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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 and of a family of merging operators defined in a way which is similar to the Borda rule. [ABSTRACT FROM AUTHOR]

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 and of a family of merging operators defined in a way which is similar to the Borda rule. [ABSTRACT FROM AUTHOR]

In this paper, we recover some traditional results in the geometry of probability distributions, and in particular the convergence of the alternating minimisation procedure, without actually referring to probability distributions. We will do this by discussing a new general concept of two types of points: admissible and agreeable, inspired by multi–agent uncertain reasoning and belief merging. On the one hand, this presents a unique opportunity to make traditional results accessible to a wider audience as no prior knowledge of the topic is required. On the other hand, it allows us to contemplate how a group of rational agents would seek an agreement given their beliefs without necessarily expressing it in terms of probability distributions, focusing instead on logical properties. Finally, we recover Euclidean and Hilbertian settings of discrete and continuous probability distributions. [ABSTRACT FROM AUTHOR]

The paper contributes to the study of belief merging in many-valued logics, taking both a theoretical and implementation approach motivated by applications in real-world scenarios. We focus, in particular, on the Horn fragment of signed logic. On the one hand, a characterization of the class of models of a signed regular Horn formula and a sufficient condition for a signed Horn merging operator to satisfy logical IC-postulates are provided. On the other hand, an implementation of the belief merging process in the signed regular Horn fragment is presented. [ABSTRACT FROM AUTHOR]

We describe a tool that allows the merging of extensions of argumentation frameworks, following the approach defined by (In Proceedings of the Fifteenth International Conference on Principles of Knowledge Representation and Reasoning (KR'16) (2016) 33–42). The tool is implemented in Java, and is highly modular thanks to Object Oriented Programming (OOP) principles. We describe a short experimental study that assesses the scalability of the approach, as well as the impact on runtime of using an integrity constraint. [ABSTRACT FROM AUTHOR]

Merging beliefs depends on the relative reliability of their sources. When this is information is absent, assuming equal reliability is unwarranted. The solution proposed in this article is that every reliability profile is possible, and only what holds according to all of them is accepted. Alternatively, one source is completely reliable, but which one is not specified. These two cases motivate two existing forms of merging: maxcons-based merging and disjunctive merging. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We pursue an account of merging through the use of geodesic semantics, the semantics based on the length of the shortest path on a graph. This approach has been fruitful in other areas of belief change such as revision and update. To this end, we introduce three binary merging operators of propositions defined on the graph of their valuations and we characterize them with a finite set of postulates. [ABSTRACT FROM AUTHOR]

Belief merging is a relatively recent technique with the aim of combining pieces of infor- mation, possibly inconsistent, coming from different sources. This process is done by a merging operator, in the literature we found mainly the theoretical basis of operators. However, this technique is still little known and there is scarce evidence about its applicability to solve real-world problems. In this paper we propose to use belief merging in order to solve everyday decision-making problems, in which participants with the same level have contradictory opinions, by “merging” these opinions and generating a common non-contradictory opinion representing the views of the majority. We describe in detail three belief merging operators with differing properties: ∆Σ, ∆GMax , y ∆ps (PS-Merge); afterwards, the classic belief merging examples are presented in natural language as decision-making practical scenarios; finally, we present an online open source Belief Merging Prototype to support on diverse decision-making processes.

Belief merging is a relatively recent technique with the aim of combining pieces of infor- mation, possibly inconsistent, coming from different sources. This process is done by a merging operator, in the literature we found mainly the theoretical basis of operators. However, this technique is still little known and there is scarce evidence about its applicability to solve real-world problems. In this paper we propose to use belief merging in order to solve everyday decision-making problems, in which participants with the same level have contradictory opinions, by “merging” these opinions and generating a common non-contradictory opinion representing the views of the majority. We describe in detail three belief merging operators with differing properties: ∆Σ, ∆GMax , y ∆ps (PS-Merge); afterwards, the classic belief merging examples are presented in natural language as decision-making practical scenarios; finally, we present an online open source Belief Merging Prototype to support on diverse decision-making processes.

