Theorems in automated theorem proving are usually proved by formal logical proofs. However, there is a subset of problems which humans can prove by the use of geometric operations on diagrams, so called diagrammatic proofs. Insight is often more clearly perceived in these proofs than in the corresponding algebraic proofs; they capture an intuitive notion of truthfulness that humans find easy to see and understand. We are investigating and automating such diagrammatic reasoning about mathematical theorems. Concrete, rather than general diagrams (...) are used to prove particular concrete instances of the universally quantified theorem. The diagrammatic proof is captured by the use of geometric operations on the diagram. These operations are the inference steps of the proof. An abstracted schematic proof of the universally quantified theorem is induced from these proof instances. The constructive -rule provides the mathematical basis for this step from schematic proofs to theoremhood. In this way we avoid the difficulty of treating a general case in a diagram. One method of confirming that the abstraction of the schematic proof from the proof instances is sound is proving the correctness of schematic proofs in the meta-theory of diagrams. These ideas have been implemented in the system, called Diamond, which is presented here. (shrink)

In this paper we present an approach to automated learning within mathematical reasoning systems. In particular, the approach enables proof planning systems to automatically learn new proof methods from well-chosen examples of proofs which use a similar reasoning pattern to prove related theorems. Our approach consists of an abstract representation for methods and a machine learning technique which can learn methods using this representation formalism. We present an implementation of the approach within the ΩMEGA proof planning system, which we call (...) LEARNΩMATIC. We also present the results of the experiments that we ran on this implementation in order to evaluate if and how it improves the power of proof planning systems. (shrink)

In order to effectively communicate information, the choice of representation is important. Ideally, a chosen representation will aid readers in making desired inferences. In this paper, we develop the theory of observation: what it means for one statement to be observable from another. Using observability, we give a formal characterization of the observational advantages of one representation of information over another. By considering observational advantages, people will be able to make better informed choices of representations of information. To demonstrate the (...) benefit of observation and observational advantages, we apply these concepts to set theory and Euler diagrams. In particular, we can show that Euler diagrams have significant observational advantages over set theory. This formally justifies Larkin and Simon’s claim that “a diagram is worth ten thousand words”. (shrink)

In this paper, we introduce Speedith which is an interactive diagrammatic theorem prover for the well-known language of spider diagrams. Speedith provides a way to input spider diagrams, transform them via the diagrammatic inference rules, and prove diagrammatic theorems. Speedith’s inference rules are sound and complete, extending previous research by including all the classical logic connectives. In addition to being a stand-alone proof system, Speedith is also designed as a program that plugs into existing general purpose theorem provers. This allows (...) for other systems to access diagrammatic reasoning via Speedith, as well as a formal verification of diagrammatic proof steps within standard sentential proof assistants. We describe the general structure of Speedith, the diagrammatic language, the automatic mechanism that draws the diagrams when inference rules are applied on them, and how formal diagrammatic proofs are constructed. (shrink)

In this contribution we propose an agent architecture for theorem proving which we intend to investigate in depth in the future. The work reported in this paper is in an early state, and by no means finished. We present and discuss our proposal in order to get feedback from the Calculemus community.

Popular culture continues fuelling public imagination with things, human and non-human, that we might beco-me or confront. Besides robots, other significant tropes in popular fiction that generated images include non-human humans and cyborgs, wired into his-torically varying sociocultural realities. Robots and artificial intelligence are re-defining the natural order and its hierar-chical structure. This is not surprising, as natural order is always in flux, shaped by new scientific discoveries, especially the reading of the genetic code, that reveal and redefine relationships between (...) life forms. However, for the first time, a new, artificial, species is being introduced into the existing diagrams, and, for the first time, it appears to hybridise the anthro-pocentric natural world order. (shrink)

Modernist Architecture and Ruins: On Ruins as a Minus, Neoclassicism and the Uncanny.

