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.

Building on the analysis of Bonanno (Artificial Intelligence, 2025) we introduce a simple modal logic containing three modal operators: a unimodal belief operator, a bimodal conditional operator and the unimodal global operator. For each AGM axiom for belief revision, we provide a corresponding modal axiom. The correspondence is as follows: each AGM axiom is characterized by a property of the Kripke-Lewis frames considered in Bonanno (Artificial Intelligence, 2025) and, in turn, that property characterizes the proposed modal axiom.

A central result in the AGM framework for belief revision is the construction of revisionfunctions in terms of total preorders on possible worlds. These preorders encode comparative plausibility: r r' states that the world r is at least as plausible as r'. Indifference in the plausibility of two worlds, r, r', denoted r r', is defined as the absence of a preference between r and r'. Herein we take a closer look at plausibility indifference. We contend that the transitivity of indifference assumed in the AGM framework is not always a desirable property for comparative plausibility. Our argument originates from similar concerns in preference modelling, where a structure weaker than a total preorder, called a semiorder, is widely consider to be a more adequate model of preference.

The AGM paradigm for belief change, as originally introduced by Alchourrón, Gärdenfors and Makinson, lacks any guidelines for the process of iterated revision. One of the most influential work addressing this problem is Darwiche and Pearl's approach (DP approach, for short), which, despite its well-documented shortcomings, remains to this date the most dominant. In this article, we make further observations on the DP approach. In particular, we prove that the DP postulates are, in a strong sense, inconsistent with Parikh's relevance-sensitive axiom (P), extending previous initial conflicts. Immediate consequences of this result are that an entire class of intuitive revision operators, which includes Dalal's operator, violates the DP postulates, as well as that the Independence postulate and Spohn's conditionalization are inconsistent with axiom (P). The whole study, essentially, indicates that two fundamental aspects of the revision process, namely, iteration and relevance, are in deep conflict, and opens the discussion for a potential reconciliation towards a comprehensive formal framework for knowledge dynamics.

In this article, the epistemic-entrenchment and partial-meet characterizations of Parikh's relevance-sensitive axiom for belief revision, known as axiom (P), are provided. In short, axiom (P) states that, if a belief set $K$ can be divided into two disjoint compartments, and the new information $\varphi$ relates only to the first compartment, then the revision of $K$ by $\varphi$ should not affect the second compartment. Accordingly, we identify the subclass of epistemic-entrenchment and that of selection-function preorders, inducing AGM revision functions that satisfy axiom (P). Hence, together with the faithful-preorders characterization of (P) that has already been provided, Parikh's axiom is fully characterized in terms of all popular constructive models of Belief Revision. Since the notions of relevance and local change are inherent in almost all intellectual activity, the completion of the constructive view of (P) has a significant impact on many theoretical, as well as applied, domains of Artificial Intelligence.

AGM contraction and revision assume an underlying logic that contains propositional logic. Consequently, this assumption excludes many useful logics such as the Horn fragment of propositional logic and most description logics. Our goal in this paper is to generalise AGM contraction and revision to (near-)arbitrary fragments of classical first-order logic. To this end, we first define a very general logic that captures these fragments. In so doing, we make the modest assumptions that a logic contains conjunction and that information is expressed by closed formulas or sentences. The resulting logic is called first-order conjunctive logic or FC logic for short. We then take as the point of departure the AGM approach of constructing contraction functions through epistemic entrenchment, that is the entrenchment-based contraction. We redefine entrenchment-based contraction in ways that apply to any FC logic, which we call FC contraction. We prove a representation theorem showing its compliance with all the AGM contraction postulates except for the controversial recovery postulate. We also give methods for constructing revision functions through epistemic entrenchment which we call FC revision; which also apply to any FC logic. We show that if the underlying FC logic contains tautologies then FC revision complies with all the AGM revision postulates. Finally, in the context of FC logic, we provide three methods for generating revision functions via a variant of the Levi Identity, which we call contraction, withdrawal and cut generated revision, and explore the notion of revision equivalence. We show that withdrawal and cut generated revision coincide with FC revision and so does contraction generated revision under a finiteness condition.

Two essential tasks in managing description logic knowledge bases are eliminating problematic axioms and incorporating newly formed ones. Such elimination and incorporation are formalised as the operations of contraction and revision in belief change. In this paper, we deal with contraction and revision for the DL-Lite family through a model-theoretic approach. Standard description logic semantics yields an infinite number of models for DL-Lite knowledge bases, thus it is difficult to develop algorithms for contraction and revision that involve DL models. The key to our approach is the introduction of an alternative semantics called type semantics which can replace the standard semantics in characterising the standard inference tasks of DL-Lite. Type semantics has several advantages over the standard one. It is more succinct and importantly, with a finite signature, the semantics always yields a finite number of models. We then define model-based contraction and revision functions for DL-Lite knowledge bases under type semantics and provide representation theorems for them. Finally, the finiteness and succinctness of type semantics allow us to develop tractable algorithms for instantiating the functions.

Two essential tasks in managing Description Logic (DL) ontologies are eliminating problematic axioms and incorporating newly formed axioms. Such elimination and incorporation are formalised as the operations of contraction and revision in belief change.In this paper, we deal with contraction and revision for the DL-Lite family through a model-theoretic approach.Standard DL semantics yields infinite numbers of models for DL-Lite TBoxes, thus it is not practical to develop algorithms for contraction and revision that involve DL models. The key to our approach is the introduction of an alternative semantics called type semantics which is more succinct than DL semantics. More importantly, with a finite signature, type semantics always yields finite humber of models.We then define model-based contraction and revision for DL-Lite TBoxesunder type semantics and provide representation theorems for them.Finally, the succinctness of type semantics allows us to develop tractable algorithms for both operations.

The dynamic nature of ontology development has motivated the formal study of ontology evolution problems. This paper presents a logical framework that enables fine-grained investigation of evolution problems at a deductive level. In our framework, the optimal evolutions of an ontology O are those ontologies O′ that maximally preserve both the structure of O and its entailments in a given preservation language. We show that our framework is compatible with the postulates of Belief Revision, and we investigate the existence of optimal evolutions in various settings. In particular, we present first results on TBox-level revision and contraction in the EL and FL0 families of Description Logics.

This paper investigates belief revision where the underlying logic is that governing Horn clauses. It proves to be the case that classical (AGM) belief revision doesn’t immediately generalise to the Horn case. In particular, a standard construction based on a total preorder over possible worlds may violate the accepted (AGM) postulates. Conversely, Horn revision functions in the obvious extension to the AGM approach are not captured by total preorders over possible worlds. We address these difficulties by first restricting the semantic construction to "well behaved" orderings; and second, by augmenting the revision postulates by an additional postulate. This additional postulate is redundant in the AGM approach but not in the Horn case. In a representation result we show that these two approaches coincide. Arguably this work is interesting for several reasons. It extends AGM revision to inferentially-weaker Horn theories; hence it sheds light on the theoretical underpinnings of belief change, as well as generalising the AGM paradigm. Thus, this work is relevant to revision in areas that employ Horn clauses, such as deductive databases and logic programming, as well as areas in which inference is weaker than classical logic, such as in description logic.