Modeling Naïve Causality in Everyday Reasonig with Fuzzy Logic

By Iandoli, Luca; Ponsiglione, Cristina et al. | Fuzzy Economic Review, May 2016 | Go to article overview

Modeling Naïve Causality in Everyday Reasonig with Fuzzy Logic

Iandoli, Luca, Ponsiglione, Cristina, Zollo, Giuseppe, Fuzzy Economic Review

1.FUZZY CAUSAL REASONING

Consider a statement like the following: "In bad weather conditions there are usually more car accidents. Bad weather always increases traffic congestion, which often escalates the probability of car accidents. We can reduce the occurrence of car accidents by increasing police patrols frequency. Indeed, more patrolling significantly reduces reckless driving behavior, which strongly reduces car accidents". This type of reasoning can be modeled through fuzzy causal maps1 (Kosko, 1992, 1997).

Fuzzy causal maps in the original formulation are similar to traditional causal maps except for the fact that they allow for degree of truth both in the activation of nodes and on the strength of the edge between any two nodes. For Kosko fuzzy causal maps are similar to neural networks, thus to each node a threshold function can be associated so that the concept Ci associated to the node i-th is activated when the causal input exceeds a give threshold Ti.

In this paper we build on Kosko's approach and similar extensionsand propose a model of fuzzy inference to capture the linguistic uncertainty contained in verbal descriptions provided by human beings when describing scenarios involving the presence of causal relationships.

This uncertainty is often expressed through the use of fuzzy qualifiers employed to weaken or strengthen causal assertions such as usually, often, most of the time, seldom, etc. For example one can say that usually bad weather causes an increase in car accidents in order to express a certain degree of confidence on the rule that bad weather is a good causal explanation for car accidents.

On the other hand, causal rules such this one can be modelled through fuzzy approximate reasoning, but it is well known that when the number of antecedent and consequent exceeds a few ones, as it happens in causal maps, rule-based systems become to cumbersome to be managed.

In many cases, however, it is important to model causal reasoning in a simpler and more manageable way by reaching a satisfying compromise between precision and complexity of the model. The approach proposed in this paper can be positioned in the literature on Linguistic Decision Making (Bonnissone, 1982; Chen and Hwang, 1992; Godo and Torra, 2000; Herrera and Herrera-Viedma, 2001 ; Yager, 1988, 1993, 1998; Zimmermann, 1991), and particularly in Zadeh's effort in modelling uncertain reasoning through the use of fuzzy probabilities and the perception based theory of decision making (Zadeh, 2000, 2002).

In section 2 we illustrate the theoretical foundation of our model based on cognitive theories on causal reasoning as explanation (Ahn and Bailenson, 1996; Goldwarg and Johnson-Laird, 2001; Johnson and Krems, 2000). In section 3 we present our inferential model; we will show that it is in fact a linguistic connective that generalize the concept of fuzzy equivalence and that there fore we term generalized fuzzy equivalence. In section 4 we analyze the properties of this connective and in section 5 we present an example of its application to the analysis of a fuzzy causal map.

2.EXPLANATION-BASED CAUSAL REASONING

It is possible to find many studies concerning explanation in many fields ranging from history of science (Hempel, 1965), philosophy of science (Thagard, 1992), cognitive psychology (Kelley, 1967), cognitive science (Keil and Watson, 2000), and artificial intelligence (Schank, 1986).

According to Thagard, explanation is an abductive form of reasoning (Peirce, 1935-1966) that is employed for the construction of rules able to produce facts that are observed in the real world. In the abductive approach, explaining new facts is like to complete a jigsaw puzzle in which one or more tiles are missing, the missing tiles being the rule able to explain a given set of facts, like in the following example:

a) Fact 1: public streets are dirtier than usual;

b) Rule construction (abduction): if public expenditures for street maintenance decrease than streets become dirtier;

c) Fact 2: public expenditures for street maintenancemight have been reduced. …

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