Machine learning employs a variety of statistical, probabilistic, fuzzy and optimization techniques that allow computers to “learn” from examples and to detect hard-to-discern patterns from large, noisy or complex datasets. This capability is well-suited to medical applications, and machine learning techniques have been frequently used in cancer diagnosis and prognosis. In general, machine learning techniques usually work in two phases: training and testing. Some parameters, with regards to the underlying machine learning technique, must be tuned in the training phase in order to best “learn” from the dataset. On the other hand, belief merging operators integrate inconsistent information, which may come from different sources, into a unique consistent belief set (base). Implementations of merging operators do not require tuning any parameters apart from the number of sources and the number of topics to be merged. This research introduces a new manner to “learn” from past examples using a non parametrised technique: belief merging. The proposed method has been used for oral cancer diagnosis using a real-world medical dataset. The results allow us to affirm the possibility of training (merging) a dataset without having to tune the parameters. The best results give an accuracy of greater than 75%. [ABSTRACT FROM AUTHOR]

With the aim of studying social properties of belief merging and having a better understanding of impossibility, we extend in three ways the framework of logic-based merging introduced by Konieczny and Pino Pérez. First, at the level of representation of the information, we pass from belief bases to complex epistemic states. Second, the profiles are represented as functions of finite societies to the set of epistemic states (a sort of vectors) and not as multisets of epistemic states. Third, we extend the set of rational postulates in order to consider the epistemic versions of the classical postulates of social choice theory: standard domain, Pareto property, independence of irrelevant alternatives and absence of dictator. These epistemic versions of social postulates are given, essentially, in terms of the finite propositional logic. We state some representation theorems for these operators. These extensions and representation theorems allow us to establish an epistemic and very general version of Arrow's impossibility theorem. One of the interesting features of our result, is that it holds for different representations of epistemic states; for instance conditionals, ordinal conditional functions and, of course, total preorders. [ABSTRACT FROM AUTHOR]

Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference orders), when consolidating conflicting views regarding the relationships between arguments in a debate (graphs as abstract argumentation frameworks), or when computing a consensus between several alternative clusterings of a given dataset (graphs as equivalence relations). In this paper, we introduce a formal framework for graph aggregation grounded in social choice theory. Our focus is on understanding which properties shared by the individual input graphs will transfer to the output graph returned by a given aggregation rule. We consider both common properties of graphs, such as transitivity and reflexivity, and arbitrary properties expressible in certain fragments of modal logic. Our results establish several connections between the types of properties preserved under aggregation and the choice-theoretic axioms satisfied by the rules used. The most important of these results is a powerful impossibility theorem that generalises Arrow's seminal result for the aggregation of preference orders to a large collection of different types of graphs. [ABSTRACT FROM AUTHOR]

The merging/fusion of belief/data collections in propositional logic form is a topic that has received due attention within the domains of database and AI research. A distinction can be made between two types of scenarios to which the process of merging can be applied. In the first type, the collections represent preferences, such as the voting choices of a group of people, that need to be aggregated so as to give a consistent result that in some way best represents the collective judgement of the group. In the second type, the collections represent factual data that is to be aggregated with an aim of obtaining a result that maximises factual correctness. After introducing a general framework for belief merging via some prominent literature on the topic, this paper then introduces and considers a method for belief merging with the second type of scenario in mind. Its suitability is corroborated by demonstrating how it can be seen as a special case of a merging procedure that combines aggregation of probabilities and maximisation of expected truthlikeness. [ABSTRACT FROM AUTHOR]

Recently, belief change within the framework of fragments of propositional logic has gained increasing attention. Previous research focused on belief contraction and belief revision on the Horn fragment. However, the problem of belief merging within fragments of propositional logic has been mostly neglected so far. We present a general approach to defining new merging operators derived from existing ones such that the result of merging remains in the fragment under consideration. Our approach is not limited to the case of Horn fragment; it is applicable to any fragment of propositional logic characterized by a closure property on the sets of models of its formulæ. We study the logical properties of the proposed operators regarding satisfaction of merging postulates, considering, in particular, distance-based merging operators for Horn and Krom fragments. [ABSTRACT FROM AUTHOR]

A common assumption in belief revision is that the reliability of the information sources is either given, derived from temporal information, or the same for all. This article does not describe a new semantics for integration but studies the problem of obtaining the reliability of the sources given the result of a previous merging. As an example, corrections performed manually on the result of merging some databases may indicate that the relative reliability of their sources is different from what was previously assumed, helping subsequent data mergings. [ABSTRACT FROM AUTHOR]

Belief merging is an active research field with many important applications. Most existing work addresses the belief merging issue using a centralised approach. In this paper, we investigate a distributed approach to the problem of belief merging. The contribution of this paper is two-fold: (i) we develop a negotiation-based model for belief merging, and (ii) we investigate the computational complexity of the belief merging problem within the proposed framework. Through the proposed model of negotiation-based belief merging, we will present and discuss several significant logical properties and computational complexity results. [ABSTRACT FROM AUTHOR]

