More SPASS with Isabelle: superposition with hard sorts and configurable simplification

Sledgehammer for Isabelle/HOL integrates automatic theorem provers to discharge interactive proof obligations. This paper considers a tighter integration of the superposition prover SPASS to increase Sledgehammer’s success rate. The main enhancements are native support for hard sorts (simple types) in SPASS, simplification that honors the orientation of Isabelle simp rules, and a pair of clause-selection strategies targeted at large lemma libraries. The usefulness of this integration is confirmed by an evaluation on a vast benchmark suite and by a case study featuring a formalization of language-based security

A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

Concrete Semantics with Coq and CoqHammer

The "Concrete Semantics" book gives an introduction to imperative programming languages accompanied by an Isabelle/HOL formalization. In this paper we discuss a re-formalization of the book using the Coq proof assistant. In order to achieve a similar brevity of the formal text we extensively use CoqHammer, as well as Coq Ltac-level automation. We compare the formalization efficiency, compactness, and the readability of the proof scripts originating from a Coq re-formalization of two chapters from the book

A formalized general theory of syntax with bindings

We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying numbers of inputs, quotiented to alpha-equivalence and sorted according to a binding signature. The theory includes a rich collection of properties of the standard operators on terms, such as substitution and freshness. It also includes induction and recursion principles and support for semantic interpretation, all tailored for smooth interaction with the bindings and the standard operators

Sharing HOL4 and HOL Light proof knowledge

New proof assistant developments often involve concepts similar to already formalized ones. When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries. In this paper we propose and evaluate a number of methods, which strengthen proof automation by learning from proof libraries of different provers. Certain conjectures can be proved directly from the dependencies induced by similar proofs in the other library. Even if exact correspondences are not found, learning-reasoning systems can make use of the association between proved theorems and their characteristics to predict the relevant premises. Such external help can be further combined with internal advice. We evaluate the proposed knowledge-sharing methods by reproving the HOL Light and HOL4 standard libraries. The learning-reasoning system HOL(y)Hammer, whose single best strategy could automatically find proofs for 30% of the HOL Light problems, can prove 40% with the knowledge from HOL4

Harnessing Higher-Order (Meta-)Logic to Represent and Reason with Complex Ethical Theories

The computer-mechanization of an ambitious explicit ethical theory, Gewirth's Principle of Generic Consistency, is used to showcase an approach for representing and reasoning with ethical theories exhibiting complex logical features like alethic and deontic modalities, indexicals, higher-order quantification, among others. Harnessing the high expressive power of Church's type theory as a meta-logic to semantically embed a combination of quantified non-classical logics, our work pushes existing boundaries in knowledge representation and reasoning. We demonstrate that intuitive encodings of complex ethical theories and their automation on the computer are no longer antipodes.Comment: 14 page

Incidence and Cost of Ankle Sprains in United States Emergency Departments

Ankle sprains represent a common injury in emergency departments, but little is known about common complications, procedures, and charges associated with ankle sprains in emergency departments

A new narrow-beam, multi-frequency, scanning radiometer and its application to in-flight icing detection

AbstractA one degree beamwidth, multi-frequency (20 to 30 and 89GHz), dual-polarization radiometer with full azimuth and elevation scanning capabilities was built with the purpose of improving the detection of in-flight icing hazards to aircraft in the near airport environment. This goal was achieved by collocating the radiometer with Colorado State University's CHILL polarized Doppler radar and leveraging the similar beamwidth and volume scan regiments of the two instruments. The collocated instruments allowed for the liquid water path and water vapor measurements derived from the radiometer to be merged with the radar moment fields to determine microphysical and water phase characteristics aloft. The radiometer was field tested at Colorado State University's CHILL radar site near Greeley, Colorado during the summer of 2009. Instrument design, calibration, and initial field testing results are discussed in this paper

Witnessing (co)datatypes

Datatypes and codatatypes are useful for specifying and reasoning about (possibly infinite) computational processes. The Isabelle/HOL proof assistant has recently been extended with a definitional package that supports both. We describe a complete procedure for deriving nonemptiness witnesses in the general mutually recursive, nested case—nonemptiness being a proviso for introducing types in higher-order logic

Chiropractic pediatric patient management and interdisciplinary collaboration: A descriptive cross-sectional study of chiropractors in Quebec

Background: Worldwide, many patients, including minors, seek chiropractic care. The purpose of this study was to investigate the practice characteristics of chiropractors who treat pediatric patients in Quebec, Canada. Methods: We conducted a web-based cross-sectional survey of all licensed chiropractors working in Quebec (Canada). Data were collected using an adapted questionnaire. Descriptive statistics were produced for all the variables collected. Results: Among our 245 participants (response rate: 21%), 63% were women, and half defined themselves as general musculoskeletal (MSK) health care practitioners. Nearly all participants reported seeing 0–5 new pediatric patients/week, and the most common pediatric age group was 6–12 years old (57%). Pediatric patients were most commonly referred by family members and “word of mouth”. The respondents most frequently indicated that they strongly agreed with statements affirming their confidence in their own diagnostic capacities regarding MSK disorders with respect to all age groups as well as non-MSK disorders with regard to young teens. They reported a moderate level of agreement with similar statements concerning the diagnosis of non-MSK disorders in newborns, preschoolers, and children. Chiropractors rarely referred their pediatric patients to a nurse/family doctor or a pediatrician. When presented with potential pediatric red flags, the respondents commonly indicated that they would refer the patient to a physician in an emergency situation or for comanagement. Conclusion: Chiropractors in Quebec are confident in their diagnoses of pediatric MSK conditions and refer patients to physicians in the rare event of a worrisome presentation. However, some chiropractors may have expectations that are unsupported by evidence regarding the diagnosis and management of non-MSK complaints