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  2. Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Propositional_calculus

    Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-order logic.

  3. Commutativity of conjunction - Wikipedia

    en.wikipedia.org/wiki/Commutativity_of_conjunction

    In propositional logic, the commutativity of conjunction is a valid argument form and truth-functional tautology. It is considered to be a law of classical logic. It is the principle that the conjuncts of a logical conjunction may switch places with each other, while preserving the truth-value of the resulting proposition. [1]

  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. Category:Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Category:Propositional...

    Propositional logic (also referred to as Sentential logic) refers to a form of logic in which formulae known as "sentences" can be formed by combining other simpler sentences using logical connectives, and a system of formal proof rules allows certain formulae to be established as theorems.

  6. Hintikka set - Wikipedia

    en.wikipedia.org/wiki/Hintikka_set

    In mathematical logic, a Hintikka set is a set of logical formulas whose elements satisfy the following properties: An atom or its conjugate can appear in the set but not both, If a formula in the set has a main operator that is of "conjuctive-type", then its two operands appear in the set,

  7. Exportation (logic) - Wikipedia

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

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

  8. Intuitionistic logic - Wikipedia

    en.wikipedia.org/wiki/Intuitionistic_logic

    As shown by Alexander V. Kuznetsov, either of the following connectives – the first one ternary, the second one quinary – is by itself functionally complete: either one can serve the role of a sole sufficient operator for intuitionistic propositional logic, thus forming an analog of the Sheffer stroke from classical propositional logic: [6]

  9. Tautological consequence - Wikipedia

    en.wikipedia.org/wiki/Tautological_consequence

    Tautological consequence can also be defined as ∧ ∧ ... ∧ → is a substitution instance of a tautology, with the same effect. [2]It follows from the definition that if a proposition p is a contradiction then p tautologically implies every proposition, because there is no truth valuation that causes p to be true and so the definition of tautological implication is trivially satisfied.