Truth-tracking in collective reasoning systems is a core challenge in domains such as e-democracy, online deliberation, and citizen opinion polling. Our prior work introduced Opinion-Based Argumentation (OBA), a framework modeling both voting and argumentation, along with collective opinion semantics (COS) designed to select sets of arguments that are mutually coherent and aligned with agents' votes. In this paper, we first formally define the truth-tracking problem within OBA. We then introduce VAST, a comprehensive evaluation framework to systematically assess the epistemic adequacy of COS. Our empirical analysis, conducted using VAST, demonstrates substantial variation in their truth-tracking performance across diverse deliberative conditions.

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.

Recently epistemic spaces have been introduced to formalize instantiations of iterated belief change operators and their translations from one concrete representation (epistemic space) to another. In this work, we build on these notions to deepen the understanding of iterated belief change and propose a general method for comparing the expressiveness of existing epistemic spaces. We introduce the notion of canonicity for epistemic spaces as a tool for identifying those that are sufficient, or necessary, to realize certain classes of iterated belief change operators. In particular, we give the canonical epistemic space (up to equivalence) that allows one to instantiate any iterated belief change operator.

Several methods have been introduced in the literature to extend preferences over items from a population to preferences over the groups they may form - a problem known as the Order Lifting problem. The converse matter of deducing preferences over items from expressed preferences over the coalitions that may be formed within a population - a problem known as the Social Ranking Problem - has also been studied more recently. In this paper, we investigate the links between these two problems: after an examination of the general case, we consider the impact of missing information, by studying which social ranking methods allow for the most accurate recovery of initial preferences over items, depending on the amount of missing information about coalitions. Finally, we consider the specific case in which preferences are only expressed over coalitions of same size, and examine the accuracy of social ranking methods when faced with impartial information about preferences over k-sized coalitions.

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.

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.

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.

We propose new operators for weighted propositional belief merging operators. We introduce distance-based operators that use the product as aggregation function. In social choice theory, the product, called the Nash welfare function, is known to be a more equitable social welfare function than the classical utilitarian welfare function (based on a sum). We study which properties are satisfied by the obtained corresponding weighted merging operators. In particular, we show that, unlike the Nash welfare function, distance-based operators using the product do not satisfy the Pigou-Dalton property. Then, we introduce a new family of weighted merging operators, which we call utility-based weighted merging operators, where the utility is roughly the converse of a distance for distance-based operators. For most well-known distance-based operators, it is easy to find the corresponding utility-based merging operators. But an interesting result is that the utility-based weighted merging operator based on the product does not correspond to any standard distance-based weighted merging operator, and this operator satisfies the Pigou-Dalton property.

Voting on arguments in a debate is a natural approach for reaching a consensual decision. Despite this, there are few formal methods of abstract argumentation dealing with the use of votes in the process of selecting accepted arguments. We introduce the Opinion Based Argumentation (OBA) framework, where individuals can vote (or abstain) for or against arguments in a Dung argumentation framework. Our research aims to determine the most appropriate collective decisions within this framework. We propose a new semantics for this framework, called Collective Satisfaction Semantics (CSS), to evaluate the acceptability of arguments and study their properties. Additionally, we compare these semantics against alternative methods adapted from related literature to provide insights into their relative effectiveness.

In this work we propose a family of methods that allow to conjointly compute the reliability of a set of information sources and the confidence of the facts on a set of objects, by confronting the sources points of view. We use a (scoring-based) voting method for the evaluation of the trust of the sources, using Condorcet’s Jury Theorem arguments in order to identify the truth and the reliable sources. We discuss general theoretical properties that such operators should satisfy, and we study what are the properties satisfied by our methods. We provide an experimental study that shows that we perform better than state of the art methods on the task of finding the truth among the possible facts. We show that we can also adequately evaluate the reliability of the sources of information.

In standard propositional belief merging, one implicit assumption is that all sources have exactly the same importance. But there are many situations where the sources have different importance/reliability/expertise that have to be taken into account in the merging process. In this work we study the problem of weighted merging operators, which aimed to take these weights into account in a sensible way. We give a syntactical characterization of these operators, and then we state a representation theorem in terms of plausibility preorders on interpretations. We also propose a general method to build weighted distance-based merging operators, and provide some concrete examples, using two different weight functions.

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.

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, 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.

In this work, we explore the links between the Borda voting rule and belief merging operators. More precisely, we define two families of merging operators inspired by the definition of the Borda voting rule. We also introduce a notion of cancellation in belief merging, inspired by the axiomatization of the Borda voting rule proposed by Young. This allows us to provide a characterization of the drastic merging operator.

