First-Order Logic Theorem Proving and Model Building via Approximation and Instantiation

In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The approximation extends the signature and preserves unsatisfiability: if the simplified clause set is satisfiable in some model, so is the original clause set in the same model interpreted in the original signature. A refutation generated by a decision procedure on the simplified clause set can then either be lifted to a refutation in the original clause set, or it guides a refinement excluding the previously found unliftable refutation. This way the approach is refutationally complete. We do not step-wise lift refutations but conflicting cores, finite unsatisfiable clause sets representing at least one refutation. The approach is dual to many existing approaches in the literature because our approximation preserves unsatisfiability

Proceedings of the 11th International Conference, TPHOLs’98 Canberra, Australia, September–October 1998. Supplementary Proceedings

Mechanical theorem provers for higher order logics have been successfully applied in many areas including hardware verification and synthesis; verification of security and communications protocols; software verification, transformation and refinement; compiler construction; and concurrency. The higher order logics used to reason about these problems and the underlying theorem prover technology that support them are also active areas of research. The International Conference on Theorem Proving in Higher Order Logics (TPHOLs) brings together people working in these and related areas for the discussion and dissemination of new ideas in the field. TPHOLs'98 continues the conference tradition of having both a completed work and work-in-progress stream. The Papers from the first stream were formally refereed, and published as volume 1479 of LNCS. This, supplementary, proceedings records work accepted under the work-in-progress category, and is intended to document emerging trends in higher-order logic research. Papers in the work-in-progress stream are vetted for relevance and contribution before acceptance. The work-in-progress stream is regarded as an important feature of the conference as it provides a venue for the presentation of ongoing research projects, where researchers invite discussion of preliminary results. Although the TPHOLs conferences have their genesis in meetings of the users of the HOL theorem proving system, each successive year has seen a higher rate of contribution from the other groups with similar goals, particularly the user communities of Coq, Isabelle, Lambda, Lego, NuPrl, and PVS. Since 1993 the proceedings have been published by Springer as volumes in Lecture Notes in Computer Science series. Bibliographic details of these publications can be found at the back of this book; more history of TPHOLs can be found with further information about the 1998 event at http://cs.anu.edu.au/TPHOLs98/.Conference Papers: Integrating TPS with Omega By Christoph Benzmuller and Volker Sorge Some Theorem Proving Aids By Paul E. Black and Phillip J. Windley Verification of the MDG Components Library in HOL By Paul Curzon, Sofiene Tahar, and Otmane Ait Mohamed Simulating Term-Rewriting in LPF and in Display Logic By Jeremy E. Dawson A Prototype Generic Tool Supporting the Embedding of Formal Notations By Andrew M. Gravell and Chris H. Pratten Embedding a Formal Notation: Experiences of Automating the Embedding of Z in the Higher Order Logics of PVS and HOL By Andrew M. Gravell and Chris H. Pratten Building HOL90 Everywhere Easily (Well Almost) By Elsa L. Gunter Program Composition in COQ-UNITY : By Francois Marques Formally Analysed Dynamic Synthesis of Hardware By Kong Woei Susanto and Tom Melham Requirements for a Simple Proof Checker By Geoffrey Watson Integrating HOL and RAISE: a practitioner's approach By Wai Wong and Karl R. P. H. Leung Effective Support for Mutually Recursive Types By Peter V. Homeie

Semiclassical collapse of a sphere of dust

The semiclassical collapse of a homogeneous sphere of dust is studied. After identifying the independent dynamical variables, the system is canonically quantised and coupled equations describing matter (dust) and gravitation are obtained. The conditions for the validity of the adiabatic (Born--Oppenheimer) and semiclassical approximations are derived. Further on neglecting back--reaction effects, it is shown that in the vicinity of the horizon and inside the dust the Wightman function for a conformal scalar field coupled to a monopole emitter is thermal at the characteristic Hawking temperature.Comment: LaTeX, 25 pages, no figures, final version accepted for publication in Class. and Quantum Gra

Symmetries of Higher Dimensional Black Holes

We prove that if a stationary, real analytic, asymptotically flat vacuum black hole spacetime of dimension $n\geq 4$ contains a non-degenerate horizon with compact cross sections that are transverse to the stationarity generating Killing vector field then, for each connected component of the black hole's horizon, there is a Killing field which is tangent to the generators of the horizon. For the case of rotating black holes, the stationarity generating Killing field is not tangent to the horizon generators and therefore the isometry group of the spacetime is at least two dimensional. Our proof relies on significant extensions of our earlier work on the symmetries of spacetimes containing a compact Cauchy horizon, allowing now for non closed generators of the horizon.Comment: 57 page