Linked from

The 31 pages that link to Logical consequence, each with the reason it gives.

• Model theoryRelated: It captures what a theory forces to hold across all its models.

• Propositional logicRelated: It captures when propositional premises guarantee a conclusion under every truth assignment.

• Formal proofRelated: Sound proof rules preserve this relation from premises to conclusion.

• SoundnessRelated: Soundness requires provability to imply this semantic relation.

• TruthRelated: Truth preservation across valid arguments is a central formal use of truth.

• Alfred TarskiRelated: Tarski gave a semantic account connecting consequence to preservation of truth across models.

• Logical equivalenceRelated: Two formulas are equivalent exactly when each is a logical consequence of the other.

• Formal logicRelated: It captures validity independently of any particular proof notation.

• Axiomatic methodRelated: It captures the relation between a theory’s assumptions and what its proofs establish.

• ConclusionRelated: It describes the strict support relation between premises and conclusion.

• Bernard BolzanoRelated: His account of consequence helped make logic an independent subject of systematic study.

• LogicRelated: It captures the central question of whether premises support a conclusion necessarily.

• Conditional proofRelated: The subproof tests whether the antecedent supports the consequent within the system.

• DemonstrationRelated: It captures the necessity connecting a demonstration’s premises to its conclusion.

• Logical formRelated: Consequence captures the truth-preserving relation that valid argument forms share.

• Axiomatic systemRelated: It captures the consequence relation that derivations are intended to represent.

• Disjunctive syllogismRelated: The syllogism is valid because its conclusion is a logical consequence of its premises.

• Affirming the consequentRelated: The premises of affirming the consequent do not logically entail its conclusion.

• Symbolic logicRelated: It states the semantic standard that valid symbolic arguments must preserve.

• Conjunction introductionRelated: The rule preserves this relation from P and Q to P ∧ Q.

• Conjunction eliminationRelated: The rule is sound because either conjunct follows from a true conjunction.

• Deduction theoremRelated: The semantic analogue connects premise-and-assumption consequence to implication.

• Lindenbaum's lemmaRelated: Consistency and maximality are defined relative to a consequence relation or proof system.

• Consequentia mirabilisRelated: The principle's antecedent says that the proposition is a consequence of its own negation.