On QBF Proofs and Preprocessing

QBFs (quantified boolean formulas), which are a superset of propositional formulas, provide a canonical representation for PSPACE problems. To overcome the inherent complexity of QBF, significant effort has been invested in developing QBF solvers as well as the underlying proof systems. At the same time, formula preprocessing is crucial for the application of QBF solvers. This paper focuses on a missing link in currently-available technology: How to obtain a certificate (e.g. proof) for a formula that had been preprocessed before it was given to a solver? The paper targets a suite of commonly-used preprocessing techniques and shows how to reconstruct certificates for them. On the negative side, the paper discusses certain limitations of the currently-used proof systems in the light of preprocessing. The presented techniques were implemented and evaluated in the state-of-the-art QBF preprocessor bloqqer.Comment: LPAR 201

A theory of resolution

We review the fundamental resolution-based methods for first-order theorem proving and present them in a uniform framework. We show that these calculi can be viewed as specializations of non-clausal resolution with simplification. Simplification techniques are justified with the help of a rather general notion of redundancy for inferences. As simplification and other techniques for the elimination of redundancy are indispensable for an acceptable behaviour of any practical theorem prover this work is the first uniform treatment of resolution-like techniques in which the avoidance of redundant computations attains the attention it deserves. In many cases our presentation of a resolution method will indicate new ways of how to improve the method over what was known previously. We also give answers to several open problems in the area

Consequence Based Procedure for Description Logics with Self Restriction

We present a consequence based classification procedure for the description logics with self restriction constructor. Due to the difficulty of constructing a concept inclusion model for self restriction, we use a different proof by showing that all the completion rules can simulate all the corresponding ordered resolution inferences

Constitutional Analogies in the International Legal System

This Article explores issues at the frontier of international law and constitutional law. It considers five key structural and systemic challenges that the international legal system now faces: (1) decentralization and disaggregation; (2) normative and institutional hierarchies; (3) compliance and enforcement; (4) exit and escape; and (5) democracy and legitimacy. Each of these issues raises questions of governance, institutional design, and allocation of authority paralleling the questions that domestic legal systems have answered in constitutional terms. For each of these issues, I survey the international legal landscape and consider the salience of potential analogies to domestic constitutions, drawing upon and extending the writings of international legal scholars and international relations theorists. I also offer some preliminary thoughts about why some treaties and institutions, but not others, more readily lend themselves to analysis in constitutional terms. And I distinguish those legal and political issues that may generate useful insights for scholars studying the growing intersections of international and constitutional law from other areas that may be more resistant to constitutional analogies

Justice Scalia\u27s Hat Trick and the Supreme Court\u27s Flawed Understanding of Twenty-First Century Arbitration

In this article, I report on the results of my close examination of more than two dozen opinions the Court has handed down interpreting the FAA--arising primarily from commercial, consumer, employment, or securities disputes--since the beginning of the twenty-first century only fifteen years ago.19 I focus on cases in which the Court was asked to decide a question of arbitrability--whether a claim is arbitrable or whether an agreement to arbitrate is enforceable under FAA section 2. I have concluded that these decisions are built on a narrative of an arbitration process that no longer exists, although it may have existed in the twentieth century when Congress passed the FAA. The Court\u27s antiquated understanding of the process threatens to undermine arbitration as a just alternative dispute resolution (ADR) mechanism. Part I of this article describes the process of arbitration, the law that regulates the process, and how both law and process have evolved from the twentieth to the twenty-first century. Part II zeroes in on three opinions enforcing arbitration agreements challenged by consumers seeking to bring statutory claims as class actions. All three opinions were authored by Justice Scalia in 2011, 2012, and 2013--what I call Scalia\u27s “Hat Trick.” As I see it, Justice Scalia scored three times in the game of arbitration--and corporate counsel were likely cheering on the sidelines as their “goals” were achieved: to suppress consumers\u27 ability to bring individual class actions against companies based on claims arising under federal statutes. Many arbitration scholars have sharply criticized those decisions as anti-consumer or anti-employee, claim suppressing, and at odds with the fundamental right to have a dispute heard in a courtroom. Part III argues that, in the Court\u27s twenty-first-century arbitration cases, when justifying its holdings, the Court assumes without factual basis that arbitration is a one-size-fits-all process that is quick and inexpensive for all disputants who have ultimate control over the procedures. This part demonstrates that the Court\u27s oversimplified and out-of-touch decisions have crafted a legal framework that regulates an arbitration process that largely no longer exists. The article concludes by arguing that the Court\u27s expansion of the FAA improperly rests on an outmoded understanding of the modern arbitration process and fails to recognize the many varieties of arbitration that exist today. Those decisions have led to concerns and criticisms that arbitration is no longer a fair process and have promoted a flight from arbitration. This flight necessarily decreases the range of ADR options that parties have at their disposal and ultimately hurts the values of process pluralism. By setting the record straight, I hope to provide some insights into challenges to the Court\u27s FAA decisions that may still exist and that have the potential to lead to a reinvigoration of many types of arbitration as appealing alternatives to litigation