With the aim of providing a natural and expressive domain for defining change operators, we introduce the epistemic space of rational rankings. We show that this epistemic space is highly useful for understanding various aspects of belief dynamics, particularly those related to the improvement of new information. It enables us to define certain classes of improvement operators, a generalization of iterated revision operators, in a natural and intuitive way. A key feature of rational rankings is the possibility of defining improvement operators in such a way that the negation of the new information does not worsen. This is impossible within the frameworks of total preorders or ordinal conditional functions, two well-known epistemic spaces. Another notable aspect of this space is that the behavior of these operators can be characterized by a few simple equations and inequalities, whose meaning remains transparent. Additionally, there are no stationary states: The epistemic state resulting from applying an operator to a prior epistemic state and new information is always distinct from the prior state. Finally, we prove that this class of operators is indeed a subclass of improvement operators. Consequently, we show that these operators exhibit desirable behavior when iterated sufficiently, ultimately converging to Darwiche and Pearl revision operators.

In this work, we introduce the notion of targeting for multi-criteria decision making. The problem involves selecting the best alternatives related to one particular alternative, called the target. We use an axiomatic approach to this problem by establishing properties that any targeting method should satisfy. We present a representation theorem and show that satisfying the main properties of targeting requires aggregating the evaluations of the alternatives related to the target. We propose various candidate targeting methods and examine the properties satisfied by each method.

We investigate the truth-tracking performance of iterated belief change operators. In particular, we show that a class of improvement operators is guaranteed to converge to the truth when the input sequence contains sufficiently many correct pieces of information, and we establish a corresponding convergence theorem. We also report experimental results indicating that this convergence typically occurs with relatively short input sequences.

In this work, we show how the class of improvement operators - a general class of iterated belief change operators - can be used to define a learning model. Focusing on binary classification, we present learning and inference algorithms suited to this learning model and we evaluate them empirically. Our findings highlight two key insights: first, that iterated belief change can be viewed as an effective form of online learning, and second, that the well-established axiomatic foundations of belief change operators offer a promising avenue for the axiomatic study of classification tasks.

In credibility-limited (CL) belief revision, an agent may reject new information if it is considered not credible relative to its current beliefs. A core principle of CL revision requires that all consequences of a credible formula must themselves be credible. We propose a new framework, context-based (CB) belief revision, which generalizes CL revision by relaxing this requirement. In CB revision, a formula may be deemed credible because it strengthens one of its non-credible consequences by providing sufficient supporting context, a situation that CL revision does not allow. We introduce an axiomatic framework for CB revision operators, identify specific subclasses, provide representation theorems, and examine the relationships between CB revision operators, their subclasses, and CL revision operators.

We introduce a new epistemic space: the space of rational rankings. This space is very useful for understanding some aspects of belief dynamics. In particular, the issues which concern improving the new information. Thus, we define in a very clear and succinct way a class of operators capturing the fact that the new information is improved. An interesting feature of this space is that the behavior of these operators can be characterized through a few equations and inequalities which are very simple and whose meaning is transparent. We prove that these operators are indeed improvement operators. Moreover, we show that these operators have good behavior when they undergo a sufficient number of iterations. In such a case, they become Darwiche and Pearl revision operators.

This paper presents BeliefFlow, a novel framework for representing how logical beliefs spread among interacting agents within a network. In a Belief Flow Network (BFN), agents communicate asynchronously. The agents' beliefs are represented using epistemic states, which encompass their current beliefs and conditional beliefs guiding future changes. When communication occurs between two connected agents, the receiving agent changes its epistemic state using an improvement operator, a well-known type of rational iterated belief change operator that generalizes belief revision operators. We show that BFNs satisfy appealing properties, leading to two significant outcomes. First, in any BFN with strong network connectivity, the beliefs of all agents converge towards a global consensus. Second, within any BFN, we show that it is possible to compute an optimal strategy for influencing the global beliefs. This strategy, which involves controlling the beliefs of a least number of agents through bribery, can be identified from the topology of the network and can be computed in polynomial time.

In this paper, we formalize the concept of relative changereluctance in iterated belief revision. We use this concept to compare different belief revision operators and analyze how an operator's behavior evolves over time when receiving new evidence. This provides deeper insights into how belief revision operators manage new information across multiple iterations, specifically regarding their reluctance to change.

In one of its simplest forms, Team Formation involves deploying the least expensive team of agents while covering a set of skills. While current algorithms are reasonably successful in computing the best teams, the resilience to change of such solutions remains an important concern: Once a team has been formed, some of the agents considered at start may be finally defective and some skills may become uncovered. Two recently introduced solution concepts deal with this issue proactively: 1) form a team which is robust to changes so that after some agent losses, all skills remain covered, and 2) opt for a recoverable team, i.e., it can be "repaired" in the worst case by hiring new agents while keeping the overall deployment cost minimal. In this paper, we introduce the problem of partially robust team formation (PR–TF). Partial robustness is a weaker form of robustness which guarantees a certain degree of skill coverage after some agents are lost. We analyze the computational complexity of PR-TF and provide two complete algorithms for it. We compare the performance of our algorithms with the existing methods for robust and recoverable team formation on several existing and newly introduced benchmarks. Our empirical study demonstrates that partial robustness offers an interesting trade-off between (full) robustness and recoverability in terms of computational efficiency, skill coverage guaranteed after agent losses and repairability. This paper is an extended and revised version of as reported by (Schwind et al., Proceedings of the 20th International Conference on Autonomous Agents and Multiagent Systems (AAMAS'21), pp. 1154–1162, 2021).

