] This method results in truth-tables such as the following table for "P ⊃ (Q ∨ R ⊃ (R ⊃ ¬P))", produced by Stephen Cole Kleene: [7]

  3. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.

  4. 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 is interpreted as material implication, a formula is true unless is true and is false.

  5. 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.

  6. Conditional statement - Wikipedia

    en.wikipedia.org/wiki/Conditional_statement

    A conditional statement may refer to: . A conditional formula in logic and mathematics, which can be interpreted as: Material conditional; Strict conditional; Variably strict conditional

  7. Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Propositional_calculus

    A well-formed formula is any atomic formula, or any formula that can be built up from atomic formulas by means of operator symbols according to the rules of the grammar. The language L {\displaystyle {\mathcal {L}}} , then, is defined either as being identical to its set of well-formed formulas, [ 48 ] or as containing that set (together with ...

  8. Propositional formula - Wikipedia

    en.wikipedia.org/wiki/Propositional_formula

    In propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, [1] or a sentential formula.

  9. Conditioned disjunction - Wikipedia

    en.wikipedia.org/wiki/Conditioned_disjunction

    In words, [p, q, r] is equivalent to: "if q, then p, else r", or "p or r, according as q or not q". This may also be stated as "q implies p, and not q implies r". So, for any values of p, q, and r, the value of [p, q, r] is the value of p when q is true, and is the value of r otherwise. The conditioned disjunction is also equivalent to