The system, following Frege, is based on implication $C $$ and negation $N $$ alone, with the elegant axiom set and three rules of inference: modus ponens, a rule of uniform substitution of formulas for propositional variables, and a rule of definitional replacement.
For a taste of what they can do, notice that they yield a succinct justification of a rule of Uniform Substitution, whereby a formula of the form $A(B/p)$ is a theorem whenever $A$ is a theorem, provided that $B$ is free for $p$ in $A$.
We conclude that in many cases the simple first-best rule of uniform emission pricing remains a practical guideline for unilateral climate policy design.
This permits the reintroduction of the rule of Uniform Substitution.
Hence, Lewis's rule of Uniform Substitution fails (if p∧¬p is substituted for p in ◊p we derive ◊(p∧¬p), which is L-false, not L-true).
Rules of uniform substitution for predicate calculi, though formulable, are mostly very complicated, and, to avoid the necessity for these rules, axioms for these systems are therefore usually given by axiom schemata in the sense explained earlier (see above Axiomatization of PC).
There is a position - not at all unfamiliar in contemporary discussion - which says that to be a citizen is essentially and simply to be under the rule of the uniform law of a sovereign state, in such a way that any other relations, commitments or protocols of behaviour belong exclusively to the realm of the private and of individual choice.
It does mean that the Fed, as the agency primarily responsible for insuring financial stability, should issue a set of uniform rules for Wall Street compensation.
A relaxation of uniform rules for the sport, allowing women to cover-up more, has been introduced for the first time for the London Olympics, but top players say they'll be sticking to their bikinis.
A uniform rule of disclosure of political contributions in corporate proxy statements once a year or through some other means would help shareholders assess the profitability of a company's political activities and protect democracy from the flood of money unleashed by the Citizens United decision.
Congress also has power, under Article I, Section 8 of the Constitution, to establish "a uniform Rule of Naturalization" -- but this provision would seem not applicable in terms of defining who exactly is automatically a citizen by virtue of being "born" here rather than being "naturalized" under congressional rule.