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 study how belief merging operators can be considered as maximum likelihood estimators, i.e., we assume that there exists a (unknown) true state of the world and that each agent participating in the merging process receives a noisy signal of it, characterized by a noise model. The objective is then to aggregate the agents' belief bases to make the best possible guess about the true state of the world. In this paper, some logical connections between the rationality postulates for belief merging (IC postulates) and simple conditions over the noise model under consideration are exhibited. These results provide a new justification for IC merging postulates. We also provide results for two specific natural noise models: the world swap noise and the atom swap noise, by identifying distance-based merging operators that are maximum likelihood estimators for these two noise models.

Iterated belief change aims to determine how the belief state of a rational agent evolves given a sequence of change formulae. Several families of iterated belief change operators (revision operators, improvement operators) have been pointed out so far, and characterized from an axiomatic point of view. This paper focuses on the inference problem for iterated belief change, when belief states are represented as a special kind of stratified belief bases. The computational complexity of the inference problem is identified and shown to be identical for all revision operators satisfying Darwiche and Pearl's (R*1-R*6) postulates. In addition, some complexity bounds for the inference problem are provided for the family of soft improvement operators. We also show that a revised belief state can be computed in a reasonable time for large-sized instances using SAT-based algorithms, and we report empirical results showing the feasibility of iterated belief change for bases of significant sizes.

In this work we define iterated change operators that do not obey the primacy of update principle. This kind of change is required in applications when the recency of the input formulae is not linked with their reliability/priority/weight. This can be translated by a commutativity postulate that asks the result of a sequence of changes to be the same whatever the order of the formulae of this sequence. Technically then we end up with a sequence of formulae that we have to combine in order to obtain a meaningful belief base. Belief merging operators are then natural candidates for this task. We show that we can define improvement operators using an incremental belief merging approach. We also show that these operators can not be encoded as simple preorders transformations, contrary to most iterated revision and improvement operators.

When one wants to draw non-trivial inferences from an inconsistent belief base, a very natural approach is to take advantage of the maximal consistent subsets of the base. But few inference relations from maximal consistent subsets exist. In this paper we point out new such relations based on selection of some of the maximal consistent subsets, leading thus to inference relations with a stronger inferential power. The selection process must obey some principles to ensure that it leads to an inference relation which is rational. We define a general class of monotonic selection relations for comparing maximal consistent sets. And we show that it corresponds to the class of rational inference relations.

We consider the problem of identifying the change formula in a belief revision scenario: given that an unknown announcement (a formula mu) led a set of agents to revise their beliefs and given the prior beliefs and the revised beliefs of the agents, what can be said about mu? We show that under weak conditions about the rationality of the revision operators used by the agents, the set of candidate formulae has the form of a logical interval. We explain how the bounds of this interval can be tightened when the revision operators used by the agents are known and/or when mu is known to be independent from a given set of variables. We also investigate the completeness issue, i.e., whether mu can be exactly identified. We present some sufficient conditions for it, identify its computational complexity, and report the results of some experiments about it.

The aim of measuring inconsistency is to obtain an evaluation of the imperfections in a set of formulas, and this evaluation may then be used to help decide on some course of action (such as rejecting some of the formulas, resolving the inconsistency, seeking better sources of information, etc). A number of proposals have been made to define measures of inconsistency. Each has its rationale. But to date, it is not clear how to delineate the space of options for measures, nor is it clear how we can classify measures systematically. To address these problems, we introduce a general framework for comparing syntactic measures of inconsistency. It is based on the notion of an inconsistency graph for each knowledgebase (a bipartite graph with a set of vertices representing formulas in the knowledgebase, a set of vertices representing minimal inconsistent subsets of the knowledgebase, and edges representing that a formula belongs to a minimal inconsistent subset). We then show that various measures can be computed using the inconsistency graph. Then we introduce abstractions of the inconsistency graph and use them to construct a hierarchy of syntactic inconsistency measures. Furthermore, we extend the inconsistency graph concept with a labeling that extends the hierarchy to include some other types of inconsistency measures.

A number of proposals have been made to define inconsistency measures. Each has its rationale. But to date, it is not clear how to delineate the space of options for measures, nor is it clear how we can classify measures systematically. In this paper, we introduce a general framework for comparing syntactic inconsistency measures. It uses the construction of an inconsistency graph for each knowledgebase. We then introduce abstractions of the inconsistency graph and use the hierarchy of the abstractions to classify a range of inconsistency measures.

