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Jape supports human-directed discovery of proofs in a logic which is defined by the user as a system of inference rules. It maps the user's gestures (e.g. typing, mouse-clicks or mouse-drags) to the assistant's proof actions.
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 .
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 ...
It is to be regretted that this first comprehensive and thorough-going presentation of a mathematical logic and the derivation of mathematics from it [is] so greatly lacking in formal precision in the foundations (contained in 1– 21 of Principia [i.e., sections 1– 5 (propositional logic), 8–14 (predicate logic with identity/equality), 20 ...
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- P {\displaystyle P} or Q {\displaystyle Q} and that either form can replace the other in ...
Due to the ability to speak about non-logical individuals along with the original logical connectives, first-order logic includes propositional logic. [7]: 29–30 The truth of a formula such as "x is a philosopher" depends on which object is denoted by x and on the interpretation of the predicate "is a philosopher".
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,
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