偏好变化的一个量化模型

偏好是哲学、博弈论、决策论和效益理论等学科的核心概念,偏好及其逻辑性质在行为哲学和理性选择理论中尤其占有十分重要的地位。偏好的概念使得我们对世界的看法变得多姿多彩,它驱使着我们在尘世的种种行为选择。然而,偏好不是静止不变的,建议、命令、以及其他的信息不断改变着我们的偏好。近年来,逻辑学家们开始对偏好的改变进行深入的研究。到目前为止,关于偏好变化的模型主要有以下两种：第一、采取AGM理论研究偏好变化,给出变化的逻辑公设。第二、采用新近发展起来的动态认知逻辑的方法,对偏好的具体变化机制进行研究,给出动态偏好逻辑系统。无论是上面提到的哪种方法,都是采用定性的视角,即,偏好被表示成一个序关系。与此相反,本文采取量化的视角来研究偏好,利用偏好赋值函数给出偏好的量化语义。就逻辑语言而言,我们给出一个包括命题常元的新语言。这个语言既简练又富于表达力。基于这样的量化语义,处理偏好变化的方法就与以往的方法有所不同。根据经典的乘积更新的机制,我们提出了新的加法规则和一个参数化规则,来刻画偏好赋值的细微变化之处。同时,我们给出一个动态认知赋值逻辑,并证明其完全性。此外,我们还考虑道义逻辑最近的一些研究成果,表明本文给出的模型同样适用于道义的情境。特别是,这个新的模型能够解决困扰人们已久的义务冲突问题。最后,针对赋值偏好模型,我们定义了适用于它“赋值互模拟”。而且,我们还进一步给出了一个新的互模拟概念“距离互模拟”以结束本文。     

从方法论的角度看动态认知逻辑的研究

本文主要探讨动态认知逻辑技术结果背后的思想,着重强调其在方法论方面的一般想法。文章在公开宣告逻辑的基础上展开讨论,重点考察了归约公理的意义,揭示了其本质是在基本语言中提前解析动态信息对认知产生的影响。文章以公共知识为例,说明了并非所有的逻辑算子都能找到归约公理,有时候我们需要丰富基本语言的表达力。而且,我们从如何给出一个逻辑的角度提出,动态认知逻辑实际上是在“动态化”认知逻辑,这种动态化的方法可以应用在其他静态的逻辑系统中。我们以动态偏好逻辑为例,说明了这一过程是如何实现的。     

基于直觉主义逻辑的隐偏好分析

根据偏好及其变化是否在逻辑语言及语义模型中有直接的反映,可以将其分为隐偏好和显偏好。本文旨在对含有隐偏好信息的逻辑进行研究,基于对直觉主义逻辑中的认知信息的分析,通过修改直觉主义逻辑的语义解释提出了隐偏好逻辑,并证明了该逻辑系统的可靠性和相对于可区分模型类的完全性;最后,通过定义哥德尔式的翻译映射将隐偏好逻辑嵌入到偏好逻辑中。     

在动态认知逻辑中融合观察与内省

一直以来,我们使用逻辑系统来描述数学的证明、结构的计算以及语言的意义。近年来,逻辑系统却越来越多地被用来研究理性行动者的很多方面。例如,如何接受单一的信息,多主体间的交流行为,以及更为一般的受目标驱动的主体间的互动。特别是,对观察和交流中的信息流的研究,大家使用所谓的知识更新、信念修正和偏好改变的动态认知逻辑。当新信息进来时,这些逻辑使用信息的“语义意义”作为被更新状态的选择范围。 然而,同样重要的是,理性主体的行动也会基于其他信息,譬如,由推理和反省得到的信息。对这些问题的研究实际上是对信息在更为语法的意义上进行理解的,即,把信息看作是可以由主体阐明的东西。也许有些奇怪,尽管在这一领域已经存在不少的研究方案,但是大家对什么是信息,信息的关键机制是什么等问题更少有一致的意见。可以看出,对“信息”的意义在逻辑中确实有很多不同的理解。 本文基于可能世界的语义,给出一个一致的信息模型,同时也赋予可能世界语法的“可及通路”。这样,我们就能把外部的“更新信息”和内部的“阐明信息”放在同一个动态逻辑系统中。特别是,我们提出了两个基本的信息行动：纯粹的基于观察的更新（“单纯的看”）和把不明显的知识变为明显知识的“知觉实现”。我们阐明为什么这些行动是自然的,同时我们也提出了一些新的研究问题。其中,很多问题探讨如何使其他的逻辑传统,包括信念修正理论、情景语义学和弗协调逻辑等适用于信息一驱使的理性行动者的图景。     

不确定性对策略性投票的影响（英文）

如果选民不确定其他选民的偏好以及其他选民对他本人偏好的知晓程度,选票操纵的策略会变得更复杂。为了研究这种认知不确定性对策略性投票的影响,本文提供了一个形式分析框架并定义了选票操纵、优势偏好、均衡票况等概念。我们发现:即使真实偏好相同但关于偏好的高阶知识不同也会影响均衡票况。另外,本文还研究了不确定性的更新对选票操纵的影响,如某位选民对他本人的偏好进行公开宣告。我们证明了有些形式的选票操纵和均衡票况可以在这样的更新下得到保持,而另一些则不能被保持。最后,我们用一个逻辑语言形式化了不确定性选举的相关概念。本文的目的是给出一个分析和设计面向不确定性的投票机制的技术基础。     