We provide a brief introduction to this special issue on social dynamics and collective rationality, and summarize the gist of the papers collected therein. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of truth approximation via belief merging, i.e., we ask whether, and under what conditions, a group of inquirers merging together their beliefs makes progress toward the truth about the underlying domain. We answer this question by proving some formal results on how belief merging operators perform with respect to the task of truth approximation, construed as increasing verisimilitude or truthlikeness. Our results shed new light on the issue of how rational (dis)agreement affects the inquirers' quest for truth. In particular, they vindicate the intuition that scientific inquiry, and rational discussion in general, benefits from some heterogeneity in opinion and interaction among different viewpoints. The links between our approach and related analyses of truth tracking, judgment aggregation, and opinion dynamics, are also highlighted. [ABSTRACT FROM AUTHOR]

Belief merging has been an active research field with many important applications. The major approaches for the belief merging problems, considered as arbitration processes, are based on the construction of the total pre-orders of alternatives using distance functions and aggregation functions. However, these approaches require that all belief bases are provided explicitly and the role of agents, who provide the belief bases, are not adequately considered. Therefore, the results are merely ideal and difficult to apply in the multi-agent systems. In this paper, we approach the merging problems from other point of view. Namely, we treat a belief merging problem as a game, in which rational agents participate in a negotiation process to find out a jointly consistent consensus trying to preserve as many important original beliefs as possible. To this end, a model of negotiation for belief merging is presented, a set of rational and intuitive postulates to characterize the belief merging operators are proposed, and a representation theorem is presented. [ABSTRACT FROM AUTHOR]

We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Our formal techniques are analogous to those of distance-based belief revision in propositional logic. In particular, we build upon the model theory of logic programs furnished by SE interpretations, where an SE interpretation is a model of a logic program in the same way that a classical interpretation is a model of a propositional formula. Hence we extend techniques from the area of belief revision based on distance between models to belief change in logic programs. We first consider belief revision: for logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P * Q. We investigate several operators, including (logic program) expansion and two revision operators based on the distance between the SE models of logic programs. It proves to be the case that expansion is an interesting operator in its own right, unlike in classical belief revision where it is relatively uninteresting. Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy all or nearly all of the AGM postulates for revision. We next consider approaches for merging a set of logic programs, P1, . . ., Pn. Again, our formal techniques are based on notions of relative distance between the SE models of the logic programs. Two approaches are examined. The first informally selects for each program Pi those models of Pi that vary the least from models of the other programs. The second approach informally selects those models of a program P0 that are closest to the models of programs P1, . . ., Pn. In this case, P0 can be thought of as a set of database integrity constraints. We examine these operators with regards to how they satisfy relevant postulate sets. Last, we present encodings for computing the revision as well as the merging of logic programs within the same logic programming framework. This gives rise to a direct implementation of our approach in terms of off-the-shelf answer set solvers. These encodings also reflect the fact that our change operators do not increase the complexity of the base formalism. [ABSTRACT FROM AUTHOR]

Belief merging aims at combining several pieces of information coming from different sources. In this paper we review the works on belief merging of propositional bases. We discuss the relationship between merging, revision, update and confluence, and some links between belief merging and social choice theory. Finally we mention the main generalizations of these works in other logical frameworks. [ABSTRACT FROM AUTHOR]

In studies of multi-agent interaction, especially in game theory, the notion of equilibrium often plays a prominent role. A typical scenario for the belief merging problem is one in which several agents pool their beliefs together to form a consistent 'group' picture of the world. The aim of this paper is to define and study new notions of equilibria in belief merging. To do so, we assume the agents arrive at consistency via the use of a social belief removal function, in which each agent, using his own individual removal function, removes some belief from his stock of beliefs. We examine several notions of equilibria in this setting, assuming a general framework for individual belief removal due to Booth et al. We look at their inter-relations as well as prove their existence or otherwise. We also show how our equilibria can be seen as a generalisation of the idea of taking maximal consistent subsets of agents. [ABSTRACT FROM AUTHOR]

