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     

Determinants of the magnitude of willingness to accept relative to willingness to pay

In this paper we test two hypotheses that stem from the work of Mellers, Chang, Birnbaum and Ordonez ( 1992 ). The first hypothesis is that in a binary gamble, the ratio of WTA to WTP is decreasing in the probability attached to a nonzero event. The second hypothesis is that this ratio is independent of the size of stakes. We find support for the first hypothesis, but mixed support for the second. The second hypothesis holds in the case of gains, but not in the case of losses. Copyright © 2001 John Wiley & Sons, Ltd.     

Slippery Slopes and Collapsing Taboos

A slippery slope argument is an argument to this twofold effect. First, that if a policy or practice P is permitted, then we lack the dialectical resources to demonstrate that a similar policy or practice P* is not permissible. Since P* is indeed not permissible, we should not endorse policy or practice P. At the heart of such arguments is the idea of dialectical impotence, the inability to stop the acceptance of apparently small deviations from a heretofore secure policy or practice from leading to apparently large and unacceptable deviations. Using examples of analogical arguments and sorites arguments I examine this phenomenon in the context of collapsing taboos.     

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.     

Free-Variable Tableaux for Propositional Modal Logics

Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux.     

"[人]在[大场所]"材料范式下观察不到信息整合的原因初探

本研究采用扇效应技术来探求推翻G．A．Radvansky针对其1993年研究结果所作解释的证据。共分为两个分实验。实验1重复Radvansky1993年研究中的实验三,以取得中文材料的基线值,为实验2做准备;实验2通过在材料中使用同样具有可“移动性”的物体的概念(例如快餐车)来探讨“可移动性”是否是“[人]在[大场所]”材料范式下观察不到信息整合的根本原因。结果表明“人的可移动性”不是“[人]在[大场所]”．材料范式下观察不到信息整合的原因。     

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.