Logic

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10 domain-specific abstractions whose origin domain is Logic.

• Conjunction Introduction — The proof rule that combines derivations of A and B available in a common context into a derivation of their conjunction A ∧ B.
• Extensionality — The principle that objects of a given kind are equal when they have the same externally observable members, values or behavior, as formalized for sets, functions and relations.
• Formation rule — A syntactic rule that recursively determines which symbol strings or expressions are well formed in a formal language, independently of their meaning or truth.
• Free variables and bound variables — The distinction between variable occurrences whose values are supplied by an external assignment and occurrences captured by a quantifier, lambda or other binder within an expression.
• Interpretation (logic) — An assignment of denotations to the nonlogical symbols of a formal language over a domain, determining the truth or satisfaction of its formulas.
• Logical connective — A formal operator that forms a compound formula from one or more formulas and whose semantics determines the compound's truth or satisfaction from its arguments.
• Logical form — A precise formal-semantic representation of a statement or argument that exposes the structure relevant to validity and interpretation.
• Monotonicity of entailment — A logical property whereby every conclusion entailed by a premise set remains entailed after any additional premises are added.
• Paraconsistent logic — A logic whose consequence relation does not validate explosion, allowing some contradictions without every proposition becoming derivable.
• Rule of replacement — Rewrite a designated subformula with a logically equivalent expression inside a larger propositional formula while preserving the whole formula's truth conditions.