A Strong Completeness Theorem for the Gentzen systems associated with finite algebras
ABSTRACT In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case of the finite linear MV-algebras, the Strong Completeness Theorem was proved in [10], as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems.
Fourth Workshop on the Implementation of Logics
Most published papers on implementation aspects of automated reasoning systems cover only a small set of new techniques. Overview papers are rare, and usually describe the fixed state of a system at a given point in the development process. Moreover, they often have to trade depth for generality. This is particularly true for system descriptions, which often are relegated to second-class status and allowed only a view pages at many major conferences. In my talk, I will try to shed some lights into the practical aspects of building a complex high-performance theorem prover. I will give an overview on our equational theorem prover E [Sch02]. However, instead of giving a purely static view, I will describe the process that has resulted in a useful and resilient code base which has, up to now, survived at least three major changes without serious problems. I will also discuss some of the design decisions that later turned out to be wrong, and how they have either been fixed or still burden us. Finally, I will describe some of the engineering tricks and tools we use to make sure that our code remains stable, mostly bug free, and, most of all, maintainable.
LYAPUNOV-BASED TRANSFER BETWEEN ELLIPTIC KEPLERIAN ORBITS
We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (- Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that the target elliptic orbit becomes a locally asymptotically stable periodic orbit in the closed-loop dynamics. We show how to perform a global transfer between two arbitrary elliptic orbits based on the local transfer result. Finally, a second Lyapunov function is presented that works only for circular target orbits.