Hierarchic Superposition Revisited

Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory

Hierarchic Superposition Revisited

Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory

Spectral theorem for the Lindblad equation for quadratic open fermionic systems

The spectral theorem is proven for the quantum dynamics of quadratic open systems of n fermions described by the Lindblad equation. Invariant eigenspaces of the many-body Liouvillean dynamics and their largest Jordan blocks are explicitly constructed for all eigenvalues. For eigenvalue zero we describe an algebraic procedure for constructing (possibly higher dimensional) spaces of (degenerate) non-equilibrium steady states.Comment: 19 pages, no figure

Scavenger 0.1: A Theorem Prover Based on Conflict Resolution

This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a first-order generalization of) unit propagation as well as a rule for assuming decision literals and a rule for deriving new clauses by (a first-order generalization of) conflict-driven clause learning.Comment: Published at CADE 201

Switzerland

Switzerland has the traditional Austro-German representative association procedures. Debate on adoption of other models, given the opportunity of the introduction of a first federal Code of Civil Procedure, reveals considerable cautious conservatism toward reform

Human Rights and Civil Litigation in United States Courts: The Holocaust-Era Cases

Human rights are a serious matter. Unfortunately, in spite of half a century of improving the civil rights of individuals through treaties and customary international law, and despite increasing attention to those rights by both governments and scholars of international law and international relations, much remains to be done to prevent and punish even the most egregious violations of human dignity. Professor Neuborne\u27s Article and the extensive briefs to which he repeatedly refers recap the atrocities committed by the German Nazi regime and ask uneasy but necessary questions about the Nazi regime\u27s accomplices and their responsibility for what transpired in the death camps of Eastern Europe some sixty years ago. It invites one so inclined both to analyze some of the more controversial issues of class action litigation--particularly settlement--as well as the role of civil litigation in the U.S. courts within transnational society. This article examines the role of civil litigation in American courts for purposes of enforcing international human rights law and the way in which such litigation affects the conduct of transnational procedure in general