We study the evolution of Artificial Intelligence conference closeness, using the coscinus tool. Coscinus computes the closeness between publication supports using the co-publication habits of authors: the more authors publish in two conferences, the closer these two conferences. In this paper we perform an analysis of the main Artificial Intelligence conferences based on principal components analysis and clustering performed on this closeness relation.

In this paper, we study the problem of aggregation of Dung’s abstract argumentation frameworks (AFs). An argumentation framework allows the representation of conflictual agent’s beliefs by using a set of arguments and interactions between them (i.e. attack or non-attack). One AF per agent can be used to represent the beliefs of a group of agents. The aggregation process aims to represent the beliefs of this group by solving the potential conflicts between them. Some aggregation operators were defined, and more recently, some rationality properties for this process were introduced. In this work, we study the existing operators as well as some new ones, which we define in light of the proposed properties. We highlight the fact that existing operators do not satisfy a lot of properties. The conclusions are that on one hand none of the existing operators seem fully satisfactory, but on the other hand some of the properties proposed so far seem too demanding.

Existing belief merging operators take advantage of all the models from the bases, including those contradicting the integrity constraint. In this paper, we argue that this is not suited to every merging scenario, especially when the integrity constraint encodes physical laws. In that case the bases have to be ‘rationalized’ with respect to the integrity constraint during the merging process. We define several conditions characterizing the operators that are independent to such a rationalization process, and we show how these conditions interact with the standard IC postulates for belief merging. Especially, we give an independence-based axiomatic characterization of a distance-based operator.

We present SAT encoding schemes for distance-based belief merging operators relying on the (possibly weighted) drastic distance or the Hamming distance between interpretations, and using sum, GMax (leximax) or GMin (leximin) as aggregation function. In order to evaluate these encoding schemes, we generated benchmarks of a time-tabling problem and translated them into belief merging instances. Then, taking advantage of these schemes, we compiled the merged bases of the resulting instances into query-equivalent CNF formulae. Experiments have shown the benefits which can be gained by considering the SAT encoding schemes we pointed out. Especially, thanks to them, we succeeded in computing query-equivalent formulae for merging instances based on hundreds of variables, which are out of reach of previous implementations.

Argumentation is a process of evaluating and comparing a set of arguments. A way to compare them consists in using a ranking-based semantics which rank-order arguments from the most to the least acceptable ones. Recently, a number of such semantics have been pro- posed independently, often associated with some desirable properties. However, there is no comparative study which takes a broader perspective. This is what we propose in this work. We provide a general comparison of all these semantics with respect to the proposed proper- ties. That allows to underline the differences of behavior between the existing semantics.

Argumentation is based on the exchange and the evaluation of interacting arguments. Unlike Dung's theory where arguments are either accepted or rejected, ranking-based semantics rank-order arguments from the most to the least acceptable ones. We propose in this work six new ranking-based semantics. We argue that, contrarily to existing ranking semantics in the literature, that focus on evaluating attacks and defenses only, it is reasonable to give a prominent role to non-attacked arguments, as it is the case in standard Dung's semantics. Our six semantics are based on the propagation of the weight of each argument to its neighbors, where the weight of non-attacked arguments is greater than the attacked ones.

In this paper, some distances between KD45n Kripke models are introduced and investigated. We define several distances between Kripke models, based on different criteria, inspired by various concepts such as bisimulation and propositional distances between valuations for different modal degrees. We study the properties of these distances. Such distances are useful for defining belief change operators in multi-agent scenarios. We show that they can be used to define belief revision operators based on the standard AGM framework and suited to KD45n Kripke models.

Belief revision games (BRGs) are concerned with the dynamics of the beliefs of a group of communicating agents. BRGs are "zero-player" games where at each step every agent revises her own beliefs by taking account for the beliefs of her acquaintances. Each agent is associated with a belief state defined on some finite propositional language. We provide a general definition for such games where each agent has her own revision policy, and show that the belief sequences of agents can always be finitely characterized. We then define a set of revision policies based on belief merging operators. We point out a set of appealing properties for BRGs and investigate the extent to which these properties are satisfied by the merging-based policies under consideration.

In this paper we introduce and study credibility-limited improvement operators. The idea is to accept the new piece of information if this information is judged credible by the agent, so in this case a revision is performed. When the new piece of information is not credible then it is not accepted (no revision is performed), but its plausibility is still improved in the epistemic state of the agent, similarly to what is done by improvement operators. We use a generalized definition of Darwiche and Pearl epistemic states, where to each epistemic state can be associated, in addition to the set of accepted formulas (beliefs), a set of credible formulas. We provide a syntactic and semantic characterization of these operators.

There are two theories of aggregation of logical formulae: merging and judgment aggregation. In this work we investigate the relationships between these theories; one of our objectives is to point out some correspondences/discrepancies between the associated rationality properties.

