Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems,definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial Intelligence and Symbolic Computation AISC 201

Kink Chains from Instantons on a Torus

We describe how the procedure of calculating approximate solitons from instanton holonomies may be extended to the case of soliton crystals. It is shown how sine-Gordon kink chains may be obtained from CP1 instantons on a torus. These kink chains turn out to be remarkably accurate approximations to the true solutions. Some remarks on the relevance of this work to Skyrme crystals are also made.Comment: latex 17 pages, DAMTP 94-7

Design, fabrication and testing of sandwich panel decking use in road freight trailers

This paper investigates the potential of sandwich structures in the novel application of road freight trailer decking. Sandwich panels are developed to be lightweight replacements to conventional birch plywood hardwood decking, which is the norm in European road freight trailers. A tailored material selection process is used to identify the most advantageous sandwich panel material combinations with respect to flexural properties and material cost. Sandwich panels with woven glass fibre reinforced polyester and an end-grain balsa are found to be the most advantageous material combination in terms of both raw material cost and mechanical performance. These panels are fabricated using a single shot fabrication technique and are approximately 30% lighter than conventional birch plywood trailer decking. This weight saving corresponds to approximately 165 kg in a standard 13.6 m long European road freight trailer. Three point bend testing has shown that these sandwich panels have superior flexural strength and comparable flexural stiffness to birch plywood. Large panel testing confirmed that these panels can withstand roughly four times the forklift wheel load likely to be seen in-service. The shear properties of two grades of rigid end-grain balsa core are also studied to illustrate the importance of using a higher density balsa core. Practical considerations, such as joining and recyclability, for using sandwich panels in this application are also discussed.Centre for Sustainable Road Freight, Engineering and Physical Sciences Research Council (Grant ID: EP/K00915X/1

TOOLympics 2019: An Overview of Competitions in Formal Methods

Evaluation of scientific contributions can be done in many different ways. For the various research communities working on the verification of systems (software, hardware, or the underlying involved mechanisms), it is important to bring together the community and to compare the state of the art, in order to identify progress of and new challenges in the research area. Competitions are a suitable way to do that. The first verification competition was created in 1992 (SAT competition), shortly followed by the CASC competition in 1996. Since the year 2000, the number of dedicated verification competitions is steadily increasing. Many of these events now happen regularly, gathering researchers that would like to understand how well their research prototypes work in practice. Scientific results have to be reproducible, and powerful computers are becoming cheaper and cheaper, thus, these competitions are becoming an important means for advancing research in verification technology. TOOLympics 2019 is an event to celebrate the achievements of the various competitions, and to understand their commonalities and differences. This volume is dedicated to the presentation of the 16 competitions that joined TOOLympics as part of the celebration of the 25th anniversary of the TACAS conference

Premise Selection and External Provers for HOL4

Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that provides machine learning-based premise selection and automated reasoning also for HOL4. We efficiently record the HOL4 dependencies and extract features from the theorem statements, which form a basis for premise selection. HOLyHammer transforms the HOL4 statements in the various TPTP-ATP proof formats, which are then processed by the ATPs. We discuss the different evaluation settings: ATPs, accessible lemmas, and premise numbers. We measure the performance of HOLyHammer on the HOL4 standard library. The results are combined accordingly and compared with the HOL Light experiments, showing a comparably high quality of predictions. The system directly benefits HOL4 users by automatically finding proofs dependencies that can be reconstructed by Metis

A new improved method for assessing brain deformation after decompressive craniectomy.

BACKGROUND: Decompressive craniectomy (DC) is a surgical intervention used following traumatic brain injury to prevent or alleviate raised intracranial pressure. However the clinical effectiveness of the intervention remains in doubt. The location of the craniectomy (unilateral or bifrontal) might be expected to change the brain deformation associated with the operation and hence the clinical outcome. As existing methods for assessing brain deformation have several limitations, we sought to develop and validate a new improved method. METHODS: Computed tomography (CT) scans were taken from 27 patients who underwent DC (17 bifrontal patients and 10 unilateral patients). Pre-operative and post-operative images were processed and registered to determine the change in brain position associated with the operation. The maximum deformation in the herniated brain, the change in volume and estimates of the craniectomy area were determined from the images. Statistical comparison was made using the Pearson's correlation coefficient r and a Welch's two-tailed T-test, with statistical significance reported at the 5% level. RESULTS: There was a reasonable correlation between the volume increase and the maximum brain displacement (r = 0.64), a low correlation between the volume increase and the craniectomy area (r = 0.30) and no correlation between the maximum displacement and the craniectomy area (r = -0.01). The maximum deformation was significantly lower (P  = 0.023) in the bifrontal patients (mean = 22.5 mm) compared with the unilateral patients (mean = 29.8 mm). Herniation volume was significantly lower (P = 0.023) in bifrontal (mean = 50.0 ml) than unilateral patients (mean = 107.3 ml). Craniectomy area was not significantly different for the two craniectomy locations (P = 0.29). CONCLUSIONS: A method has been developed to quantify changes in brain deformation due to decompressive craniectomy from CT images and allow comparison between different craniectomy locations. Measured displacement is a reasonable way to characterise volume changes.TLF acknowledges funding from the Engineering and Physical Sciences Research Council (EPSRC). AGK is supported by a Royal College of Surgeons of England Research Fellowship (funded by the Freemasons and the Rosetrees Trust), a National Institute of Health Research (NIHR) Academic Clinical Fellowship and a Raymond and Beverly Sackler Studentship. PJH is supported by a NIHR Research Professorship and the NIHR Cambridge Biomedical Research Centre. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.This is the final published version. It is also available from PLOS at http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0110408

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