Ovaj rad bavi se presjekom umjetnosti, imaginacije, emocija i etičkog obrazovanja iz perspektive inovativne sinteze kognitivne teorije emocija i Gestalt pedagogije. Jedan od elemenata ove sinteze kognitivna je teorija emocija kakvu podržava Martha Nussbaum. Emocije se shvaćaju kao procjene koje se odnose na percepciju svijeta oko nas. Emocije su naši stavovi, razumijevanja i evaluacije svijeta iz perspektive naših ciljeva i projekata. To se pokazalo kao odlična polazišna točka za proučavanje emocija i drugih domena unutar etike obrazovanja. U ovom radu uvodim (...) pojam ‘iskustvene imaginacije’ i ukazujem na njezine metodologije koje smo razvili kao dio istraživanja preklapanja Gestalt pedagogije, kognitivne teorije emocija i pristupa etici iz perspektive umijeća življenja. Potom predstavljam sintezu kognitivne teorije emocija i Gestalt pedagogije, nakon čega razjašnjavam koncept iskustvene imaginacije, naglašavam njezinu ulogu u etičkom obrazovanju te zaključujem s nekolicinom osvrta na pristup umijeća življenja etici i etičkom obrazovanju. The paper discusses the intersection between art, imagination, emotions, and ethical education from the perspective of an innovative synthesis of cognitive theory of emotion and Gestalt pedagogy. One of the elements of this synthesis is the cognitive theory of emotion as endorsed by Martha Nussbaum. Emotions are understood as evaluative judgments that are related to our perception of the world around us. Emotions are our attitudes, understandings, and assessments of the world from the perspective of our goals and projects. This proves an excellent starting point from which to address them as an essential part of ethics education. Next, art and imagination are considered as a vehicle by which to address emotions and other domains within ethics education. Here, I introduce the concept of “experiential imagining” and point to the methodologies that sustain it. I have developed this concept as part of my research on the overlap between Gestalt pedagogy, cognitive theory of emotion, and the art of life approaches to ethics. Next, I present the synthesis between cognitive theory of emotion and Gestalt pedagogy. I then illuminate the concept of experiential imagination, emphasise its role in ethics education, and conclude with some reflections on the art of life approach to ethics and ethics education. (shrink)

The paper discusses the intersection between art, imagination, emotions, and ethical education from the perspective of an innovative synthesis of cognitive theory of emotion and Gestalt pedagogy. One of the elements of this synthesis is the cognitive theory of emotion as endorsed by Martha Nussbaum. Emotions are understood as evaluative judgments that are related to our perception of the world around us. Emotions are our attitudes, understandings, and assessments of the world from the perspective of our goals and projects. This (...) proves an excellent starting point from which to address them as an essential part of ethics education. Next, art and imagination are considered as a vehicle by which to address emotions and other domains within ethics education. Here, I introduce the concept of “experiential imagining” and point to the methodologies that sustain it. I have developed this concept as part of my research on the overlap between Gestalt pedagogy, cognitive theory of emotion, and the art of life approaches to ethics. Next, I present the synthesis between cognitive theory of emotion and Gestalt pedagogy. I then illuminate the concept of experiential imagination, emphasise its role in ethics education, and conclude with some reflections on the art of life approach to ethics and ethics education. (shrink)

Entrepreneurs’ wellbeing is of unprecedented importance given their crucial role in national economies in terms of job creation and innovation. In this research, we used a mixed methods approach to investigate the direct and indirect mechanisms by which entrepreneurs’ wellbeing mediates the effects of stress on perceived entrepreneurial success. We theorize that entrepreneurs experience work-related stress and that the level of perceived wellbeing mediates the relationship between the entrepreneurs’ stress and perceived success. We also hypothesize moderation effects by dispositional positive (...) affect. We find that stress has direct negative effects on entrepreneurs’ wellbeing and perceived success. However, an experience of positive affect significantly weakens the negative effects of stress by broadening and building entrepreneurs’ cognitions. Drawing from our theoretical and empirical findings, we discuss implications for theory and practice in the domain of entrepreneurs’ wellbeing. (shrink)