Belief merging is concerned with the integration of several belief bases such that a coherent belief base is developed. Various belief merging models that use a belief negotiation game have been developed. These models often consist of two key functions, namely, negotiation and weakening. A negotiation function finds and selects the weakest belief bases among the available belief bases, while the weakening function removes the least valuable set of information from the selected belief base. This process is iteratively repeated until a consistent belief base is developed. In this paper, we extend the current game-based belief merging models by introducing the Subjective belief game model. The Subjective belief game model operates over a Subjective belief profile, which consists of belief bases with Subjectively annotated formulas. The Subjective information attached to each formula enables the proposed model to prioritize the formulas in the merging process. One of the advantages of the proposed game is that it provides room for enhancing the content of the weak belief bases, instead of enforcing their further weakening. Trustworthiness of the information sources is also considered. We provide several instantiations of the model. The Subjective belief game model can be useful for formalizing a negotiation process between the human participants of a design process in cases where discrepancies and conflicts arise. We apply this belief game model to an example case study of collaboratively designing some parts of unified modeling language (UML) class diagram for vehicle design. [ABSTRACT FROM PUBLISHER]

Abstract: When aggregating information from a group of agents, accepting the pieces of information shared by all agents is a natural requirement. In this paper, we investigate such a unanimity condition in the setting of propositional merging. We discuss two interpretations of the unanimity condition. We show that the first interpretation is captured by existing postulates for merging. But the second interpretation is not, and this leads to the introduction of a new disjunction postulate (Disj). It turns out that existing operators satisfying (Disj) do not perform well with respect to the standard criteria used to evaluate merging operators: logical properties, computational complexity and strategy-proofness. To fill this gap, we introduce two new families of propositional merging operators, quota operators and Gmin operators, which satisfy (Disj), and achieve interesting trade-offs with respect to the logical, computational, and strategy-proofness criteria. [Copyright &y& Elsevier]

In the last decade, several approaches have been proposed for merging multiple and potentially conflicting pieces of information. Egalitarian fusion modes pick solutions that minimize the local dissatisfaction of each source (agent, expert), which is involved in the fusion process. When pieces of information to merge are prioritized, or ranked, most existing approaches assume that these priority degrees are commensurable, namely sources are assumed to share the same meaning of uncertainty scales. This article provides useful strategies for an egalitarian fusion of incommensurable ranked belief bases under constraints. In particular, it focuses on Max-based merging operators, and proposes a merging operator that allows to aggregate a set of ranked belief bases E. This operator is based on the concept of compatible scales. We provide three equivalent characterizations of this operator. The first one shows that Max-based merging of incommensurable belief bases can also be defined in terms of a Pareto-like ordering on possible worlds, denominated SMP ordering. The second one is based on the notion of compatible rankings defined on finite scales. The third one is only based on total pre-orders induced by ranked bases to merge. The last part of the article analyses rational postulates satisfied by our merging operator and compare it with some related works. [ABSTRACT FROM PUBLISHER]

The theory of belief revision and merging has recently been applied to judgement aggregation. In this article I argue that judgements are best aggregated by merging the evidence on which they are based, rather than by directly merging the judgements themselves. This leads to a three-step strategy for judgement aggregation. First, merge the evidence bases of the various agents using some method of belief merging. Second, determine which degrees of belief one should adopt on the basis of this merged evidence base, by applying objective Bayesian theory. Third, determine which judgements are appropriate given these degrees of belief by applying a decision-theoretic account of rational judgement formation. [ABSTRACT FROM AUTHOR]

The present paper introduces a belief merging procedure by majority using the standard format of Adaptive Logics. The core structure of the logic ADM c ( Adaptive Doxastic Merging by Counting) consists in the formulation of the conflicts arising from the belief bases of the agents involved in the procedure. A strategy is then defined both semantically and proof-theoretically which selects the consistent contents answering to a majority principle. The results obtained are proven to be equivalent to a standard majority operator for bases with partial support. [ABSTRACT FROM AUTHOR]

Abstract: Recently, several belief negotiation models have been introduced to deal with the problem of belief merging. A negotiation model usually consists of two functions: a negotiation function and a weakening function. A negotiation function is defined to choose the weakest sources and these sources will weaken their point of view using a weakening function. However, the currently available belief negotiation models are based on classical logic, which makes them difficult to define weakening functions. In this paper, we define a prioritized belief negotiation model in the framework of possibilistic logic. The priority between formulae provides us with important information to decide which beliefs should be discarded. The problem of merging uncertain information from different sources is then solved by two steps. First, beliefs in the original knowledge bases will be weakened to resolve inconsistencies among them. This step is based on a prioritized belief negotiation model. Second, the knowledge bases obtained by the first step are combined using a conjunctive operator which may have a reinforcement effect in possibilistic logic. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]