We present an approach to incorporating qualitative assertions of conditional irrelevance into belief revision, in order to address the limitations of existing work which considers only unconditional irrelevance. These assertions serve to enforce the requirement of minimal change to existing beliefs, while also suggesting a route to reducing the computational cost of belief revision by excluding irrelevant beliefs from consideration. In our approach, a knowledge engineer specifies a collection of multivalued dependencies that encode domain-dependent assertions of conditional irrelevance in the knowledge base. We consider these as capturing properties of the underlying domain which should be taken into account during belief revision. We introduce two related notions of what it means for a multivalued dependency to be taken into account by a belief revision operator: partial and full compliance. We provide characterisations of partially and fully compliant belief revision operators in terms of semantic conditions on their associated faithful rankings. Using these characterisations, we show that the constraints for partially and fully compliant belief revision operators are compatible with the AGM postulates. Finally, we compare our approach to existing work on unconditional irrelevance in belief revision.

The policy of rational belief revision is encoded in the so-called AGM revision functions. Such functions are characterized (both axiomatically and constructively) within the well-known AGM paradigm, proposed by Alchourrón, Gärdenfors and Makinson. In this article, we show that - although not in a straightforward way - a sufficient extension of the underlying language allows for the modelling of any AGM revision function (defined at the initial language), by means of a Hamming-based rule for belief revision introduced by Dalal (defined at the extended language). The established results enrich the applicability of Dalal's proposal, leading to a conceptual and ontological reduction, as well as open new doors for the construction of any type of revision function in a practical context, given the intuitive appeal and simplicity of Dalal's construction.

The AGM paradigm for belief change, as originally introduced by Alchourron, 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.

Abstract Parikh’s relevance-sensitive axiom (P) for belief revision is open to two different interpretations, i.e. the weak and the strong version of (P), both of which are plausible depending on the context. Given that strong (P) has not received the attention it deserves, in this article, an extended examination of it is conducted. In particular, we point out interesting properties of the semantic characterization of the strong version of (P), as well as a vital feature of it that, potentially, results in a significant drop on the resources required for an implementation of a belief-revision system. Lastly, we shed light on the natural connection between global and local revision functions, via their corresponding semantic characterization, hence, a means for constructing global revision functions from local ones, and vice versa, is provided.

Notwithstanding the extensive work on iterated belief revision, there is, still, no fully satisfactory solution within the classical AGM paradigm. The seminal work of Darwiche and Pearl (DP approach, for short) remains the most dominant, despite its well-documented shortcomings. In this article, we make further observations on the DP approach. Firstly, 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 (P). Lastly, we show that the DP postulates allow for more revision polices than the ones that can be captured by identifying belief states with total preorders over possible worlds, a fact implying that a preference ordering (over possible worlds) is an insufficient representation for a belief state.

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.

Answer Set Programming is a declarative problem solving approach, initially tailored to modelling problems in the area of Knowledge Representation and Reasoning. In this article, we provide a knowledge-based system, capable of representing and reasoning about legal knowledge in the context of Answer Set Programming - thus, modelling non-monotonicity that is inherent in legal arguments. The work, although limited to a specific indicative domain, namely, university regulations, has a variety of extensions. The overall approach constitutes a representative implementation of the Answer Set Programming's modelling methodology, as well as an enhancing of the bond between Artificial Intelligence and Legal Science, bringing us a step closer to a successful development of an automated legal reasoning system for real-world applications.

In artificial intelligence, a key question concerns how an agent may rationally revise its beliefs in light of new information. The standard (AGM) approach to belief revision assumes that the underlying logic contains classical propositional logic. This is a significant limitation, since many representation schemes in AI don’t subsume propositional logic. In this article, we consider the question of what the minimal requirements are on a logic, such that the AGM approach to revision may be formulated. We show that AGM-style revision can be obtained even when extremely little is assumed of the underlying language and its semantics; in fact, one requires little more than a language with sentences that are satisfied at models, or possible worlds. The classical AGM postulates are expressed in this framework and a representation result is established between the postulate set and certain preorders on possible worlds. To obtain the representation result, we add a new postulate to the AGM postulates, and we add a constraint to preorders on worlds. Crucially, both of these additions are redundant in the original AGM framework, and so we extend , rather than modify , the AGM approach. As well, iterated revision is addressed and the Darwiche/Pearl postulates are shown to be compatible with our approach. Various examples are given to illustrate the approach, including Horn clause revision, revision in extended logic programs, and belief revision in a very basic logic called literal revision .

In this article, we provide the epistemic-entrenchment characterization of the weak version of Parikh’s relevance-sensitive axiom for belief revision — known as axiom (P) — for the general case of incomplete theories. Loosely speaking, axiom (P) states that, if a belief set K can be divided into two disjoint compartments, and the new information φ relates only to the first compartment, then the second compartment should not be affected by the revision of K by φ. The above-mentioned characterization, essentially, constitutes additional constraints on epistemic-entrenchment preorders, that induce AGM revision functions, satisfying the weak version of Parikh’s axiom (P).