Arhitektura se kot veščina in kasneje kot lepa umetnost od antike naprej vpisuje v polje filozofskega raziskovanja. Namen članka je prikazati razumevanje arhitekture v sklopu hermenevtične filozofije s prikazom mišljenja njenih treh velikih mislecev: Heideggra, Gadamerja in Vattima, ki bodo na področje arhitekture stopali z ontološkega in z estetskega vidika. Heidegger tako arhitekturo razume kot temeljno potezo biti, Gadamerju je najodličnejša umetnostna forma, kjer je tudi oblika presežena z vsebino, Vattimo pa poda tri vidike arhitekture v postmoderni dobi, ki jih (...) poveže s simultanostjo, simulakri in vprašanjem ornamentalnosti.Architecture as a skill, and later as a form of fine art, has been included in the field of philosophical research since Antiquity. The purpose of this article is to present the understanding of architecture within the field of hermeneutic philosophy by describing the ideas of three great hermeneutic philosophers: Heidegger, Gadamer and Vattimo, who approach architecture from the ontological and aesthetic point of view. Heidegger interprets architecture as a fundamental trait of existence; Gadamer values it as the artistic form par excellence, with the form surpassed by the contents, too; and Vattimo discusses three possible ways of perceiving architecture in the postmodern society, related to simultaneity, simulacra and the question of ornamentality. (shrink)

Many surveys confirm a substantial number of discipline problems in schools, but not many surveys are aimed at their identification. Identification of discipline violations is indispensable for prudent planning of their interventions in and prevention of their occurrence. Earlier studies focused mostly on the teachers’ perceptions of discipline problems and they were not interested in how discipline problems are perceived by students. In this study, teachers and students identified the most frequent and disturbing discipline violations. Given the results of the (...) survey, it would be necessary to pay more attention to preventing disruption of lessons and improper attitude, which are, in the views of teachers and students alike, the most frequent and disturbing violations. (shrink)

Digital piracy as a continuing problem significantly impacts various stakeholders, including consumers, enterprises, and countries. This study develops a three-level mechanism of determinants of consumer digital piracy behavior, with personal risk as an individual factor, susceptibility to interpersonal influence as an inter-personal factor, and moral intensity as a broad societal factor. Further, it explores the role of rationalization and future piracy intent as outcomes of past piracy behaviors. The authors use survey data from four countries in the European Union to (...) test the system of structural relationships. With an exception of the effect of consumers’ susceptibility to interpersonal influence on piracy behavior, the conceptual model receives remarkably consistent support across the four countries. Specifically, perception of personal risk and moral intensity negatively affected the reported piracy behavior in all four countries. The results further support the negative influence of moral intensity and the positive influence of past digital piracy behavior on consumers’ use of rationalization. Lastly, personal risk, rationalization, and past digital piracy behavior directly influenced consumers’ intention to engage in digital piracy in the future. The study also discusses implications of the findings and identifies areas of future research. (shrink)

In recent decades, the development of sciences and technologies had a significant impact in society. This impact has been object of analysis from several standpoints, i.e., scientific, communication, historical and anthropological. Consequently, serious changes were required by the society. One of these has been the emerging relationship science in society and its foundations of applied sciences. A related foundational challenging is the educational process, which was and still is an unlimited challenge for teachers and professors: i.e., levels of understanding, curricula, (...) activing critical engagement, transfer knowledge—and—skills, management, classroom and subsequently pre-service teachers need special teacher education. Taking into account Joule’s bicentenary commemoration in physics and Nature of Science teaching (NoS) this paper introduces to a level of inquiring within historical and NoS approaches in the pre-service teachers, typically science, technology, engineering and mathematics. In particular, history and historiography of Joule’s physics (e.g., his arguments on electric–magnetic engine, mechanical equivalent of heat and free expansion) are dealt with. (shrink)

We give a sound and complete axiomatization of a probabilistic extension of intuitionistic logic. Reasoning with probability operators is also intuitionistic (in contradistinction to other works on this topic), i.e., measure functions used for modeling probability operators are partial functions. Finally, we present a decision procedure for our logic, which is a combination of linear programming and an intuitionistic tableaux method.

