Set Theory or Higher Order Logic to Represent Auction Concepts in Isabelle?

When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL system, and we have produced verified code for combinatorial Vickrey auctions. A fundamental question in this was how to represent some basic concepts: since set theory is available inside Isabelle/HOL, when introducing new definitions there is often the issue of balancing the amount of set-theoretical objects and of objects expressed using entities which are more typical of higher order logic such as functions or lists. Likewise, a user has often to answer the question whether to use a constructive or a non-constructive definition. Such decisions have consequences for the proof development and the usability of the formalization. For instance, sets are usually closer to the representation that economists would use and recognize, while the other objects are closer to the extraction of computational content. In this paper we give examples of the advantages and disadvantages for these approaches and their relationships. In addition, we present the corresponding Isabelle library of definitions and theorems, most prominently those dealing with relations and quotients.Comment: Preprint of a paper accepted for the forthcoming CICM 2014 conference (cicm-conference.org/2014): S.M. Watt et al. (Eds.): CICM 2014, LNAI 8543, Springer International Publishing Switzerland 2014. 16 pages, 1 figur

Following the Mobile Student: Can We Develop the Capacity for a Comprehensive Database to Assess Student Progression?

Presents a study of state-level databases on postsecondary student retention and completion rates and the feasibility of tracking students across state lines. Outlines challenges and recommendations, including establishing a common reporting standard

Investigation of a moving-model technique for measuring ground effect

A ground-based testing technique is under development for the measurement of dynamic or time-dependent ground effects which may be present during aircraft approach and landing. The technique utilizes a model moving horizontally over an upwardly-inclined ground plane to simulate rate of descent. Results were obtained in the Langley Research Center (LaRC) Vortex Research Facility (VRF) for a generic 60 delta wing and for an F-18 configuration, both with and without thrust reversing, at forward speeds up to 100 ft/sec. These same models and support hardware were also tested in the LaRC 14 by 22 Foot Subsonic Tunnel at identical conditions (but without rate of descent) with and without a moving-belt ground plane to obtain data for comparison

An assessment of ground effects determined by static and dynamic testing techniques

A new testing technique was developed wherein the rate of descent can be included as a parameter in ground effects investigations. This technique simulates the rate of descent by horizontal motion of a model over an inclined ground board in the Langley Vortex Research Facility (VRF) During initial evaluations of the technique, dynamic ground effects data were obtained over the inclined ground board, steady state ground effects data were obtained over a flat portion of the ground board, and the results were compared to conventional static wind tunnel ground effect data both with and without a moving belt ground plane simulation. Initial testing and analysis led to the following conclusions: the moving belt ground plane had little effect on static ground effects for the configurations tested unless thrust reversers were employed; in general, rate-of-descent reduced ground effects to the point that for reversed thrust cases an expected loss of lift due to ground effects was eliminated at approach conditions; and, in general, the steady state results from the VRF matched static results obtained from the wind tunnel once the flow field stabilized over the flat portion of the ground board

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

Evaluation of Four Advanced Nozzle Concepts for Short Takeoff and Landing Performance

Four advanced nozzle concepts were tested on a canard-wing fighter in the Langley 14- by 22-Foot Subsonic Tunnel. The four vectoring-nozzle concepts were as follows: (1) an axisymmetric nozzle (AXI); (2) an asymmetric, load balanced exhaust nozzle (ALBEN); (3) a low aspect ratio, single expansion ramp nozzle (LASERN); and (4) a high aspect ratio, single expansion ramp nozzle (HASERN). The investigation was conducted to determine the most suitable nozzle concept for short takeoff and landing (STOL) performance. The criterion for the best STOL performance was a takeoff ground roll of less than 1000 ft. At approach, the criteria were high lift and sufficient drag to maintain a glide slope of -3 to -6 deg with enough pitching-moment control from the canards. The test was performed at a dynamic pressure of 45 lb/sq ft and an angle-of-attack range of 0 to 20 deg. The nozzle pressure ratio was varied from 1.0 to 4.3 at both dry power and after burning nozzle configurations with nozzle vectoring to 60 deg. In addition, the model was tested in and out of ground effects. The ALBEN concept was the best of the four nozzle concepts tested for STOL performance

A Guatemalan Soycow Cooperative: Is the Whole Greater than the Sum of its Parts?

Teaching Notes available upon request: [email protected]; Author video:http://www.youtube.com/user/ifamr1?feature=mhum#p/u/8/FhUZu2lt6NsSoycow, cooperative, Guatemala, teaching case, Agribusiness, Q10,

\u3cem\u3eDe Novo\u3c/em\u3e [PSI\u3csup\u3e+\u3c/sup\u3e] Prion Formation Involves Multiple Pathways to Form Infectious Oligomers

Prion and other neurodegenerative diseases are associated with misfolded protein assemblies called amyloid. Research has begun to uncover common mechanisms underlying transmission of amyloids, yet how amyloids form in vivo is still unclear. Here, we take advantage of the yeast prion, [PSI +], to uncover the early steps of amyloid formation in vivo. [PSI +] is the prion form of the Sup35 protein. While [PSI +] formation is quite rare, the prion can be greatly induced by overexpression of the prion domain of the Sup35 protein. This de novo induction of [PSI +] shows the appearance of fluorescent cytoplasmic rings when the prion domain is fused with GFP. Our current work shows that de novoinduction is more complex than previously thought. Using 4D live cell imaging, we observed that fluorescent structures are formed by four different pathways to yield [PSI +] cells. Biochemical analysis of de novo induced cultures indicates that newly formed SDS resistant oligomers change in size over time and lysates made from de novo induced cultures are able to convert [psi −] cells to [PSI +] cells. Taken together, our findings suggest that newly formed prion oligomers are infectious

From LCF to Isabelle/HOL

Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search, borrowing techniques from the world of first order theorem proving, but also the automatic search for counterexamples. They include a highly readable structured language of proofs and a unique interactive development environment for editing live proof documents. Everything rests on the foundation conceived by Robin Milner for Edinburgh LCF: a proof kernel, using abstract types to ensure soundness and eliminate the need to store proofs. Compared with the research prototypes of the 1970s, Isabelle is a practical and versatile tool. It is used by system designers, mathematicians and many others

Scalia in the Casebooks

In the time since Justice Antonin Scalia’s untimely death, much has been written about what his influence has been and what his influence will be. In this Essay, we try to quantify Scalia’s influence in law school constitutional-law curricula by studying how often his ideas are explored in constitutional-law casebooks. In particular, relative to other justices, we look at how often Scalia’s opinions (for the Court, or his separate opinions) are excerpted in the principal cases and how often he is referred to by name in the notes preceding and following the principal cases. We find that Scalia is at or near the top of most of the metrics we explore here, but he does not tower over the competition. Indeed, the data reveal that perhaps the most important factor driving inclusion in our casebooks is seniority: chief justices and justices who led their ideological wings of the Court have a great deal of power to assign themselves opinions that are likely to end up in our casebooks. We find that the most notable exception in the data is not Scalia, but Justice Samuel Alito: he is included in our casebooks to an especially surprising extent given that, until this year, he has always been the most junior member of his wing of the Court