In this paper we show that, contrary to what is the case in what concerns contractions by a single sentence, there is not a system of spheres-based construction of multiple contractions which generates each and every transitively relational partial meet multiple contraction. Furthermore, we propose two system of spheres-based constructions of multiple contractions which generate (only) transitively relational partial meet multiple contractions.

Multiple Belief Change extends the classical AGM framework for Belief Revision introduced by Alchourron, Gardenfors, and Makinson in the early ’80s. The extended framework includes epistemic input represented as a (possibly infinite) set of sentences , as opposed to a single sentence assumed in the original framework. The transition from single to multiple epistemic input worked out well for the operation of belief revision. The AGM postulates and the system-of-spheres model were adequately generalized and so was the representation result connecting the two. In the case of belief contraction however, the transition was not as smooth. The generalized postulates for contraction, which were shown to correspond precisely to the generalized partial meet model , failed to match up to the generalized epistemic entrenchment model . The mismatch was fixed with the addition of an extra postulate, called the limit postulate , that relates contraction by multiple epistemic input to a series of contractions by single epistemic input. The new postulate however creates problems on other fronts. First, the limit postulate needs to be mapped into appropriate constraints in the partial meet model. Second, via the Levi and Harper Identities, the new postulate translates into an extra postulate for multiple revision, which in turn needs to be characterized in terms of systems of spheres. Both these open problems are addressed in this article. In addition, the limit postulate is compared with a similar condition in the literature, called (K*F), and is shown to be strictly weaker than it. An interesting aspect of our results is that they reveal a profound connection between rationality in multiple belief change and the notion of an elementary set of possible worlds (closely related to the notion of an elementary class of models from classical logic).

The original AGM paradigm focuses only on one-step belief revision and leaves open the problem of revising a belief state with whole sequences of evidence. Darwiche and Pearl later addressed this problem by introducing extra (intuitive) postulates as a supplement to the AGM ones. A second shortcoming of the AGM paradigm, seemingly unrelated to iterated revision, is that it is too liberal in its treatment of the notion of relevance. Once again this problem was addressed with the introduction of an extra (also very intuitive) postulate by Parikh. The main result of this paper is that Parikh postulate for relevance-sensitive belief revision is inconsistent with each of the Darwiche and Pearl postulates for iterated belief revision.

The theme of this special issue is the formalization of commonsense reasoning, i.e. the kind of reasoning that people perform in their everyday lives. Its very name suggests that there is nothing much to it—everyone does it, so how hard can it be? It turns out however that commonsense reasoning is a rather intricate business, much harder to formalize than other more classical types of reasoning, such as mathematical reasoning. The main difficulty with commonsense reasoning is that, in contrast to expert reasoning (e.g. economic, legal, medical, etc.), much of the knowledge that is required for commonsense inferences is implicit. Take for example the following scenario: ‘John picked up the newspaper and walked to the kitchen. He made some coffee and started reading about last night's soccer match’. Based on this information alone, the average person would infer that John is now in the kitchen (and therefore he is not in the garden), drinking coffee and reading his newspaper, which is also in the kitchen, and which contains an article about a soccer match that took place the night before.

In his seminal paper in 1988, Grove provided possible-world semantics for the axiomatic approach to belief revision proposed by Alchourron, Gardenfors, and Makinson. Grove's semantics are based on a system of spheres, which is essentially a total preorder on possible worlds, satisfying a particular smoothness condition called the limit assumption. In this article we build upon Grove's representation result working in two (related) directions. In particular, the first part of the article considers a number of smoothness conditions (variants of the limit assumption) as additional constraints to systems of spheres, and studies their implications for AGM belief revision. Such smoothness conditions are of particular importance in the context of multiple revision, that is, revision with respect to a (possibly infinite) set of sentences. In the second part of the article we examine closely this process and, in the spirit of Grove, we provide a constructive model for multiple revision based on systems of spheres and prove the corresponding representation result. Finally, we examine ways of reducing multiple revision to classical AGM sentence revision, and we devise a particular smoothness condition which is shown to be necessary and sufficient for such a reduction.

The Possible Models Approach (PMA) introduced by Winslett, proposes, among other things, a domain-independent criterion for measuring similarity between different states of a dynamic system. The concept of similarity between states (possible worlds) appears also in the area of Belief Revision in the form of a system of spheres. Systems of spheres are in turn connected to epistemic entrenchments by means of the AGM revision functions that the two structures induce. In view of these connections, in this article we study the implications of adopting PMA's criterion of similarity in the context of Belief Revision. More precisely, we formulate conditions that capture PMA's criterion of similarity in terms of systems of spheres (PMA systems of spheres) and we provide an axiomatic characterization of the class of epistemic entrenchments corresponding to systems of spheres that comply with PMA's criterion of similarity (PMA epistemic entrenchments). We also discuss some interesting properties of the class of PMA system of spheres and PMA epistemic entrenchments. Our study is primarily motivated by the role that PMA epistemic entrenchments can play in Reasoning about Action.