"Boring formal methods" or "Sherlock Holmes deduction methods"?

This paper provides an overview of common challenges in teaching of logic and formal methods to Computer Science and IT students. We discuss our experiences from the course IN3050: Applied Logic in Engineering, introduced as a "logic for everybody" elective course at at TU Munich, Germany, to engage pupils studying Computer Science, IT and engineering subjects on Bachelor and Master levels. Our goal was to overcome the bias that logic and formal methods are not only very complicated but also very boring to study and to apply. In this paper, we present the core structure of the course, provide examples of exercises and evaluate the course based on the students' surveys.Comment: Preprint. Accepted to the Software Technologies: Applications and Foundations (STAF 2016). Final version published by Springer International Publishing AG. arXiv admin note: substantial text overlap with arXiv:1602.0517

Carnap: an Open Framework for Formal Reasoning in the Browser

This paper presents an overview of Carnap, a free and open framework for the development of formal reasoning applications. Carnap’s design emphasizes flexibility, extensibility, and rapid prototyping. Carnap-based applications are written in Haskell, but can be compiled to JavaScript to run in standard web browsers. This combination of features makes Carnap ideally suited for educational applications, where ease-of-use is crucial for students and adaptability to different teaching strategies and classroom needs is crucial for instructors. The paper describes Carnap’s implementation, along with its current and projected pedagogical applications

Mutation testing on an object-oriented framework: An experience report

This is the preprint version of the article - Copyright @ 2011 ElsevierContext The increasing presence of Object-Oriented (OO) programs in industrial systems is progressively drawing the attention of mutation researchers toward this paradigm. However, while the number of research contributions in this topic is plentiful, the number of empirical results is still marginal and mostly provided by researchers rather than practitioners. Objective This article reports our experience using mutation testing to measure the effectiveness of an automated test data generator from a user perspective. Method In our study, we applied both traditional and class-level mutation operators to FaMa, an open source Java framework currently being used for research and commercial purposes. We also compared and contrasted our results with the data obtained from some motivating faults found in the literature and two real tools for the analysis of feature models, FaMa and SPLOT. Results Our results are summarized in a number of lessons learned supporting previous isolated results as well as new findings that hopefully will motivate further research in the field. Conclusion We conclude that mutation testing is an effective and affordable technique to measure the effectiveness of test mechanisms in OO systems. We found, however, several practical limitations in current tool support that should be addressed to facilitate the work of testers. We also missed specific techniques and tools to apply mutation testing at the system level.This work has been partially supported by the European Commission (FEDER) and Spanish Government under CICYT Project SETI (TIN2009-07366) and the Andalusian Government Projects ISABEL (TIC-2533) and THEOS (TIC-5906)

An Inquiry into the Practice of Proving in Low-Dimensional Topology

The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used in the practice are an integral part of the mathematical reasoning. As a matter of fact, they convey in a material form the relevant transitions and thus allow experts to draw inferential connections. Second, in low-dimensional topology experts exploit a particular type of manipulative imagination which is connected to intuition of two- and three-dimensional space and motor agency. This imagination allows recognizing the transformations which connect different pictures in an argument. Third, the epistemic—and inferential—actions performed are permissible only within a specific practice: this form of reasoning is subject-matter dependent. Local criteria of validity are established to assure the soundness of representationally heterogeneous arguments in low-dimensional topology

Design of teaching materials informed by consideration of learning-impaired students

The general aim of this project is to fundamentally re-think the design of teaching materials in view of what is now known about cognitive deficits and about what Howard Gardner has termed ‘multiple intelligences’. The applicant has implemented this strategy in two distinct areas, the first involving the writing of an English language programme for Chinese speakers, the second involving the construction of specialized equipment for teaching elementary logic to blind students. The next phase (for which funding is sought) is to test the effectiveness of the logic device, because in theory – the one to be tested – materials the design of which is informed by the above rationale will provide a richer learning experience for non-impaired users

Computer-Aided Argument Mapping as a Tool for Teaching Critical Thinking

As individuals we often face complex issues about which we must weigh evidence and come to conclusions. Corporations also have to make decisions on the basis of strong and compelling arguments. Legal practitioners, compelled by arguments for or against a proposition and underpinned by the weight of evidence, are often required to make judgments that affect the lives of others. Medical doctors face similar decisions. Governments make purchasing decisions—for example, for expensive military equipment—or decisions in the areas of public or foreign policy. These issues involve many arguments on all sides of difficult debates. These issues involve understanding the arguments of others and being able to make objections and provide rebuttals to objections. Students in universities deal with arguments all the time. A major purpose of a university education—regardless of subject matter—is to teach students how to read, understand, and respond to complex arguments. The ability to do this makes for highly employable, adaptable, and reflectively critical individuals. We often call the skill of marshaling arguments and assessing them “critical thinking.” All universities claim to instill the skill of critical thinking in their graduates and routinely note this in their advertising and promotional documents. This short paper outlines one way this skill can be taught

Tools for Thought: The Case of Mathematics

The objective of this article is to take into account the functioning of representational cognitive tools, and in particular of notations and visualizations in mathematics. In order to explain their functioning, formulas in algebra and logic and diagrams in topology will be presented as case studies and the notion of manipulative imagination as proposed in previous work will be discussed. To better characterize the analysis, the notions of material anchor and representational affordance will be introduced

Theoretical models of the role of visualisation in learning formal reasoning

Although there is empirical evidence that visualisation tools can help students to learn formal subjects such as logic, and although particular strategies and conceptual difficulties have been identified, it has so far proved difficult to provide a general model of learning in this context that accounts for these findings in a systematic way. In this paper, four attempts at explaining the relative difficulty of formal concepts and the role of visualisation in this learning process are presented. These explanations draw on several existing theories, including Vygotsky's Zone of Proximal Development, Green's Cognitive Dimensions, the Popper-Campbell model of conjectural learning, and cognitive complexity. The paper concludes with a comparison of the utility and applicability of the different models. It is also accompanied by a reflexive commentary[0] (linked to this paper as a hypertext) that examines the ways in which theory has been used within these arguments, and which attempts to relate these uses to the wider context of learning technology research