In this work, we address one important problem of Katsuno and Mendelzon update operators, that is to require that any updated belief base must entail any new input in a consistent way. This assumes that any situation can be updated into one satisfying that input, which is unrealistic. To solve this problem, we must relax either the success or the consistency principle. Each case leads to a distinct family of update operators, that we semantically characterize by plausibility relations over possible worlds, considering a credibility limit that aims to forbid unrealistic changes. We discuss in which cases one family is more adequate than the other one.

This paper is about editing Boolean classifiers, i.e., determining how a Boolean classifier should be modified when new pieces of evidence must be incorporated. Our main goal is to delineate what are the rational ways of making such edits. This goes through a number of rationality postulates inspired from those considered so far for belief revision. We give a representation theorem and present some families of edit operators satisfying the postulates.

The behavior of Iterated Belief Revision operators with respect to iteration has been characterized by a set of four postulates proposed by Darwiche and Pearl. These postulates give constraints on a single iteration step, and this is not enough to forbid some pathological operators. In this paper, we propose a generalization of these postulates to solve this issue and we study its implications. One surprising consequence is that, for TPO-representable operators (i.e., for operators defined as transitions on total pre-orders on interpretations), there are very few operators that satisfy this generalization.

Belief revision aims at incorporating a new piece of information into the beliefs of an agent. This process can be modelled by the standard Katsuno and Mendelzon's (KM) rationality postulates. However, these postulates suppose a classical setting and do not govern the case where (some parts of) the beliefs of the agent are not consistent. In this work we discuss how to adapt these postulates when the underlying logic is Priest's Logic of Paradox, in order to model a rational change, while being a conservative extension of KM belief revision. This paper is a summary of [5].

The seminal characterization of iterated belief revision was proposed by Darwiche and Pearl, which uses an abstract notion of epistemic states. In this work we look for a canonical representation of these epistemic states. Total preorders are not expressive enough to be used as such a canonical representation. Actually, we show that some operators can even not be represented on a countable epistemic space. Nonetheless, under a very reasonable assumption on the epistemic space, we show that OCFs (Ordinal Conditional Functions) can be considered as a canonical representation.

Belief revision aims at incorporating, in a rational way, a new piece of information into the beliefs of an agent. Most works in belief revision suppose a classical logic setting, where the beliefs of the agent are consistent. Moreover, the consistency postulate states that the result of the revision should be consistent if the new piece of information is consistent. But in real applications it may easily happen that (some parts of) the beliefs of the agent are not consistent. In this case then it seems reasonable to use paraconsistent logics to derive sensible conclusions from these inconsistent beliefs. However, in this context, the standard belief revision postulates trivialize the revision process. In this work we discuss how to adapt these postulates when the underlying logic is Priest's LP logic, in order to model a rational change, while being a conservative extension of AGM/KM belief revision. This implies, in particular, to adequately adapt the notion of expansion. We provide a representation theorem and some examples of belief revision operators in this setting.

This paper introduces a novel method for merging open-domain terminological knowledge. It takes advantage of the Region Connection Calculus (RCC5), a formalism used to represent regions in a topological space and to reason about their set-theoretic relationships. To this end, we first propose a faithful translation of terminological knowledge provided by several and potentially conflicting sources into region spaces. The merging is then performed on these spaces, and the result is translated back into the underlying language of the input sources. Our approach allows us to benefit from the expressivity and the flexibility of RCC5 while dealing with conflicting knowledge in a principled way.

Team formation is the problem of deploying the least expensive team of agents while covering a set of skills. Once a team has been formed, some of the agents considered at start may be finally defective and some skills may become uncovered. Two solution concepts have been recently introduced to deal with this issue in a proactive manner: one may form a team which is robust to changes so that after some agent losses, all skills remain covered; or one may opt for a recoverable team, i.e., it can be “repaired” in the worst case by hiring new agents while keeping the overall deployment cost minimal. In this paper, we introduce the problem of partially robust team formation (PR-TF). Partial robustness is a weaker form of robustness which guarantees a certain degree of skill coverage after some agents are lost. We analyze the computational complexity of PR-TF, and provide a complete algorithm for it. The performance of our algorithm is empirically compared with the existing methods for robust and recoverable team formation, on a number of existing benchmarks and some newly introduced ones. Partial robustness is shown to be an interesting trade-off notion between (full) robustness and recoverability in terms of computational efficiency, skill coverage guarantees after agent losses, and repairability.