We present locally complete inference rules for probabilistic deduction from taxonomic and probabilistic knowledge-bases over conjunctive events. Crucially, in contrast to similar inference rules in the literature, our inference rules are locally complete for conjunctive events and under additional taxonomic knowledge. We discover that our inference rules are extremely complex and that it is at first glance not clear at all where the deduced tightest bounds come from. Moreover, analyzing the global completeness of our inference rules, we find examples of globally very incomplete probabilistic deductions. More generally, we even show that all systems of inference rules for taxonomic and probabilistic knowledge-bases over conjunctive events are globally incomplete. We conclude that probabilistic deduction by the iterative application of inference rules on interval restrictions for conditional probabilities, even though considered very promising in the literature so far, seems very limited in its field of application.
But the GOP framework didn't include this provision just as an aside that it could take or leave. Even partially restoring the SALT deduction would eliminate a central way to raise revenue for a framework that's short on that. The SALT deduction is estimated to be worth about $1.3 trillion in revenue over the 10-year budgeting window, money that's needed to cover the rate cuts the GOP envisions elsewhere. The SALT deduction elimination isn't an island, either: It's deeply connected to other ideas within the framework. Restoring this deduction would hamper both the legislative efforts' delicate balance sheet and the very idea behind the effort of simplifying the tax code.
Ryan was defending the new Republican tax proposal to eliminate the popular state-local tax deduction, a move that's angered GOP lawmakers from those states and made them balk at supporting the tax plan. The deduction is claimed by around 44 million people and costs the government an estimated $1.3 trillion in lost revenue over 10 years.
We study the problem of probabilistic deduction with conditional constraints over basic events. We show that globally complete probabilistic deduction with conditional constraints over basic events is NP-hard. We then concentrate on the special case of probabilistic deduction in conditional constraint trees. We elaborate very efficient techniques for globally complete probabilistic deduction. In detail, for conditional constraint trees with point probabilities, we present a local approach to globally complete probabilistic deduction, which runs in linear time in the size of the conditional constraint trees. For conditional constraint trees with interval probabilities, we show that globally complete probabilistic deduction can be done in a global approach by solving nonlinear programs. We show how these nonlinear programs can be transformed into equivalent linear programs, which are solvable in polynomial time in the size of the conditional constraint trees.
To the editor: Harold Meyerson's view of the tax plan proposed by President Trump and Republican leaders in Congress is curiously slanted. As an income and wealth redistributor, he should be happy that the new tax plan will severely impact the wealthy in California. Since the richest 1% of Californians pay nearly half the income taxes and the top 10% pay about 80%, it's mostly the wealthy who benefit from the federal deduction for taxes paid to state and local governments, known as the SALT deduction. Most middle-class taxpayers in California will likely see a decrease in taxes under the Republican plan. The increased federal tax revenue from wealthy Californians will be redistributed to the many other states that have lower rates.