A Map of Common Knowledge Logics

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole.     

人格特质与认知操作关系的初步研究

本研究采用NEO PI R测试 ,以逻辑推理为认知操作指标 ,初步考察了人格特质与大学生认知操作的关系。结果表明 :①神经质、外倾性与逻辑推理有显著负相关 ,开放性则与之呈正相关 ;②人格特质和认知操作关系的偏相关分析与相关分析的结果基本一致 ;③多元逐步回归分析显示 ,外倾性与逻辑推理有负性预测关系 ,开放性及严谨性则与逻辑推理有正性预测关系 ;④人格特质与认知操作的关系受操作难度、认知任务和兴趣类型等因素制约。     

Living up to one's commitments: Agency, strategies and trust

In human social interaction, the notions of commitment and trust are strongly interrelated. A formal model for this interrelation will enable artificial agents to benefit from the associated reduction of complexity and improved possibilities for cooperation. We argue that the notion of living up to one's commitments, rather than actual fulfillment, plays the key role in the trust–commitment interrelation, and we propose a formal analysis of that notion in the framework of agents and strategies in branching time. The main technical innovation is a stringency ordering on an agent's strategies that allows one to classify what an agent does as more or less appropriate with respect to a given commitment, leading to a fine-grained assessment of trustworthiness.     

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.     

回到思想史:先秦名学研究的新路向

Discussions of name (ming, 名) during the pre-Qin and Qin-Han period of Chinese history were very active. The concept ming at that time can be divided into two categories, one is the ethical-political meaning of the term and the other is the linguistic-logical understanding. The former far exceeds the latter in terms of overall influence on the development of Chinese intellectual history. But it is the latter that has received the most attention in the 20th century, due to the influence of Western logic. This has led to the result of a bias in the contemporary studies of ming. Changing course by returning to the correct path of intellectual history can providing an objective and thorough ordering of the pre-Qin discourse on ming. Translated by Joseph E. Harroff from Shandong Daxue Xuebao 山东大学学报 (Journal of Shandong University), 2007, (2): 59–64     

A new formulation of the Principle of Indifference

The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for.     

The Craig Interpolation Theorem in abstract model theory

The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics is small.     

Formal Methods in the Philosophy of Science

In this article, we reflect on the use of formal methods in the philosophy of science. These are taken to comprise not just methods from logic broadly conceived, but also from other formal disciplines such as probability theory, game theory, and graph theory. We explain how formal modelling in the philosophy of science can shed light on difficult problems in this domain.     

Dynamic Deontic Logic and its Paradoxes

In Meyer’s promising account [7] deontic logic is reduced to a dynamic logic. Meyer claims that with his account “we get rid of most (if not all) of the nasty paradoxes that have plagued traditional deontic logic.” But as was shown by van der Meyden in [4], Meyer’s logic also contains a paradoxical formula. In this paper we will show that another paradox can be proven, one which also effects Meyer’s “solution” to contrary to duty obligations and his logic in general. Presented by Hannes Leitgeb     

Quantified coalition logic

We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in game-like multi-agent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express such properties as “every coalition satisfying property P can achieve φ” and “there exists a coalition C satisfying property P such that C can achieve φ”. We give an axiomatisation of QCL, and show that while it is no more expressive than Coalition Logic, it is nevertheless exponentially more succinct. The complexity of QCL model checking for symbolic and explicit state representations is shown to be no worse than that of Coalition Logic, and satisfiability for QCL is shown to be no worse than satisfiability for Coalition Logic. We illustrate the formalism by showing how to succinctly specify such social choice mechanisms as majority voting, which in Coalition Logic require specifications that are exponentially long in the number of agents.