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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.
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]
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 ...
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.
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,
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]
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
Quantum logic has been proposed as the correct logic for propositional inference generally, most notably by the philosopher Hilary Putnam, at least at one point in his career. This thesis was an important ingredient in Putnam's 1968 paper " Is Logic Empirical? " in which he analysed the epistemological status of the rules of propositional logic.