亚里士多德对“偏好”如是说

亚里士多德在《前分析篇》和《论辩篇》中提出了关于“偏好”的理论。本文从现代偏好逻辑的观点分析亚里士多德的偏好理论,作者认为亚里士多德提出了“强偏好”和“无差别偏好”等概念,提出了“强偏好的完全性”、“强偏好的不对称性”、“强偏好的换质位”以及“强偏好的合取扩展”等等原理。作者希望本文的分析能对现代偏好逻辑的研究提供一些资料。     

一个用于表达因果关系的ATL的扩展

CTL模型检测技术已被广泛应用于形式验证领域。交互时态逻辑（ATL）是对CTL的一个扩展,用于表达多主体博弈结构上的性质。ATL使用合作算子来表达多个主体能够通过合作保证系统的设计目标。在实际应用中,我们需要知道主体的行动与系统的输出状态之间具有因果关系。在本文中,我们通过引入新的模态算子扩展ATL,使得这种因果关系得到表达。我们使用两种方式的扩展。其中之一是从主体的能力出发,直观上,如果一些主体可以通过合作的行动来保证系统进入某个状态,同时,这些主体也可以通过合作的行动保证系统不进入这个状态,则这些主体的行动与该系统状态间具有更强的因果关系。我们使用的另一种方式是从系统状态出发。我们考虑要想使系统进入某状态,哪些主体的行动的必不可少的,哪些主体的行动是充分的但非必要的条件。在本文中,我们扩展后的逻辑CATL和SATL表达力强于ATL,但计算复杂性与ATL相同。     

读逻辑RL与任意读逻辑AL

本文认为文献(van Ditmarsch et.al.,2007)对认知行动"读"形式化时,语法与语义混淆,给出的语法和语义不够直观、自然。本文在形式化认知行动"读"时,严格区分语法和语义,在形式上更直观自然、更易理解;在此基础上,给出读逻辑RL的公理系统,并证明其可靠性和完全性。另外,本文还对认知行动"读"的量化进行研究,给出了这个量化逻辑AL的形式化。在表达力方面,本文还得到如下结果:(1)读逻辑RL、公开宣告逻辑、认知逻辑以及单认知主体的任意读逻辑AL表达力相等;(2)多认知主体的任意读逻辑AL的表达力要严格大于认知逻辑、读逻辑和公开宣告逻辑。     

群体中的知识和行为（英文）

本文讨论关于世界的信念和关于他人信念的信念如何指导主体(成人、儿童和动物)行动。如果我们知道一个人的偏好和他的信念,那么我们可以某种程度上预测他的行为。而如果我们知道他们的偏好,那么我们就可以通过他们的行为来推测他们信念。文学作品和现实生活中都有一些相关的例子。我们还给出了一个形式框架,这个框架是不依赖纳什均衡,而是接受非确定论,并且采用信息观点下的被占优策略概念。     

论康德义务第一命题的调和式主张

康德认为只有出于义务而不出于任何偏好的行为才具有道德价值。这个"义务的第一命题"在当代遭到了来自德性伦理学的强烈反对,他们认为情感才能表达对人的关切,也才具有真正的道德价值。当代一些康德学者试图维护康德的主张,认为在康德那里并不排斥情感,情感或偏好可以融入康德的行动理论。帕顿、亨森、赫尔曼以及阿利森采取了不同的方案,或认为康德的论述更多地出于方法上的考虑,或构筑行动模型表明情感在有道德价值行动中的地位。这种解释方式可以被称为调和式主张。但是他们的解释存在着各自的问题,不仅不符合康德的原意,且本身也问题丛生。调和式主张的根本问题在于以经验性动机理论解释行动,而康德是在意志的规定根据上来确定行动的道德价值。     

社会群体中的偏好逻辑

在许多多主体偏好逻辑系统中,主体之间是没有联系的,因而无法描述主体间的偏好互动。借鉴＂The Logic in the Community＂一文中称为＂群体压力＂的例子对偏好的影响,本文在＂The Logic in the Community＂所提出的系统构架上,加入偏好算子和两个动态算子,通过构造归约公理说明这些算子可以被无偿添加,并借助这些规约公理证明了系统的完全性。     

Hintikka’s Logical Revolution

Hintikka thinks that second-order logic is not pure logic, and because of Gödel’s incompleteness theorems, he suggests that we should liberate ourselves from the mistaken idea that first-order logic is the foundational logic of mathematics. With this background he introduces his independence friendly logic (IFL). In this paper, I argue that approaches taking Hintikka’s IFL as a foundational logic of mathematics face serious challenges. First, the quantifiers in Hintikka’s IFL are not distinguishable from Linström’s general quantifiers, which means that the quantifiers in IFL involve higher order entities. Second, if we take Wright’s interpretation of quantifiers or if we take Hale’s criterion for the identity of concepts, Quine’s thesis that second-order logic is set theory will be rejected. Third, Hintikka’s definition of truth itself cannot be expressed in the extension of language of IFL. Since second-order logic can do what IFL does, the significance of IFL for the foundations of mathematics is weakened.     

