We consider the problem of modifying a description logic concept in light of models represented as pointed interpretations. We call this setting model change, and distinguish three main kinds of changes: eviction, which consists of only removing models; reception, which incorporates models; and revision, which combines removal with incorporation of models in a single operation. We introduce a formal notion of revision and argue that it does not reduce to a simple combination of eviction and reception, contrary to intuition. We provide positive and negative results on the compatibility of eviction and reception for EL-bottom and ALC description logic concepts and on the compatibility of revision for ALC concepts.

Despite significant efforts towards extending the AGM paradigm of belief change beyond finitary logics, the computational aspects of AGM have remained almost untouched. We investigate the computability of AGM contraction on non-finitary logics, and show an intriguing negative result: there are infinitely many uncomputable AGM contraction functions in such logics. Drastically, we also show that the current de facto standard strategies to control computability, which rely on restricting the space of epistemic states, fail: uncomputability remains in all non-finitary cases. Motivated by this disruptive result, we propose new approaches to controlling computability beyond the finitary realm. Using Linear Temporal Logic (LTL) as a case study, we identify an infinite class of fully-rational AGM contraction functions that are computable by design. We use Büchi automata to construct such functions, and to represent and reason about LTL beliefs.

We introduce novel classes of fully rational contraction operators for belief bases. These operators are founded on a plausibility relation on models, called tracks, that allow distinguishing between suitable and unsuitable models. We obtain three main representation theorems: the first one semantically characterises the class of partial-meet operators, which are related to the rationality postulate of relevance; while the second one semantically characterises the class of smooth kernel contraction operators, which are related to the postulates of core-retainment and relative closure. The third representation theorem semantically characterises the supplementary postulates (conjunction and intersection). We consider logics that are both Tarskian and compact.

We propose a new paradigm for Belief Change in which the new information is represented as sets of models, while the agent's body of knowledge is represented as a finite set of formulae, that is, a finite base. The focus on finiteness is crucial when we consider limited agents and reasoning algorithms. Moreover, having the input as arbitrary set of models is more general than the usual treatment of formulas as input. In this setting, we define new Belief Change operations akin to traditional expansion and contraction, and we identify the rationality postulates that emerge due to the finite representability requirement. We also analyse different logics concerning compatibility with our framework.

Restoring consistency of a knowledge base, known as consolidation, should preserve as much information as possible of the original knowledge base. On the one hand, the field of belief change captures this principle of minimal change via rationality postulates. On the other hand, within the field of inconsistency measurement, culpability measures have been developed to assess how much a formula participates in making a knowledge base inconsistent. We look at culpability measures as a tool to disclose epistemic preference relations and build rational consolidation functions. We introduce tacit culpability measures that consider semantic counterparts between conflicting formulae, and we define a special class of these culpability measures based on a fixed-point characterisation: the stable tacit culpability measures. We show that the stable tacit culpability measures yield rational consolidation functions and that these are also the only culpability measures that yield rational consolidation functions.

Belief change and non-monotonic reasoning are arguably different perspectives on the same phenomenon, namely, jettisoning of currently held beliefs in response to some incompatible evidence. Investigations in this area typically assume, among other things, that the underlying (background) logic is compact, that is, whatever can be inferred from a set of sentences X can be inferred from a finite subset of X. Recent research in the field shows that this compactness assumption can be dispensed without inflicting much damage on the AGM paradigm of belief change. In this paper we investigate the impact of such relaxation on non-monotonic logics instead. In particular, we show that, when compactness is not guaranteed, while the bridge from the AGM paradigm of belief change to expectation logics remains unaffected, the “return trip” from expectation logics to AGM paradigm is no longer guaranteed. We finally explore the conditions under which such guarantee can be given.

The main paradigms of belief change require the background logic to be Tarskian and finitary. We look at belief update when the underlying logic is not necessarily finitary. We show that in this case the classical construction for KM update does not capture all the rationality postulates for KM belief update. Indeed, this construction, being fully characterised by a subset of the KM update postulates, is weaker. We explore the reason behind this, and subsequently provide an alternative constructive accounts of belief update which is characterised by the full set of KM postulates in this more general framework.