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 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

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

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

Modulations of stratospheric ozone by volcanic eruptions

We have used a time series of aerosol surface based on the measurements of Hofmann to investigate the modulation of total column ozone caused by the perturbation to gas phase chemistry by the reaction N2O5(gas) + H2O(aero) yields 2HNO3(gas) on the surface of stratospheric aerosols. We have tested a range of values for its reaction probability, gamma = 0.02, 0.13, and 0.26 which we compared to unperturbed homogeneous chemistry. Our analysis spans a period from Jan. 1974 to Oct. 1994. The results suggest that if lower values of gamma are the norm then we would expect larger ozone losses for highly enhanced aerosol content that for larger values of gamma. The ozone layer is more sensitive to the magnitude of the reaction probability under background conditions than during volcanically active periods. For most conditions, the conversion of NO2 to HNO3 is saturated for reaction probability in the range of laboratory measurements, but is only absolutely saturated following major volcanic eruptions when the heterogeneous loss dominates the losses of N2O5. The ozone loss due to this heterogeneous reaction increases with the increasing chlorine load. Total ozone losses calculated are comparable to ozone losses reported from TOMS and Dobson data

Hammering towards QED

This paper surveys the emerging methods to automate reasoning over large libraries developed with formal proof assistants. We call these methods hammers. They give the authors of formal proofs a strong “one-stroke” tool for discharging difficult lemmas without the need for careful and detailed manual programming of proof search. The main ingredients underlying this approach are efficient automatic theorem provers that can cope with hundreds of axioms, suitable translations of the proof assistant’s logic to the logic of the automatic provers, heuristic and learning methods that select relevant facts from large libraries, and methods that reconstruct the automatically found proofs inside the proof assistants. We outline the history of these methods, explain the main issues and techniques, and show their strength on several large benchmarks. We also discuss the relation of this technology to the QED Manifesto and consider its implications for QED-like efforts.Blanchette’s Sledgehammer research was supported by the Deutsche Forschungs- gemeinschaft projects Quis Custodiet (grants NI 491/11-1 and NI 491/11-2) and Hardening the Hammer (grant NI 491/14-1). Kaliszyk is supported by the Austrian Science Fund (FWF) grant P26201. Sledgehammer was originally supported by the UK’s Engineering and Physical Sciences Research Council (grant GR/S57198/01). Urban’s work was supported by the Marie-Curie Outgoing International Fellowship project AUTOKNOMATH (grant MOIF-CT-2005-21875) and by the Netherlands Organisation for Scientific Research (NWO) project Knowledge-based Automated Reasoning (grant 612.001.208).This is the final published version. It first appeared at http://jfr.unibo.it/article/view/4593/5730?acceptCookies=1

Frequent Gain and Loss of Functional Transcription Factor Binding Sites

Cis-regulatory sequences are not always conserved across species. Divergence within cis-regulatory sequences may result from the evolution of species-specific patterns of gene expression or the flexible nature of the cis-regulatory code. The identification of functional divergence in cis-regulatory sequences is therefore important for both understanding the role of gene regulation in evolution and annotating regulatory elements. We have developed an evolutionary model to detect the loss of constraint on individual transcription factor binding sites (TFBSs). We find that a significant fraction of functionally constrained binding sites have been lost in a lineage-specific manner among three closely related yeast species. Binding site loss has previously been explained by turnover, where the concurrent gain and loss of a binding site maintains gene regulation. We estimate that nearly half of all loss events cannot be explained by binding site turnover. Recreating the mutations that led to binding site loss confirms that these sequence changes affect gene expression in some cases. We also estimate that there is a high rate of binding site gain, as more than half of experimentally identified S. cerevisiae binding sites are not conserved across species. The frequent gain and loss of TFBSs implies that cis-regulatory sequences are labile and, in the absence of turnover, may contribute to species-specific patterns of gene expression

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

Cancer incidence and stage at diagnosis among people with psychotic disorders: Systematic review and meta-analysis.

Research regarding the incidence of cancer among people with psychotic disorders relative to the general population is equivocal, although the evidence suggests that they have more advanced stage cancer at diagnosis. We conducted a systematic review and meta-analysis to examine the incidence and stage at diagnosis of cancer among people with, relative to those without, psychotic disorders. We searched the MEDLINE, EMBASE, PsycINFO, and CINAHL databases. Articles were included if they reported the incidence and/or stage at diagnosis of cancer in people with psychotic disorders. Random effects meta-analyses were used to determine risk of cancer and odds of advanced stage cancer at diagnosis in people with psychosis, relative to those without psychotic disorders. A total of 40 articles were included in the review, of which, 31 were included in the meta-analyses. The pooled age-adjusted risk ratio for all cancers in people with psychotic disorders was 1.08 (95% CI: 1.01-1.15), relative to those without psychotic disorders, with significant heterogeneity by cancer site. People with psychotic disorders had a higher incidence of breast, oesophageal, colorectal, testicular, uterine, and cervical cancer, and a lower incidence of skin, prostate, and thyroid cancer. People with psychotic disorders also had 22% higher (95% CI: 2-46%) odds of metastases at diagnosis, compared to those without psychotic disorders. Our systematic review found a significant difference in overall cancer incidence among people diagnosed with psychotic disorders and people with psychotic disorders were more likely to present with advanced stage cancer at diagnosis. This finding may reflect a need for improved access to and uptake of cancer screening for patients diagnosed with psychotic disorders