Logical dynamics of some speech acts that affect obligations and preferences

In this paper, illocutionary acts of commanding will be differentiated from perlocutionary acts that affect preferences of addressees in a new dynamic logic which combines the preference upgrade introduced in DEUL (dynamic epistemic upgrade logic) by van Benthem and Liu with the deontic update introduced in ECL II (eliminative command logic II) by Yamada. The resulting logic will incorporate J. L. Austin’s distinction between illocutionary acts as acts having mere conventional effects and perlocutionary acts as acts having real effects upon attitudes and actions of agents, and help us understand why saying so can make it so in explicit performative utterances. We will also discuss how acts of commanding give rise to so-called “deontic dilemmas” and how we can accommodate most deontic dilemmas without triggering so-called “deontic explosion”.     

Preschoolers are able to take merit into account when distributing goods

Classic studies in developmental psychology demonstrate a relatively late development of equity, with children as old as 6 or even 8-10 years failing to follow the logic of merit--that is, giving more to those who contributed more. Following Piaget (1932), these studies have been taken to indicate that judgments of justice develop slowly and follow a stagelike progression, starting off with simple rules (e.g., equality: everyone receives the same) and only later on in development evolving into more complex ones (e.g., equity: distributions match contributions). Here, we report 2 experiments with 3- and 4-year-old children (N = 195) that contradict this constructivist account. Our results demonstrate that children as young as 3 years old are able to take merit into account by distributing tokens according to individual contributions but that this ability may be hidden by a preference for equality.     

萨奎斯特逻辑的格

以萨奎斯特公式为额外公理添加到极小正规逻辑K上得到的逻辑都是完全的。这样得到的逻辑被称为萨奎斯特逻辑。所有的萨奎斯特逻辑组成了一个格。这个格中有可数无穷长的链以及可数无穷长的反链,格中的每个逻辑相对于格的不完全度是1。另外,萨奎斯特逻辑格的子格E具有规整的结构。     

Preference-based belief revision for rule-based agents

Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief revision for agents which reason in a simpler logic than full first-order logic, namely rule-based reasoners. We show that it is possible to define a contraction operation for rule-based reasoners, which we call McAllester contraction, which satisfies all the basic Alchourrón, Gärdenfors and Makinson (AGM) postulates for contraction (apart from the recovery postulate) and at the same time can be computed in polynomial time. We prove a representation theorem for McAllester contraction with respect to the basic AGM postulates (minus recovery), and two additional postulates. We then show that our contraction operation removes a set of beliefs which is least preferred, with respect to a natural interpretation of preference. Finally, we show how McAllester contraction can be used to define a revision operation which is also polynomial time, and prove a representation theorem for the revision operation.     

Von Wright’s <Emphasis Type="Italic">“The Logic of Preference”</Emphasis> revisited

Preference is a key area where analytic philosophy meets philosophical logic. I start with two related issues: reasons for preference, and changes in preference, first mentioned in von Wright’s book The Logic of Preference but not thoroughly explored there. I show how these two issues can be handled together in one dynamic logical framework, working with structured two-level models, and I investigate the resulting dynamics of reason-based preference in some detail. Next, I study the foundational issue of entanglement between preference and beliefs, and relate the resulting richer logics to belief revision theory and decision theory.     

Monism, Emergence, and Plural Logic

In this paper I argue that we need to take irreducibly plural logic more seriously in metaphysical debates due to the fact that the verdict of many metaphysical debates hangs on it. I give two examples. The main example I focus on is the debate recently revived by Jonathan Schaffer over the fundamental cardinality of the world. I show how the three main arguments provided by Schaffer are unsound in virtue of an employment of plural logic. The second example I give is a more general issue about the possibility of emergent properties of mereological wholes. Employing plural logic there is a new way to understand such cases. The upshot is that plural logic greatly matters to metaphysics and hence can no longer be ignored the way it has in this area.     

Extreme malleability of preferences: Absolute preference sign changes under uncertainty

Malleability of preferences is a central tenet of behavioral decision theory. How malleable preferences really are, however, is a topic of debate. Do preference reversals imply preference construction? We argue that to claim preferences are construed, a demonstration of more extreme preference malleability than simple preference reversals is required: absolute preference sign changes within participants. If respondents value a prospect positively in 1 condition but negatively in a different condition, preferences cannot be considered stable. Such absolute preference sign changes are possible under uncertainty. In 2 incentive‐compatible experiments, we found participants were willing to pay to take part in a gamble and also demanded to be compensated to take part in a subsequent gamble with identical outcomes and probabilities. Such absolute preference sign changes within participants led to simultaneous risk aversion and risk seeking for the same risky prospect, suggesting that, at least in the domain of risky decisions, consumers' preferences are indeed malleable and construed.