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.     

Social skills training for juvenile delinquents

Twenty-seven incarcerated juvenile delinquents matched on the number of previous offenses, age, WISC-R IQ, and locus of control were assigned to a Social Skills. Discussion or Control group. Social skills training consisted of instruction, feedback, modeling, behavior rehearsal, social reinforcement and graduated homework assignments. All subjects were assessed before and after treatment on a variety of self-report, role-play and behavioral measures. Analyses of variance for difference scores indicated that the Social Skills group improved significantly more than the Discussion and Control groups, which did not differ. Appropriate interpersonal skills were learned, state anxiety was reduced, internal locus of control was increased, and significant shifts in adjustment to the institutional program were evidenced for the Social Skills group.     

Dispositional inference from effects of actions: Effects chosen and effects forgone

One hundred and forty-six subjects made comparative judgments as to which of two hypothetical actors they were most confident possessed a choice-related trait, and which was most extreme on that trait dimension. Each actor was portrayed as making a choice from a set of actions; the choice sets varied independently in the number of effects eliminated by the choice and in the number of effects remaining after choice. Results confirmed Jones and Davis' (1965) hypothesis that correspondence would be inversely related to the number of effects remaining after choice. In addition, correspondence was directly related to number of effects eliminated by the choice when effects remaining did not differ. When given both sources of information, subjects preferred to use information from effects remaining.     

高校学生医疗保障制度改革的设想：目标、原则与模式

提出了高校学生医疗保障制度改革的目标是建立与我国经济发展水平相适应的新的医疗保障制度,指出改革应遵循公平、责任共担和强制性等原则,并构建了以社会基本医疗保险为基础,以医疗救助和补充医疗保险为辅助的高校学生医疗保障新模式。     

中国历史上的农村贫困医疗救助

从医学史的角度回顾我国历史上的济贫思想和实践,分析不同时代农村医疗救助的形式、内容和特点,指出农村贫困医疗救助具有悠久历史传统,现代意义上的医疗救助是社会保障体制的重要组成部分,充分利用我国乡村社会以情感和道德为主体的互助历史传统,建立与经济社会发展相适应的贫困医疗救助制度是当今政府和社会的重要任务,也是历史发展的必然要求。     

Reasons and Requirements

In this essay I defend the claim that all reasons can ground final requirements. I begin by establishing a prima facie case for the thesis by noting that on a common-sense understanding of what finality is, it must be the case that all reasons can ground such requirements. I spend the rest of the paper defending the thesis against two recent challenges. The first challenge is found in Joshua Gert’s recent book, Brute Rationality. In it he argues that reasons play two logically distinct roles – requiring action and justifying action. He argues, further, that some reasons – ‘purely justificatory’ reasons – play only the latter role. Jonathan Dancy offers the second challenge in his Ethics Without Principles, where he distinguishes between the ‘favoring’ and ‘ought-making’ roles of reasons. While all reasons play the former role, some do not play the latter, and are therefore irrelevant to what one ought to do. My contention is that both Gert and Dancy are going to have trouble accounting for our intuitions in a number of cases.

The seven virtues of simple type theory

Simple type theory, also known as higher-order logic, is a natural extension of first-order logic which is simple, elegant, highly expressive, and practical. This paper surveys the virtues of simple type theory and attempts to show that simple type theory is an attractive alternative to first-order logic for practical-minded scientists, engineers, and mathematicians. It recommends that simple type theory be incorporated into introductory logic courses offered by mathematics departments and into the undergraduate curricula for computer science and software engineering students.     

Addressing moral problems through practical reasoning

In this paper, following the work of Hare, we consider moral reasoning not as the application of moral norms and principles, but as reasoning about what ought to be done in a particular situation, with moral norms perhaps emerging from this reasoning. We model this situated reasoning drawing on our previous work on argumentation schemes, here set in the context of Action-Based Alternating Transition Systems. We distinguish what prudentially ought to be done from what morally ought to be done, consider what legislation might be appropriate and characterise the differences between morally correct, morally praiseworthy and morally excusable actions. We also describe an implementation which simulates this reasoning and discuss some issues arising from the simulation.     

Kant and Rousseau on the Critique of Philosophical Theology: The Primacy of Practical Reason

This paper explores the Rousseauian background to Kant’s critique of metaphysics and philosophical theology. The core idea is that the rejection of metaphysics and philosophical theology is part of a turn from theoretical to practical reason influential on European philosophy of religion, a turn we associate with Kant but that is prefigured by Rousseau. Rousseau is not, however, a thinker normally associated with the notion of metaphysical criticism, nor the notion of the primacy of practical reason. The paper draws out this dimension of Rousseau’s thinking and its importance for Kantian thought. It will proceed by discussing the Kant-Rousseau connection; demonstrate the importance of practical philosophy for Kant and the critical project generally; overview Kant’s critique of metaphysics; and turn to a consideration of Rousseau, particularly from the text émile. Given the indisputable influence of Rousseau on Kant, the purpose of this paper is to explore the ways that Rousseau’s own rejection of philosophical theology might be suggestive to those interested in Kant and the way in which it throws new light on Kant’s philosophy of religion. As well as drawing out the Kant-Rousseau connection, it also, implicitly, defends the general orientation of these philosophers as one that is important, perhaps vital, to philosophy of religion.