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

ENIGMA: Efficient Learning-based Inference Guiding Machine

ENIGMA is a learning-based method for guiding given clause selection in saturation-based theorem provers. Clauses from many proof searches are classified as positive and negative based on their participation in the proofs. An efficient classification model is trained on this data, using fast feature-based characterization of the clauses . The learned model is then tightly linked with the core prover and used as a basis of a new parameterized evaluation heuristic that provides fast ranking of all generated clauses. The approach is evaluated on the E prover and the CASC 2016 AIM benchmark, showing a large increase of E's performance.Comment: Submitted to LPAR 201

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

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

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

Does regulating private long-term care facilities lead to better care? a study from Quebec, Canada

Objective. In the province of Quebec, Canada, long-term residential care is provided by 2 types of facilities: publicly-funded accredited facilities and privately-owned facilities in which care is privately financed and delivered. Following evidence that private facilities were delivering inadequate care, the provincial government decided to regulate this industry. We assessed the impact of regulation on care quality by comparing quality assessments made before and after regulation. In both periods, public facilities served as a comparison group. Design: A cross-sectional study conducted in 2010-2012 that incorporates data collected in 1995-2000. Settings. Random samples of private and public facilities from 2 regions of Quebec. Participants. Random samples of disabled residents aged 65 years and over. In total, 451 residents from 145 care settings assessed in 1995-2000 were compared to 329 residents from 102 care settings assessed in 2010-2012. Intervention. Regulation introduced by the province in 2005, effective February 2007. Main outcome measure. Quality of care measured with the QUALCARE Scale. Results. After regulation, fewer small-size facilities were in operation in the private market. Between the 2 study periods, the proportion of residents with severe disabilities decreased in private facilities while it remained over 80% in their public counterparts. Meanwhile, quality of care improved significantly in private facilities, while worsening in their public counterparts, even after controlling for confounding. Conclusions. The private industry now provides better care to its residents. Improvement in care quality likely results in part from the closure of small homes and change in resident case-mix

Foundational (co)datatypes and (co)recursion for higher-order logic

We describe a line of work that started in 2011 towards enriching Isabelle/HOL's language with coinductive datatypes, which allow infinite values, and with a more expressive notion of inductive datatype than previously supported by any system based on higher-order logic. These (co)datatypes are complemented by definitional principles for (co)recursive functions and reasoning principles for (co)induction. In contrast with other systems offering codatatypes, no additional axioms or logic extensions are necessary with our approach

Gender-Sensitive Violence Risk Assessment:Predictive Validity of Six Tools in Female Forensic Psychiatric Patients

Most violence risk assessment tools have been validated predominantly in males. In this multicenter study, the Historical, Clinical, Risk Management-20 (HCR-20), Historical, Clinical, Risk Management-20 Version 3 (HCR-20(V3)), Female Additional Manual (FAM), Short-Term Assessment of Risk and Treatability (START), Structured Assessment of Protective Factors for violence risk (SAPROF), and Psychopathy Checklist-Revised (PCL-R) were coded on file information of 78 female forensic psychiatric patients discharged between 1993 and 2012 with a mean follow-up period of 11.8 years from one of four Dutch forensic psychiatric hospitals. Notable was the high rate of mortality (17.9%) and readmission to psychiatric settings (11.5%) after discharge. Official reconviction data could be retrieved from the Ministry of Justice and Security for 71 women. Twenty-four women (33.8%) were reconvicted after discharge, including 13 for violent offenses (18.3%). Overall, predictive validity was moderate for all types of recidivism, but low for violence. The START Vulnerability scores, HCR-20(V3), and FAM showed the highest predictive accuracy for all recidivism. With respect to violent recidivism, only the START Vulnerability scores and the Clinical scale of the HCR-20(V3) demonstrated significant predictive accuracy

Formalizing Bachmair and Ganzinger’s Ordered Resolution Prover

We present a formalization of the first half of Bachmair and Ganzinger’s chapter on resolution theorem proving in Isabelle/HOL, culminating with a refutationally complete first-order prover based on ordered resolution with literal selection. We develop general infrastructure and methodology that can form the basis of completeness proofs for related calculi, including superposition. Our work clarifies several of the fine points in the chapter’s text, emphasizing the value of formal proofs in the field of automated reasoning