Idempotency of entailment is a property of logical systems that states that one may derive the same consequences from many instances of a hypothesis as...

for the conclusion. Linear logic, which lacks monotonicity and idempotency of entailment. Contraction Exchange rule Substructural logic No-cloning theorem...

rejects the law of the excluded middle, double negation elimination, and part of De Morgan's laws; Linear logic rejects idempotency of entailment as well; Paraconsistent...

{\displaystyle {\overline {\alpha ,\alpha \vdash \beta }}} Rule of contraction (or idempotency of entailment) (aka no-deleting theorem) α , α , γ ⊢ β _ {\displaystyle...

using resolution. Known as idempotency of entailment in classical logic. Exchange, where two members on the same side of a sequent may be swapped. Symbolically:...

noncontradiction Principle of explosion Monotonicity of entailment Idempotency of entailment Commutativity of conjunction De Morgan duality – every logical operator...

of excluded middle and double negation elimination Law of noncontradiction, and the principle of explosion Monotonicity of entailment and idempotency...

Idée reçue Idempotency of entailment Identity (philosophy) Identity formation Identity of indiscernibles Identity politics Identity theory of mind Identity...

{\displaystyle (a\lor (b\equiv c))\equiv ((a\lor b)\equiv (a\lor c))} Idempotency: a ∨ a ≡ a {\displaystyle a\lor a\equiv a} Monotonicity: ( a → b ) →...

Associativity x ∧ (y ∧ z) = (x ∧ y) ∧ z Commutativity x ∧ y = y ∧ x Idempotency x ∧ x = x A meet-semilattice ⟨ S , ∧ ⟩ {\displaystyle \langle S,\land...

multiplication and addition operations of a field GF(2), and as in any field they obey the distributive law.) Idempotency: no Monotonicity: no Truth-preserving:...

Morgan, and idempotence inferences (for conjunction and disjunction). Furthermore, inconsistency-robust proof of negation holds for entailment: (A⇒(B∧¬B))⊢¬A...

and order (entailment). Both conjunction and disjunction are associative, commutative and idempotent in classical logic, most varieties of many-valued...

the conjunction of its propositions, the succedent as the disjunction of its propositions, and the sequent itself as the entailment of the succedent by...

value of one function of these data given another function of these data does depend on θ, but the very definition of sufficiency given above entails that...

10th edition. Wadsworth Publishing. p. 392. Beth, Evert W.; "Semantic entailment and formal derivability", series: Mededlingen van de Koninklijke Nederlandse...

{\mathcal {I}}}C_{i}\in {\mathfrak {S}}[\mathbf {c} ]} . Notice that, by idempotency [K3], one may succinctly write S [ c ] = im ⁡ ( c ) {\displaystyle {\mathfrak...

tautologies of MTL. The notion of global entailment (or: global consequence) is defined for MTL as follows: a set of formulae Γ entails a formula A (or:...