We address the problem of multi-objective constraint optimization problems (MO-COPs). Solving a MO-COP traditionally consists in computing the set of all Pareto optimal solutions, which is an exponentially large set in the general case. So this causes two main problems: first is the time complexity concern, second is a lack of decisiveness. In this paper, we formalize the notion of a MO-COP operator which associates every MO-COP with a subset of Pareto optimal solutions satisfying some desirable additional properties. Then, we present two specific classes of MO-COP operators that give preference to some subsets of Pareto optimal solutions. These operators correspond to two classical doctrines in Decision Theory: utilitarianism and egalitarianism. They compute solutions much more efficiently than standard operators computing all Pareto optimal solutions. In practice, they return a very few number of solutions even for problems involving a high number of objectives.

Recently, Dunne et al. [9,10] introduced the concept of WAF (Weighted Argumentation Framework). Such frameworks extend standard Dung's ones for abstract argumentation by associating weights with attacks. In the WAF setting, weights are used for relaxing extensions, which proves useful when there are too few extensions. In this paper, we exploit weights in a different perspective. We show how to take advantage of attacks weights within an argumentation process for selecting some extensions among Dung's ones, which proves useful when there are too many extensions, in order to improve the inferential power of the argumentation framework.

Belief merging is often described as the process of defining a base which best represents the beliefs of a group of agents (a profile of belief bases). The resulting base can be viewed as a synthesis of the input profile. In this paper another view of what belief merging aims at is considered: the epistemic view. Under this view the purpose of belief merging is to best approximate the true state of the world. We point out a generalization of Condorcet's Jury Theorem from the belief merging perspective. Roughly, we show that if the beliefs of sufficiently many reliable agents are merged then in the limit the true state of the world is identified. We introduce a new postulate suited to the truth tracking issue. We identify some merging operators from the literature which satisfy it and other operators which do not.

In the propositional setting, a well-studied family of merging operators are distance-based ones: the models of the merged base are the closest interpretations to the given profile. Closeness is, in this context, measured as a number resulting from the aggregation of the distances to each base of the profile. In this work we define a new familly of propositional merging operators, close to such distance-based merging operators, but relying on a set-theoretic definition of closeness, already at work in several revision/update operators from the literature. We study a specific merging operator of this family, obtained by considering set-product as the aggregation function.

We introduce and study qualitative multiple outcomes games. These games are noncooperative games with qualitative utilities (i.e., values over an ordinal scale), strictly qualitative uncertainty and possible coordination. By strictly qualitative uncertainty, we mean that when there is a set of possible events, the probability of each event is unknown. Coordination is a way offered to the players to remove uncertainty. Qualitative multiple outcomes games is a model for a number of multi-agent problems where agents have minimal information about the interaction effects and where probabilites are unavailable. Among them is multi-agent planning where autonomous planning agents do not share the same goals, and have to generate plans that interact with those of others in a way they cannot unilaterally predict or control.

This paper is centered on a family of propositional multivalued logics, based on bilattices. The semantics of such logics relies on a set of “truth values,” with two orderings that give the set a bilattice structure. Many interesting inference relations can be defined on these grounds, especially paraconsistent ones and/or nonmonotonic ones. The focus is laid on Belnap's fundamental bilattice logic FOUR, with four “epistemic truth values,” which proves sufficient for the purpose of inference. We show how the bilattice can be associated with a second biordinal structure, which no longer is bilatticial but bipolar. We show how additional inference relations in the logic FOUR can be obtained by exploiting the two preorders associated with this structure. © 2008 Wiley Periodicals, Inc.

Merging operators aim at defining the beliefs/goals of a group of agents from the beliefs/goals of each member of the group. Whenever an agent of the group has preferences over the possible results of the merging process (i.e., the possible merged bases), she can try to rig the merging process by lying on her true beliefs/goals if this leads to better merged base according to her point of view. Obviously, strategy-proof operators are highly desirable in order to guarantee equity among agents even when some of them are not sincere. In this paper, we draw the strategy-proof landscape for many merging operators from the literature, including model-based ones and formula-based ones. Both the general case and several restrictions on the merging process are considered.

Two families of conciliation processes for intelligent agents based on an iterated merge-then-revise change function for belief profiles are introduced and studied. The processes from the first family are sceptical in the sense that at any revision step, each agent considers that her current beliefs are more important than the current beliefs of the group, while the processes from the other family are credulous. Some key features of such conciliation processes are pointed out for several merging operators; especially, the stationarity issue, the existence of consensus and the properties of the induced iterated merging operators are investigated.