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In this study, we start by proposing a causal induction model that incorporates symmetry bias. This model is important in two aspects. First, it can reproduce causal induction of human judgment with higher accuracy than conventional models. Second, it allows us to estimate the level of symmetry bias of subjects from experimental data. We further propose an inference method that incorporates the aforementioned causal induction model into Bayesian inference. In this method, the component of Bayesian inference, which updates the degree of confidence for each hypothesis, and the component of inverse Bayesian inference that modifies the model of the hypothesis coexist. Our study demonstrates that inverse Bayesian inference enables us to deal flexibly with unstable situations where the object of inference changes from time to time.nnAuthor summaryWe acquire knowledge through learning and make various inferences based on such knowledge and observational data (evidence). If the evidence is insufficient, then the certainty of the conclusion will decline. Moreover, even if the evidence is sufficient, the conclusion may be wrong if the knowledge is incomplete in the first place. In order to model such inference based on incomplete knowledge, we proposed an inference system that performs learning and inference simultaneously and seamlessly. Prepare two coins A and B with different probabilities of landing heads, and repeat the coin toss using either of them. However, the coin that is being tossed is also replaced repeatedly. The system observes only the result of coin toss each time, and estimates the probability of landing heads of coin tossed at the moment. In this task, it is necessary not only to estimate the probabilities of the landing heads of coin A and B, but also to estimate which coin is being used at the moment. In this paper, we show that the proposed system handles such tasks very efficiently by simultaneously performing inference and learning.

In the present paper the self-consistency or operational closure of autopoiesis is described by introducing time explicitly. It is an extension of Spencer-Brown's idea of time, however. The definition of time is segregated into two parts, corresponding to the syntax and semantics of language, respectively. In this context, time reversibility is defined by the formalization of the relationship between time and self-consistency. This idea has also been discussed in the context of designation and/or naming. Here we will discuss it in the context of cellular automata and explain the structure of one-to-many type mappings. Our approach is the first attempt to extend autopoietic systems in terms of dynamics. It illustrates how to introduce an autopoietic time which looks irreversible, but without the concept of entropy.

Pigment color patterns of molluscs are studied from the viewpoint of autonomy. Brownian algebra developed by Spencer-Brown (1969) is extensively used for the expression of cellular-automaton rules. When asynchronous updating is introduced for the transition of cellular automata, various kinds of patterns such as traveling waves, kinks, oscillatory local patterns etc. are generated from the same transitional rule. The type of patterns depends more sensitively on the asynchronous updating relationship rather than the transitional rule itself. Therefore, pattern changes in ontogeny can be explained without any changes in transitional rules or reaction processes. It is proposed that asynchronousness is intrinsic to living systems and that recognition of the intrinsic time is essential in understanding living systems.