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  2. Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Propositional_calculus

    It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [4] [1] or sometimes zeroth-order logic. [ b ] [ 6 ] [ 7 ] [ 8 ] Sometimes, it is called first-order propositional logic [ 9 ] to contrast it with System F , but it should not be confused with first-order logic .

  3. List of valid argument forms - Wikipedia

    en.wikipedia.org/wiki/List_of_valid_argument_forms

    In syllogistic logic, there are 256 possible ways to construct categorical syllogisms using the A, E, I, and O statement forms in the square of opposition. Of the 256, only 24 are valid forms. Of the 24 valid forms, 15 are unconditionally valid, and 9 are conditionally valid.

  4. List of axiomatic systems in logic - Wikipedia

    en.wikipedia.org/wiki/List_of_axiomatic_systems...

    Classical propositional calculus is the standard propositional logic. Its intended semantics is bivalent and its main property is that it is strongly complete, otherwise said that whenever a formula semantically follows from a set of premises, it also follows from that set syntactically. Many different equivalent complete axiom systems have ...

  5. Exportation (logic) - Wikipedia

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

    Print/export Download as PDF; Printable version; ... Import-export is a name given to the statement as a theorem or truth-functional tautology of propositional logic

  6. Logic - Wikipedia

    en.wikipedia.org/wiki/Logic

    Unlike predicate logic where terms and predicates are the smallest units, propositional logic takes full propositions with truth values as its most basic component. [121] Thus, propositional logics can only represent logical relationships that arise from the way complex propositions are built from simpler ones.

  7. 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.

  8. 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-or and that either form can replace the other in logical proofs.

  9. Bernays–Schönfinkel class - Wikipedia

    en.wikipedia.org/wiki/Bernays–Schönfinkel_class

    Ramsey proved that, if is a formula in the Bernays–Schönfinkel class with one free variable, then either {: ()} is finite, or {: ()} is finite. [ 1 ] This class of logic formulas is also sometimes referred as effectively propositional ( EPR ) since it can be effectively translated into propositional logic formulas by a process of grounding ...