One way to prove the completeness of this calculus is to observe that it is sufficient to reduce every sentence to a conjunctive normal form i.e., to a conjunction of disjunctions of single letters and their negations.
The general idea is to be able to express a problem's formulation as a set of clauses or, equivalently, as a formula in conjunctive normal form (CNF), that is, as a conjunction of clauses.
As Humberstone points out, it fails for the negation, conjunctions, disjunction fragment of CPL, since in classical propositional logic the Bendall normal form (bnf) of a conjunction of atomic formulas $pp \wedge \osim q)$ is $\osim (p \rightarrow q)$.
A conjunction of them is harder to imagine.
THEATER is a group effort, a conjunction of an idea, a writer and actors, she said.
He's a great writer, but it's a conjunction of luck, talent, and the moment.
A conjunction of unusual circumstances aided the film and television industry.
They are a conjunction of cosmic fantasies, tough realities and dramatic exaggerations.
She says her work arises from a conjunction of humor, language, and emotional difficulty.
We say a formula (phi in mathcal {L}) is in normal form if it is the conjunction of two formulas Ψ∧Γ, where Ψ is the conjunction of 3-clauses over probabilistic assessments in the form P(A i )≥α, in which each assessment is over a different atomic proposition A i, and Γ is a probabilistic assignment P≥1, in which γ is a conjunction of propositional 3-clauses.
