Rational belief revision is commonly viewed as being based on a preference order between possible worlds, with the resulting new belief set being those sentences true in all the most preferred models of the incoming new information. Usually, such a preference order is taken to be a total preorder. Nevertheless, there are other, more general classes of ordering that can also be employed. In this paper, we explore two such classes that have been studied within the theory of rational choice but have seen limited or no application in belief revision. We begin with interval orders, introduced by Fishburn in the ’80s, which associate to each possible world a nonnegative ‘interval’ of plausibility. We then move on to biorders, studied by Aleskerov, Bouyssou, and Monjardet, which generalise interval orders by allowing the intervals to have negative lengths, a feature that can be used to capture a notion of dissonance or instability. We provide axiomatic characterisations of these two resulting families of belief revision operators, as well as of two further families of interest that lie between interval orders and biorders. We show that while biorder-based revisions satisfy the Success postulate, they do not always yield consistent outputs. By modifying their definition to discard inputs that lead to inconsistency as ‘incredible’, we derive new families of so-called nonprioritised revision that satisfy the Consistency postulate, but not the Success one. These families are linked to credibility-limited revision operators of Hansson et al., but for which the set of credible sentences does not satisfy the single-sentence closure condition. We argue that the biorder-based approach is well-suited for scenarios where an agent might initially reject new information, but may accept it when presented with additional explanation.

One of the most widely investigated decision problems in symbolic AI is that of which conditional sentences of the form “if α , then normally β ” should follow from a knowledge base containing this type of statements. Probably, the most notable approach to this problem is the rational closure construction put forward by Lehmann and Magidor in the'90s, which has been adapted to logical languages of various expressive powers since then. At the core of rational closure is the Rational Monotonicity property, which allows one to retain existing (defeasible) conclusions whenever new information cannot be negated by existing conclusions. As it turns out, Rational Monotonicity is not universally accepted, with many researchers advocating the investigation of weaker versions thereof leading to a larger class of consequence relations. A case in point is that of the Disjunctive Rationality property, which states that if one may draw a (defeasible) conclusion from a disjunction of premises, then one should be able to draw this conclusion from at least one of the premises taken alone. While there are convincing arguments that the rational closure forms the ‘simplest’ rational consequence relation extending a given set of conditionals, the question of what the simplest disjunctive consequence relation in this setting is has not been explored in depth. In this article, we do precisely that by motivating and proposing a concrete construction of the disjunctive rational closure of a conditional knowledge base, of which the properties and consequences of its adoption we also investigate in detail. (Previous versions of this work have been selected for presentation at the 18th International Workshop on Nonmonotonic Reasoning (NMR 2020) [1] and at the 35th AAAI Conference on Artificial Intelligence (AAAI 2021) [2] . The present submission extends and elaborates on both papers.)

The question of conditional inference, i.e., of which conditional sentences of the form ``if A then, normally, B'' should follow from a set KB of such sentences, has been one of the classic questions of AI, with several well-known solutions proposed. Perhaps the most notable is the rational closure construction of Lehmann and Magidor, under which the set of inferred conditionals forms a rational consequence relation, i.e., satisfies all the rules of preferential reasoning, *plus* Rational Monotonicity. However, this last named rule is not universally accepted, and other researchers have advocated working within the larger class of *disjunctive* consequence relations, which satisfy the weaker requirement of Disjunctive Rationality. While there are convincing arguments that the rational closure forms the ``simplest'' rational consequence relation extending a given set of conditionals, the question of what is the simplest *disjunctive* consequence relation has not been explored. In this paper, we propose a solution to this question and explore some of its properties.

We extend the expressivity of classical conditional reasoning by introducing context as a new parameter. The enriched conditional logic generalises the defeasible setting in the style of Kraus, Lehmann and Magidor, and allows for a more refined representation of an agent’s epistemic state, distinguishing, for example, between expectations and counterfactuals. In this paper we introduce the language for the enriched logic, and define an appropriate semantic framework for it. We analyse which properties generally associated with conditional reasoning are still satisfied by the new semantic framework, provide an appropriate representation result, and define an entailment relation based on Lehmann and Magidor’s notion of Rational Closure.

