keywords: causal induction, symmetry bias, mutual exclusivity bias, n-armed bandit problem, trade-off between exploration and exploitation SummaryThrough numbers of studies on the formation of equivalence relations and causal induction, it is known that human beings tend to consider conditional statements "if p then q" as biconditional statements "if and only if p then q": we call the tendency to perceive "if p then q" as "if q then p" the "symmetry bias". On the other hand, many studies on children's word learning have pointed out that children tend to expect each object has only one label. This is so-called the "mutual exclusivity bias". This bias implies that children infer "if not p then not q" from "if p then q".These biases logically mislead human beings. What is the merit of these illogical induction? In this paper we address this question. First, we clarify the relationship between causal induction and the symmetry bias or and the mutual exclusivity bias. Secondly, we propose a new model of causal induction. Thirdly, we construct an agent which makes illogical decision based on causality, and assess the agent's performance for the task called "n-armed bandit problem" in the field of reinforcement learning. In this problem, it is known that there is a "trade-off between exploration and exploitation". According to our simulation, the agent can resolve the trade-off and achieve quite better performance than an agent without these biases.

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be circumvented by exploiting an elementary mechanics that surface bending strain decreases linearly with a thickness of a substrate. For example, flexible substrates with a thicknesses of 10 µm experience peak surface strain of only 0.1% upon bending to the radius of curvature of 5 mm, and this strain remains well below the fracture limits of semiconductors (≈1%), metals (1-2%), and hard coatings (1-3%); indeed, the use of a substrate within a range below tens of micrometers enables comparable growth, resulting in high-performance durable flexible devices for epidermal, implantable, and wearable applications (Figure 1b). [10-20] On the other hand, the development of foldable electronics devices that have thicknesses of hundreds of micrometers is an emerging challenge. This highlights the ever-growing importance of the substrates strategically designed to reduce surface strain without thinning (Figure 1a right and 1b). However, it is not yet possible to measure nanoscale surface bending strain in real time: none of the currently available advanced methods fulfill all of the necessary spatial-temporal resolution, accuracy, precision, and a wide range of measurable materials. Electrical strain sensors including strain gauges exemplify the most common strain analytical method. [21-23] Although they provide surface bending strains of materials targeted in real time, their With the rapid development of flexible electronics and soft robotics, there is an emerging topic of preventing fracture in materials and devices integrated on largely bending film substrates of >100 µm thickness. The high demand for strategically reducing strain in bending materials requires a facile method that enables one to accurately and precisely analyze the surface bending strain in a wide variety of materials. This study proposes the surface-labeled grating method that is the fundamental and efficient technique for measuring surface bending strains merely by labeling a thin, soft grating onto various film substrates composed of flexible polymeric and rigid inorganic materials. The surface strain with a single-nanoscale (<1.0 nm) can be quantified in real time with no need of material information such as Poisson's ratio, Young's modulus, and film thickness. The fracture limit of a hard coating overlying flexible substrates is successfully determined by the accurate and precise quantification of surface bending strains. Furthermore, a multilayer film substrate with surface bending strain reduced by 50% prevents fractures of hard coatings and organic thin film transistors (OTFTs) since the strains remain below the fracture limit under large bending.