Towards Ranking Geometric Automated Theorem Provers

The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other areas by the strong connection between the axiomatic theories and its standard models. In many cases the geometric constructions are used to establish the theorems' statements, geometric constructions are, in some provers, used to conduct the proof, used as counter-examples to close some branches of the automatic proof. Synthetic geometry proofs are done using geometric properties, proofs that can have a visual counterpart in the supporting geometric construction. With the growing use of geometry automatic deduction tools as applications in other areas, e.g. in education, the need to evaluate them, using different criteria, is felt. Establishing a ranking among geometric automated theorem provers will be useful for the improvement of the current methods/implementations. Improvements could concern wider scope, better efficiency, proof readability and proof reliability. To achieve the goal of being able to compare geometric automated theorem provers a common test bench is needed: a common language to describe the geometric problems; a comprehensive repository of geometric problems and a set of quality measures.Comment: In Proceedings ThEdu'18, arXiv:1903.1240

The problem of evaluating automated large-scale evidence aggregators

In the biomedical context, policy makers face a large amount of potentially discordant evidence from different sources. This prompts the question of how this evidence should be aggregated in the interests of best-informed policy recommendations. The starting point of our discussion is Hunter and Williams’ recent work on an automated aggregation method for medical evidence. Our negative claim is that it is far from clear what the relevant criteria for evaluating an evidence aggregator of this sort are. What is the appropriate balance between explicitly coded algorithms and implicit reasoning involved, for instance, in the packaging of input evidence? In short: What is the optimal degree of ‘automation’? On the positive side: We propose the ability to perform an adequate robustness analysis as the focal criterion, primarily because it directs efforts to what is most important, namely, the structure of the algorithm and the appropriate extent of automation. Moreover, where there are resource constraints on the aggregation process, one must also consider what balance between volume of evidence and accuracy in the treatment of individual evidence best facilitates inference. There is no prerogative to aggregate the total evidence available if this would in fact reduce overall accuracy

Machine-assisted Cyber Threat Analysis using Conceptual Knowledge Discovery

Over the last years, computer networks have evolved into highly dynamic and interconnected environments, involving multiple heterogeneous devices and providing a myriad of services on top of them. This complex landscape has made it extremely difficult for security administrators to keep accurate and be effective in protecting their systems against cyber threats. In this paper, we describe our vision and scientific posture on how artificial intelligence techniques and a smart use of security knowledge may assist system administrators in better defending their networks. To that end, we put forward a research roadmap involving three complimentary axes, namely, (I) the use of FCA-based mechanisms for managing configuration vulnerabilities, (II) the exploitation of knowledge representation techniques for automated security reasoning, and (III) the design of a cyber threat intelligence mechanism as a CKDD process. Then, we describe a machine-assisted process for cyber threat analysis which provides a holistic perspective of how these three research axes are integrated together

Towards sound refactoring in erlang

Erlang is an actor-based programming language used extensively for building concurrent, reactive systems that are highly available and suff er minimum downtime. Such systems are often mission critical, making system correctness vital. Refactoring is code restructuring that improves the code but does not change behaviour. While using automated refactoring tools is less error-prone than performing refactorings manually, automated refactoring tools still cannot guarantee that the refactoring is correct, i.e., program behaviour is preserved. This leads to lack of trust in automated refactoring tools. We rst survey solutions to this problem proposed in the literature. Erlang refactoring tools as commonly use approximation techniques which do not guarantee behaviour while some other works propose the use of formal methodologies. In this work we aim to develop a formal methodology for refactoring Erlang code. We study behavioural preorders, with a special focus on the testing preorder as it seems most suited to our purpose.peer-reviewe

Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support

A framework and methodology---termed LogiKEy---for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and governance of intelligent autonomous systems. LogiKEy's unifying formal framework is based on semantical embeddings of deontic logics, logic combinations and ethico-legal domain theories in expressive classic higher-order logic (HOL). This meta-logical approach enables the provision of powerful tool support in LogiKEy: off-the-shelf theorem provers and model finders for HOL are assisting the LogiKEy designer of ethical intelligent agents to flexibly experiment with underlying logics and their combinations, with ethico-legal domain theories, and with concrete examples---all at the same time. Continuous improvements of these off-the-shelf provers, without further ado, leverage the reasoning performance in LogiKEy. Case studies, in which the LogiKEy framework and methodology has been applied and tested, give evidence that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure