Artificial Neural Networks (ANNs) are powerful machine-learning models capable of capturing intricate non-linear relationships. They are widely used nowadays across numerous scientific and engineering domains, driving advancements in both research and real-world applications. In our recent work, we focused on the statics and dynamics of a particular subclass of ANNs, which we refer to as binary ANNs. A binary ANN is a feed-forward network in which both inputs and outputs are restricted to binary values, making it particularly suitable for a variety of practical use cases. Our previous study approached binary ANNs through the lens of belief-change theory, specifically the Alchourron, Gardenfors and Makinson (AGM) framework, yielding several key insights. Most notably, we demonstrated that the knowledge embodied in a binary ANN (expressed through its input-output behaviour) can be symbolically represented using a propositional logic language. Moreover, the process of modifying a belief set (through revision or contraction) was mapped onto a gradual transition through a series of intermediate belief sets. Analogously, the training of binary ANNs was conceptualized as a sequence of such belief-set transitions, which we showed can be formalized using full-meet AGM-style belief change. In the present article, we extend this line of investigation by addressing some critical limitations of our previous study. Specifically, we show that Dalal's method for belief change naturally induces a structured, gradual evolution of states of belief. More importantly, given the known shortcomings of full-meet belief change, we demonstrate that the training dynamics of binary ANNs can be more effectively modelled using robust AGM-style change operations -- namely, lexicographic revision and moderate contraction -- that align with the Darwiche-Pearl framework for iterated belief change.

Traditional approaches to non-monotonic reasoning fail to satisfy a number of plausible axioms for belief revision and suffer from conceptual difficulties as well. Recent work on ranked preferential models (RPMs) promises to overcome some of these difficulties. Here we show that RPMs are not adequate to handle iterated belief change. Specifically, we show that RPMs do not always allow for the reversibility of belief change. This result indicates the need for numerical strengths of belief.

In action domains where agents may have erroneous beliefs, reasoning about the effects of actions involves reasoning about belief change. In this paper, we use a transition system approach to reason about the evolution of an agent's beliefs as actions are executed. Some actions cause an agent to perform belief revision while others cause an agent to perform belief update, but the interaction between revision and update can be non-elementary. We present a set of rationality properties describing the interaction between revision and update, and we introduce a new class of belief change operators for reasoning about alternating sequences of revisions and updates. Our belief change operators can be characterized in terms of a natural shifting operation on total pre-orderings over interpretations. We compare our approach with related work on iterated belief change due to action, and we conclude with some directions for future research.