By censoring I mean a specific technique for forcing the consistency of a possibly inconsistent set of axioms.
Suppose you have a set of deduction rules D over a language ℓ.
You can construct a function fD:P(ℓ)→P(ℓ) that takes a set of sentences S and outputs all the sentences that can be proved in one step using D and the sentences in S.
You can also construct a censored f′D by letting
f′D(S)={ϕ|ϕ∈fD(S)∧¬ϕ∉S}.
Can you define more precisely what you mean by “censoring contradictions”?
By censoring I mean a specific technique for forcing the consistency of a possibly inconsistent set of axioms.
Suppose you have a set of deduction rules D over a language ℓ. You can construct a function fD:P(ℓ)→P(ℓ) that takes a set of sentences S and outputs all the sentences that can be proved in one step using D and the sentences in S. You can also construct a censored f′D by letting f′D(S)={ϕ | ϕ∈fD(S)∧¬ϕ∉S}.