Defeasible Linear Temporal Logic is a defeasible temporal formalism for representing and verifying exception-tolerant systems. It is based on Linear Temporal Logic (LTL) and builds on the preferential approach of Kraus et al. for non-monotonic reasoning, which allows us to formalize and reason with exceptions. In this paper, we tackle the satisfiability checking problem for defeasible LTL. One of the methods for satisfiability checking in LTL is the one-pass tree shaped analytic tableau proposed by Reynolds. We adapt his tableau to defeasible LTL by integrating the preferential semantics to the method. The novelty of this work is in showing how the preferential semantics works in a tableau method for defeasible linear temporal logic. We introduce a sound and complete tableau method for a fragment that can serve as the basis for further exploring tableau methods for this logic.

The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition. We start by investigating a notion ofdefeasible subsumptionin the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for bothpreferentialandrationalsubsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level ofentailmentand present an algorithm for the computation ofrational closureof a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DLALC.

Conceptual knowledge, encoded in ontologies or knowledge graphs, plays an essential role in many areas, including Semantic Web, Information Retrieval, and Natural Language Processing. Considerable attention has recently been devoted to the problem of unifying and linking available ontologies. While the vast majority of existing work focuses on matching or aligning resources, in this paper, we investigate the application of belief merging theory to ontology merging to obtain a unique perspective. We consider the setting where different ontologies share the same terminology (i.e., assuming that they are already mapped to each other). However, they express knowledge in different and potentially conflicting ways. In order to get a unified view of the knowledge conveyed by the different ontologies, we start by providing a semantic-based merging model. Our method retrieves all the interpretations in which the outcome can be found. We support demonstrating the method's effectiveness by an experimental evaluation of the method on existing open-domain ontologies.

We present a formal framework for modelling belief change within a nonmonotonic reasoning system. Belief change and non-monotonic reasoning are two areas that are formally closely related, with recent attention being paid towards the analysis of belief change within a non-monotonic environment. In this paper we consider the classical AGM belief change operators, contraction and revision, applied to a defeasible setting in the style of Kraus, Lehmann, and Magidor. The investigation leads us to the consideration of the problem of iterated change, generalising the classical work of Darwiche and Pearl. We characterise a family of operators for iterated revision, followed by an analogous characterisation of operators for iterated contraction. We start considering belief change operators aimed at preserving logical consistency, and then characterise analogous operators aimed at the preservation of coherence—an important notion within the field of logic-based ontologies.

Linear Temporal Logic (LTL) has found extensive applications in Computer Science and Artificial Intelligence, notably as a formal framework for representing and verifying computer systems that vary over time. Non-monotonic reasoning, on the other hand, allows us to formalize and reason with exceptions and the dynamics of information. The goal of this paper is therefore to enrich temporal formalisms with non-monotonic reasoning features. We do so by investigating a preferential semantics for defeasible LTL along the lines of that extensively studied by Kraus et al. in the propositional case and recently extended to modal and description logics. The main contribution of the paper is a decidability result for a meaningful fragment of preferential LTL that can serve as the basis for further exploration of defeasibility in temporal formalisms.

In this paper we introduce and investigate a very basic semantics for conditionals that can be used to define a broad class of conditional reasoning. We show that it encompasses the most popular kinds of conditional reasoning developed in logic-based KR. It turns out that the semantics we propose is appropriate for a structural analysis of those conditionals that do not satisfy the property of Right Weakening. We show that it can be used for the further development of an analysis of the notion of relevance in conditional reasoning.

We show that Booth et al.'s Horn contraction based on infra-remainder sets corresponds exactly to kernel contraction for belief sets. This result is obtained via a detour through Horn contraction for belief bases, which supports the conjecture that Horn belief change is best viewed as a “hybrid” version of belief set change and belief base change. Moreover, the link with base contraction gives us a more elegant representation result for Horn contraction for belief sets in which a version of the Core-retainment postulate features.

As historically acknowledged in the Reasoning about Actions and Change community, intuitiveness of a logical domain description cannot be fully automated. Moreover, like any other logical theory, action theories may also evolve, and thus knowledge engineers need revision methods to help in accommodating new incoming information about the behavior of actions in an adequate manner. The present work is about changing action domain descriptions in multimodal logic. Its contribution is threefold: first we revisit the semantics of action theory contraction proposed in previous work, giving more robust operators that express minimal change based on a notion of distance between Kripke-models. Second we give algorithms for syntactical action theory contraction and establish their correctness with respect to our semantics for those action theories that satisfy a principle of modularity investigated in previous work. Since modularity can be ensured for every action theory and, as we show here, needs to be computed at most once during the evolution of a domain description, it does not represent a limitation at all to the method here studied. Finally we state AGM-like postulates for action theory contraction and assess the behavior of our operators with respect to them. Moreover, we also address the revision counterpart of action theory change, showing that it benefits from our semantics for contraction.