Monotonicity of entailment

Entailment is monotonic when every conclusion that follows from a set of premises still follows after additional premises are added.

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Logical consequence: A relation in which a conclusion holds whenever its premises hold under the relevant interpretation. Monotonicity describes how this relation behaves as its premise set grows.
Nonmonotonic logic: A family of logical systems in which adding premises can invalidate earlier conclusions. It rejects the defining preservation property of monotonic entailment.
Classical logic: The standard bivalent logic governed by classical truth-functional connectives and quantifiers. Its semantic entailment is monotonic: added premises cannot remove an existing consequence.
Premise: A proposition assumed or asserted as support for a conclusion. Monotonicity compares entailment from one premise set with entailment from a larger one.
Tarskian consequence operator: An operator mapping sets of sentences to all sentences that follow from them, subject to structural conditions. Its extensiveness and monotonicity express entailment’s preservation under added premises.
Default logic: A formalism for drawing tentative conclusions when information does not rule them out. A new premise can defeat a default conclusion, making its consequence relation nonmonotonic.
Database query: A request for information evaluated against a database, often expressed in a formal query language. Queries based on positive relational facts commonly preserve answers when database facts are added.
Entailment: A relation in which premises guarantee a conclusion according to a logic’s rules or semantics. Monotonicity is a structural property of this relation, not of any single conclusion.
Model theory: The study of mathematical structures that satisfy formal languages and theories. In classical semantics, adding premises restricts the models, preserving truths shared by the original models.
Defeasible reasoning: Reasoning with conclusions that may be withdrawn when relevant counterinformation appears. Its revisable conclusions contrast with entailments preserved under every premise extension.