MizarMode—an integrated proof assistance tool for the Mizar way of formalizing mathematics

The Emacs authoring environment for Mizar (MizarMode) is today the authoring tool of choice for many (probably the majority of) Mizar authors. This article describes the MizarMode and focuses on the proof assistance functions and tools available in it.

We start with the explanation of the design principles behind the Mizar system, and show how these design principles—mainly the concentration on simple and intuitive human-oriented proofs—have helped Mizar in developing and maintaining a very large body of formalized mathematics.

Mizar is a non-programmable and non-tactical verifier: the proofs are developed in the traditional “write—compile—correct” software programming loop. While this method is in the beginning more laborious than the methods employed in tactical and programmable proof assistants, it makes the “proof code” in the long-run more readable, maintainable and reusable. This seems to be a crucial factor for a long-term and large-scale formalization effort.

MizarMode has been designed with the aim to facilitate this kind of proof development by a number of “code-generating”, “code-browsing” and “code-searching” methods, and tools programmed or integrated within it. These methods and tools now include, e.g., the automated generation of proof skeletons, semantic browsing of the articles and abstracts, structured viewing, proof advice using trained machine learning tools like the Mizar Proof Advisor, deductive tools like MoMM, etc. We give an overview of these proof-assistance tools and their integration in the MizarMode, and also discuss some emerging and future extensions such as integration of external theorem proving assistance.     

SAD as a mathematical assistant—how should we go from here to there?

The System for Automated Deduction (SAD) is developed in the framework of the Evidence Algorithm research project and is intended for automated processing of mathematical texts. The SAD system works on three levels of reasoning: (a) the level of text presentation where proofs are written in a formal natural-like language for subsequent verification; (b) the level of foreground reasoning where a particular theorem proving problem is simplified and decomposed; (c) the level of background deduction where exhaustive combinatorial inference search in classical first-order logic is applied to prove end subgoals.

We present an overview of SAD describing the ideas behind the project, the system's design, and the process of problem formalization in the fashion of SAD. We show that the choice of classical first-order logic as the background logic of SAD is not too restrictive. For example, we can handle binders like Σ or lim without resort to second order or to a full-powered set theory. We illustrate our approach with a series of examples, in particular, with the classical problem .     

从郭靖习武管窥中国人的教育心理观

郭靖习武的过程蕴涵着许多教育学和心理学的深刻道理。本文从郭靖习武的四个阶段来管窥我国传统文化下浓厚的教育心理学思想,由此得出了在学习中的一个理论：多元智力理论,两个误区：学生先天缺陷观和重德轻才观,三点建议：激发学生兴趣、摒弃“齐步走”的做法和学以致用。     

Factors associated with a positive attitude towards change among employees during the early phase of a downsizing process

Most research on organizational changes in working life, including downsizing, focuses on the negative attitudes and negative consequences of the change. The aim of this study was to evaluate if the employee's previous learning experience and characteristics of the working environment were associated with positive attitudes towards organizational change. The 467 employees (73.5% males) working in a global oil company in the early phases of a downsizing process were asked to answer a questionnaire with demographic variables, perception of the working environment, and attitude to change (93% response rate). Corporate social responsibility (CSR), involvement and participation, team leadership and team effectiveness were important factors related to positive attitudes towards organizational change. Non-leaders and older employees were positive to change. We conclude that employees' perceptions of their psychosocial working environment, in particular the CSR, were highly related to their attitude to organizational change.     

Post hoc versus predictive accounts of children’s theory of mind: A reply to Ruffman

Ruffman (2014) argues for a minimalist account of infants’ performance on theory of mind tasks. This commentary argues that because Ruffman’s minimalist account is post hoc, it neither generates testable predictions about how infants will respond in new situations, nor does it offer a coherent explanation for existing false-belief findings. An alternative, mentalist account is presented. This account integrates infancy findings with prior theory of mind literature and generates novel predictions about children’s false belief performance.     

A Book for None? Teaching Biblical Studies to Millennial Nones

The millennial generation is distinctive for several reasons, not the least is its growing religious disaffiliation. Given a growing disinterest in religion in general and the Bible in particular especially among the fast growing group of millennial “nones” how can biblical studies classes still be seen as appealing and relevant? This article seeks to answer this question by examining the identity and concomitant values of millennials. As a result of this analysis I argue that while the Bible as inherent authority may be quickly losing its appeal, the Bible as an example of human creativity, group reflection, political rhetoric, and social discourse makes the study of the Bible particularly relevant for millennials contemplating careers in the global marketplace even if the importance of the Bible itself is waning for this generation. I show how in my introductory New Testament class I attempt to implement these ideas.     

Counterfactual thinking and false belief: the role of executive function

The purpose of the current study was to examine further the relationship between counterfactual thinking and false belief (FB) as examined by Guajardo and Turley-Ames (Cognitive Development, 19 (2004) 53-80). More specifically, the current research examined the importance of working memory and inhibitory control in understanding the relationship between counterfactual thinking and FB. Participants were 3-, 4-, and 5-year-olds (N = 76). Counterfactual thinking statements generated accounted for significant variance in FB performance beyond age and language. Working memory and inhibitory control each partially mediated the relationship between counterfactual thinking and FB performance. The maturation of executive functioning skills is important in children’s developing understanding of counterfactual reasoning and FB.     

A Farewell to Countertransference

The "discovery" of countertransference provided a much-needed corrective to the one-sided view of transference and a patient's pathology. Even if its usefulness in the development of psychoanalysis was indisputable, its days are numbered. When I present my clinical work at conferences, I am often asked questions about my countertransference. These questions contain numerous assumptions that are challenged in this paper. Treatment is discussed from a self psychological perspective to highlight the therapeutic value of enabling the patient to engage a selfobject transference. The concept of "projective identification" is also challenged. Systems theory, in which the therapeutic relationship is understood as a co-construction between therapist and patient, is proposed as a more effective model to deal with the issues formerly included under transference-countertransference.     

Belonging without commitment: the Christocentric view and the traditionist perspective on modern religion

This essentially theoretical article suggests a novel way to conceptualise the middle spaces of people whose link to religion is perceived as partial and fragmentary – the vast majority of the population in the world of the twenty-first century, who belong to a religious tradition but are quite selective in their observances. We first argue that current conceptualisation of the middle spaces suffers from a predisposition we view as ‘Christocentric’. As the key to an alternative and non-Christocentric approach, we suggest the concept of ‘traditionism’, which permits a new theoretical discussion of the meanings of religion for contemporary individuals who belong to a religious tradition but are not fully committed to its current authorities or affiliated with recognised denominations. As a case study to clarify the new, non-Christocentric conceptualisation, we suggest the religious identity of contemporary ‘Arab Jews’ – Jews whose families originated in the Muslim Middle East – to highlight the potential contribution of a certain Jewish perspective to an understanding of modern religion as tradition and of modern practitioners of religion who belong to no denomination as ‘traditionists’.