On the Logic of β-pregroups

In this paper we concentrate mainly on the notion of β-pregroups, which are pregroups (first introduced by Lambek [18] in 1999) enriched with modality operators. β-pregroups were first proposed by Fadda [11] in 2001. The motivation to introduce them was to limit (locally) the associativity in the calculus considered. In this paper we present this new calculus in the form of a rewriting system, prove the very important feature of this system - that in a given derivation the non-expanding rules must always proceed non-contracting ones in order the derivation to be minimal (normalization theorem). We also propose a sequent system for this calculus and prove the cut elimination theorem for it. As an illustration we show how to use β-pregroups for linguistical applications. Special Issue Categorial Grammars and Pregroups Edited by Wojciech Buszkowski and Anne Preller     

Dynamic doxastic logic: why,how, and where to?

We investigate the research programme of dynamic doxastic logic (DDL) and analyze its underlying methodology. The Ramsey test for conditionals is used to characterize the logical and philosophical differences between two paradigmatic systems, AGM and KGM, which we develop and compare axiomatically and semantically. The importance of Gärdenfors’s impossibility result on the Ramsey test is highlighted by a comparison with Arrow’s impossibility result on social choice. We end with an outlook on the prospects and the future of DDL.     

Covenants and reputations

In their classic analyses, Hobbes and Hume argue that offensively violating a covenant is irrational because the offense ruins one’s reputation. This paper explores conditions under which reputation alone can enforce covenants. The members of a community are modeled as interacting in a Covenant Game repeated over time. Folk theorems are presented that give conditions under which the Humean strategy of performing in covenants only with those who have never offensively violated or performed with an offensive violator characterizes an equilibrium of the repeated Covenant Game. These folk theorems establish that for certain ideal settings Hobbes’ and Hume’s arguments against offensively violating covenants are compelling. However, these ideal settings presuppose that the community has certain mechanisms that generate common knowledge of the identities of those with whom one should perform. I analyze the results of computer simulations of the interactions in a community whose members must rely upon private communication alone. The computer simulation data show that in this community, reputation effects cannot effectively deter members from offensively violating covenants. I conclude that Hobbes’ and Hume’s warnings against offensive violation are compelling only on condition that the community is sufficiently structured to generate common knowledge among its members. I also conclude that even in such structured communities, the Humean strategy is not the uniquely “correct” policy.     

More on Putnam’s models: a reply to Belloti

In an earlier paper, I claimed that one version of Putnam's model-theoretic argument against realism turned on a subtle, but philosophically significant, mathematical mistake. Recently, Luca Bellotti has criticized my argument for this claim. This paper responds to Bellotti's criticisms.     

How are base‐rates used,when they are used: a comparison of additive and Bayesian models of base‐rate use

Previous research has uncovered many conditions that encourage base‐rate use. The present research investigates how base‐rates are used when conditions are manipulated to encourage their use in the lawyer/engineer paradigm. To examine the functional form of the response to base‐rate, a factorial design was employed in which both base‐rate and the individuating information were varied within‐subject. We compared the performance of several models of base‐rate use, including a model that allows base‐rate and individuating information to be combined in a strictly additive fashion, and a model which presumes that respondents use Bayes' Rule in forming their judgments. Results from 1493 respondents showed that the additive model is a stronger predictor of base‐rate use than any other model considered, suggesting that the base‐rate and individuating information are processed independently in the lawyer/engineer paradigm. A possible mechanism for this finding is discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Analogy Between the Theorem of Pythagoras and the Relations of Uncertainty of Heisenberg

In this work I propose an analogy between Pythagoras's theorem and the logical-formal structure of Werner Heisenberg's “relations of uncertainty.” The reasons that they have pushed to me to place this analogy have been determined from the following ascertainment: Often, when in exact sciences a problem of measurement precision arises, it has been resolved with the resource of the elevation to the square. To me it seems also that the aporie deriving from the uncertainty principle can find one solution with the resource to this stratagem. In fact, if the first classic example of the argument is the solution of the incommensurability between catheti and the hypotenuse of the triangle rectangle, one of the last cases is that which is represented from Heisenberg's principle of uncertainty.     

一种可融入额外信息的机器学习诊断法

研究将PNN和曼哈顿距离、贝叶斯定理相结合,提出了一种相对简洁的可融入额外信息的认知诊断法MB-PNN,通过模拟和实证研究考察了MB-PNN的有效性和适宜性,得到以下结论:(1)M-PNN的判准率高于PNN,表明将PNN中的ED修改为MD是适宜的;(2)MB-PNN的判准率较M-PNN和PNN高,表明基于多种信息的判别较基于单一信息的判别更为精准;(3)MB-PNN保留了PNN原有的非参数优势,基本不受知识状态分布和样本容量影响;(4)MB-PNN最能区分不同类型的学生,在认知诊断评估实践中更为适宜。     

Improving Accuracy on Bayesian Inference Problems Using a Brief Tutorial

Research suggests that most people struggle when asked to interpret the outcomes of diagnostic tests such as those presented as Bayesian inference problems. To help people interpret these difficult problems, we created a brief tutorial, requiring less than 10 minutes, that guided participants through the creation of an aid (either graph or table) based on an example inference problem and then showed the correct way to calculate the positive predictive value of the problem (i.e., likelihood that positive tests correctly indicate presence of condition). Approximately 70% of those in each training condition found the correct response on at least one problem in the format for which they were trained. Just under 55% of those in the control condition (i.e., no training) were able to find the correct response on at least one table or graph problem. We demonstrated a relationship between numeracy and performance on both problem formats, although we did not find evidence for a relationship between graph literacy and performance for either problem format. Potential improvements to and applications of the tutorial are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

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.