Plagiarism and other transgressions of the norms of academic integrity appear to be a persistent problem among upper secondary students. Numerous surveys have revealed high levels of infringement of what appear to be clearly stated rules. Less attention has been given to students’ understanding of academic integrity, and to the potential misconceptions and false beliefs that may make it difficult for them to comply with existing rules and handle complex real-life situations.In this paper we report findings from a survey of (...) European upper secondary students’ views on issues relating to academic integrity. We relate these findings to the students’ training about academic integrity, self-reported level of questionable behavior and country of study.A total of 1654 students at 51 institutions located in 6 European countries participated in the study. The participants generally believed they had a good understanding of the rules applying to them and knew how to behave in compliance with norms of academic integrity. The results indicate, however, that often, in practice, this belief was mistaken. Many students had an inadequate understanding of core elements of academic integrity. They were uncertain about how to act, and they struggled in the handling of complex situations that require context-sensitive judgement. While some differences between countries were identified, they were modest and exhibited no clear pattern. Our results also suggest that reducing students’ level of uncertainty and, to a lesser degree, improving their level of knowledge could lead them to engage less in certain types of questionable behaviours. Surprisingly, the effect of academic training is modest and ambiguous. The study also confirms that perception of peer behaviour has the strongest association with student engagement in questionable behaviours. Thus, academic integrity at the upper secondary level cannot be explained simply in terms of individual ethics or knowledge. (shrink)

In recent decades, the development of sciences and technologies had a significant impact in society. This impact has been object of analysis from several standpoints, i.e., scientific, communication, historical and anthropological. Consequently, serious changes were required by the society. One of these has been the emerging relationship science in society and its foundations of applied sciences. A related foundational challenging is the educational process, which was and still is an unlimited challenge for teachers and professors: i.e., levels of understanding, curricula, (...) activing critical engagement, transfer knowledge—and—skills, management, classroom and subsequently pre-service teachers need special teacher education. Taking into account Joule’s bicentenary commemoration in physics and Nature of Science teaching this paper introduces to a level of inquiring within historical and NoS approaches in the pre-service teachers, typically science, technology, engineering and mathematics. In particular, history and historiography of Joule’s physics are dealt with. (shrink)

Good academic practice is more than the avoidance of clear-cut cheating. It also involves navigation of the gray zones between cheating and good practice. The existing literature has left students’ understanding of gray zone practices largely unexplored. To begin filling in this gap, we present results from a questionnaire study involving N = 1639 undergraduate students from seven European countries representing all major disciplines. We show that large numbers of these students are unable to identify gray area issues and lack (...) sensitivity to the context dependence of these. We also show that a considerable proportion of students have a poor understanding of concepts like plagiarism and falsification, not only in gray zone scenarios, but also in cases of relatively clear-cut cheating. Our results are similar across the faculties and countries of study, and even for students who have attended academic integrity training. We discuss the implications of this for academic integrity training. (shrink)

In response to the growing importance of environmental issues, more and more consumers are turning to anti-consumption by reducing, rejecting, or avoiding consumption. Covering the intersection of sustainable consumption and anti-consumption, previous studies relied on socio-cognitive models to explain this decision. In order to extend their findings, we consider the moral and emotional perspectives to examine reducing consumption for environmental reasons in a particular context, i.e. air travel. It is against this backdrop that we propose a conceptual model that includes (...) moral foundations as the main antecedent, followed by anticipated guilt and personal responsibility, while intention to reduce consumption (i.e. air travel) for environmental reasons, positive word of mouth about reducing air travel (WOM) and environmental activism represent the outcomes. The proposed model is tested on a sample of 511 respondents from a UK online consumer panel. Our results confirm the importance of moral foundations, anticipated guilt and personal responsibility and their interplay in the prediction of intention to reduce consumption for environmental reasons. Anticipated guilt influences WOM, while personal responsibility influences activism. In addition, intentions to reduce consumption for environmental reasons have a positive impact on WOM and environmental activism. There are several implications for public policy makers and NGOs that fight against climate change that derive from these findings, as well as research opportunities for academics interested in this topic. (shrink)

Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.