﻿ 条件句推理与基于Bayes法则的概率模型<br>Conditional Reasoning and Probabilistic Model Based on Bayes Rule

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Vol.2 No.5(2012), Article ID:7148,5 pages DOI:10.4236/AP.2012.25040

Conditional Reasoning and Probabilistic Model Based on Bayes Rule

Dingzhou Fei

Department of Psychology, Wuhan University, Wuhan

Email: dzhfei@yahoo.com.cn

Received: Sep. 19th, 2012; revised: Oct. 2nd, 2012; accepted: Oct. 13th, 2012

ABSTRACT：

Conditional reasoning is the difficult and central points in psychology of reasoning. The current models include the mental logic, mental model, Logic Programming and recent probabilistic model based on Bayes rule. This paper discusses the strengths and shortcomings of these models. It must be pointed out that the probabilistic model has many advantages in explaining relevant experimental results over the mental logic and mental model theories. However, this model can not successfully deal with the reasoning about counterfactuals. This paper ends with the comments that the graph model which derives from the Bayes rule may be a better theory than the probabilistic model related to the counterfactuals reasoning.

Keywords: Conditional Reasoning; Reasoning about Counterfactuals; Bayes Rule; Graph Model

Email: dzhfei@yahoo.com.cn

1. 推理心理学与条件句的研究

1) 如果天下雨，那么地是湿的

2) 如果天下雨，那么天是湿的

3) 如果天下雨，那么地是湿的

4) 如果天下雨，那么地是湿的

MP是指演绎推理的分离规则，MT是后件否定，AC是前件肯定，DA前件否定。

Source: Marcus and Rips, 1979

Figure 1. The comparison between the four forms of conditional reasoning

Johnson-Larid对推理心理学中的条件句推理提出了如下问题(Byrne and Johnson-Larid, 2009)：

1) 为什么有些条件句推理特别难？而当且仅当(if and only if)的推理很容易？

2) 条件句究竟是什么？

3) 在什么条件下条件句为真？

4) 为什么反事实条件句特别？

5) 一个条件句的否定是什么？

6) 什么是一个条件句的概率？

2. 有关条件句推理的假设和争论

H, B1, B2, …, Bn称为Horn子句，对应于通常的命题。

ALP理论的最大功劳是合理地解释了为什么选MT的人的比例为什么少，而且更重要的是它的发现：。而这与Mental rule理论和Mental model理论的共同假设和基础相矛盾，而反事实条件句就是这样的特征！这也是为什么把反事实条件句称为各种理论和模型的试金石。下面我们来讨论基于Bayes规则的模型。

3. 为什么是Bayes模型？

Bayes模型为什么是条件句推理的较为合适的模型？最主要的理由是它给出了不同的条件句推理现象的统一而简明的定量解释，使推理心理学的研究向模型和理论的完善前进了不少。Bayes模型是建立在Bayes规则概率模型，它使用信息增值的期望来表达人们在作假设选择时偏爱能带来最大不确定性的信息或证据的心理特征(Wason纸牌选择任务可以看做人们在作假设选择的过程)，它是对人类推理能力的理解作理性分析的组成部分(Anderson, 1991)。接下来是关于Bayes模型的主要内容。

Bayes规则是：用分别表示随机事件A，B， (条件事件)的概率，如果，则Bayes规则是

，且

Source: Oaksford & Chater, 1994

Figure 2. The fitting of optimal data selection (information selection) model for the experimental results

Source: Schroyens and Schaeken, 2003

Figure 3. The comprison between the mental rule model and the probabilistic model (A, B are the mental rule models; C, D are the probabilistic model based on the Bayes rule)

Bayes模型的数据最优选择分析程序是一个通用的解释模式，应用它可以解释范围广泛的选择任务实验结果，例如，条件句前件和后件是归纳相关的，涉及双向条件的，涉及否定形式的，涉及内容和主题效应的，基于社会规范的推理等(Oaksford & Chater, 1994)。到目前为止，Bayes模型是推理心理学里解释力最强的又有较为合理的理论基础的假设。从理论的简洁和解释力来比较，基于Bayes规则的概率模型是最优的。

4. 反事实条件句为什么是特殊的？

Anderson, J. (1991). Is human cognition adaptive? Behavioral and Brain Sciences, 14, 471-484.

Braine, M. D. S., & O’Brien, M. D. S. B. D. P. (1998). Mental logic. London: Routledge.

Byrne, R. M., & Johnson-Larid, P. N. (2009). “If” and the problems of conditional reasoning. Trends in Cognitive Science, 13, 282-287.

Evans, J. S., et al. (2005). Suppostion, extensionality and conditionals: A critique of Johnson-larid and Byrne (2002). Psychological Review, 112, 1040-1052.

Kowalski, R., & Sadri, F. (2009). Integrating logic programming and production systems in abductive logic programming agents. In: A Polleres, & T. Swift, (Eds)., Web reasoning and rule system. Springer, 5837.

Marcus, S. L., & Rips, L. J. (1979). Conditional reasoning. Journal of Verbal Learning and Verbal Behavior, 1, 199-223.

Oaksford, M., & Chater, N. (1994). A rational analysis of the selection task as optimal data selection. Psychological Review, 101, 608-631.

Oaksford, M., & Chater, N. (1996). Rational explanation of the selection task. Psychological Review, 103, 381-391.

Pearl, J. (2003). Causality: Models, reasoning and inference. Cambridge: Cambridge University.

Schroyens, W., & Schaeken, W. (2003). A critique of Oaksford, Chater and Larkin’s (2000) conditional probability model of conditional reasoning. Journal of Experimental Psychology: Learning, Memory and Cognition, 29, 140-149.

Stenning, K., & Van Lambalgen, M. (2008). Human reasoning and cognitive science. London: MIT press.