Fragments of propositional logic, i.e., tailored sub-languages designed for neatly structured data, are relevant in many practical settings. This paper studies belief update in fragments (e.g., Horn, Krom, affine) that obey a desirable semantic closure condition. We assume update is guided by the well-known Katsuno-Mendelzon (KM) postulates, which in full propositional logic characterize update operators as choice functions guided by total or partial preorders over possible worlds. Because many useful fragments cannot express every connective (e.g., they often lack closure under disjunction), the KM axioms must be rephrased and supplemented to keep updates rational in these less expressive environments. Our main result is a set of representation theorems: once the KM postulates are adjusted, they capture exactly the update operators generated by suitably constrained total or partial preorders within the fragment. In addition, we clarify how revision works in fragments when partial preorders are allowed and also present concrete, fragment-friendly update operators.

Apportionment is the task of assigning resources to entities with different entitlements in a fair manner, and specifically a manner that is as proportional as possible. The best-known application is the assignment of parliamentary seats to political parties based on their share in the popular vote. Here we enrich the standard model of apportionment by associating each seat with a weight representing the (objective) value of that seat. A seat’s weight reflects the fact that different seats might come with different roles, such as chair or treasurer. We define several apportionment methods and natural fairness requirements for this new setting, and we study the extent to which our methods satisfy these requirements. Our findings show that full fairness is harder to achieve than in the standard apportionment setting. Yet, for several natural relaxations of those requirements we can achieve stronger results than in the more expressive model of fair division with entitlements, where the values of objects are subjective.

Approval-based multiwinner voting, one of the central topics in computational social choice, addresses collective decision-making scenarios in which n voters select a committee of k candidates from a larger pool of alternatives. A fundamental aim is to ensure that the elected committee proportionately represents the preferences of the electorate. Consequently, much effort has gone into exploring various proportionality notions and developing voting rules to achieve them. A key intuition underlying many fairness axioms and voting rules is that an optimal outcome is attained when no subset of voters can improve their position by reallocating their endorsements. In this paper, we formalize this intuition by defining a new class of games, which we call budgeting games, where committees occur as a result of voters' decisions about how to allocate a given budget. Our primary contribution lies in introducing this new class of normal-form games and showing that key notions in multiwinner voting theory, such as priceability, the core and EJR (Extended Justified Representation) can be thought of as equilibria of budgeting games. Remarkably, our budgeting games do not just capture existing concepts, but also give rise to entirely new families of voting rules. These rules, which are guaranteed to satisfy desirable fairness axioms, are based on improving-move dynamics in the respective budgeting games, and include the well-known Method of Equal Shares. Finally, we showcase the applicability of our game-theoretic perspective by proving existence of strong equilibria in a restricted version of our budgeting games, which implies that the core in a novel special case of multiwinner elections is non-empty.

We study a model inspired by deliberative practice, in which agents selectively disclose evidence about a set of alternatives prior to taking a final decision on them. We are interested in whether such a process, when iterated to termination, results in the objectively best alternatives being selected—thereby lending support to the idea that groups can be wise even when their members communicate with each other. We find that, under certain restrictions on the relative amounts of evidence, together with the actions available to the agents, there exist deliberation protocols in each of the two families we look at (i.e., simultaneous and sequential) that offer desirable guarantees. Simulation results further complement this picture, by showing how the distribution of evidence among the agents influences parameters of interest, such as the outcome of the protocols and the number of rounds until termination.

We study a model of preference revision in which a prior preference over a set of alternatives is adjusted in order to accommodate input from an authoritative source, while maintaining certain structural constraints (e.g., transitivity, completeness), and without giving up more information than strictly necessary. We analyze this model under two aspects: the first allows us to capture natural distance-based operators, at the cost of a mismatch between the input and output formats of the revision operator. Requiring the input and output to be aligned yields a second type of operator, which we characterize using preferences on the comparisons in the prior preference Prefence revision is set in a logic-based framework and using the formal machinery of belief change, along the lines of the well-known AGM approach: we propose rationality postulates for each of the two versions of our model and derive representation results, thus situating preference revision within the larger family of belief change operators.

We study epistemic voting on binary issues where voters are characterized by their competence, i.e., the probability of voting for the correct alternative, and can choose between two actions: voting or abstaining. In our setting voting involves the expenditure of some effort, which is required to achieve the appropriate level of competence, whereas abstention carries no effort. We model this scenario as a game and characterize its equilibria under several variations. Our results show that when agents are aware of everyone's incentives, then the addition of effort may lead to Nash equilibria where wisdom of the crowds is lost. We further show that if agents' awareness of each other is constrained by a social network, the topology of the network may actually mitigate this effect.

In this paper we introduce proportionality to belief merging. Belief merging is a framework for aggregating information presented in the form of propositional formulas, and it generalizes many aggregation models in social choice. In our analysis, two incompatible notions of proportionality emerge: one similar to standard notions of proportionality in social choice, the other more in tune with the logic-based merging setting. Since established merging operators meet neither of these proportionality requirements, we design new proportional belief merging operators. We analyze the proposed operators against established rationality postulates, finding that current approaches to proportionality from the field of social choice are, at their core, incompatible with standard rationality postulates in belief merging. We provide characterization results that explain the underlying conflict, and provide a complexity analysis of our novel operators.

Classical axiomatizations of belief revision include a postulate stating that if new information is consistent with initial beliefs, then revision amounts to simply adding the new information to the original knowledge base. This postulate assumes a conservative attitude towards initial beliefs, in the sense that an agent faced with the need to revise them will seek to preserve initial beliefs as much as possible. In this work we look at operators that can assume different attitudes towards original beliefs. We provide axiomatizations of these operators by varying the aforementioned postulate and obtain representation results that characterize the new types of operators using preorders on possible worlds. We also present concrete examples for each new type of operator, adapting notions from decision theory.

In line with recent work on belief change in fragments of propositional logic, we study belief update in the Horn fragment. We start from the standard KM postulates used to axiomatize belief update operators; these postulates lend themselves to semantic characterizations in terms of partial (resp. total) preorders on possible worlds. Since the Horn fragment is not closed under disjunction, the standard postulates have to be adapted for the Horn fragment. Moreover, a restriction on the preorders (i.e., Horn compliance) and additional postulates are needed to obtain sensible characterizations for the Horn fragment, and this leads to our main contribution: a representation result which shows that the class of update operators captured by Horn compliant partial (resp. total) preorders over possible worlds is precisely that given by the adapted and augmented Horn update postulates. With these results at hand, we provide concrete Horn update operators and are able to shed light on Horn revision operators based on partial preorders.

We study the problem of finding a social ranking over individuals given a ranking over coalitions formed by them. We investigate the use of a ceteris paribus majority principle as a social ranking solution inspired from the classical axioms of social choice theory. Faced with a Condorcet-like paradox, we analyze the consequences of restricting the domain according to an adapted version of single-peakedness. We conclude with a discussion on different interpretations of incompleteness of the ranking over coalitions and its exploitation for defining new social rankings, providing a new rule as an example.

We study a type of change on knowledge bases inspired by the dynamics of formal argumentation systems, where the goal is to enforce acceptance of certain arguments. We put forward that enforcing acceptance of arguments can be viewed as a member of the wider family of belief change operations, and that an axiomatic treatment of it is therefore desirable. In our case, laying down axioms enables a precise account of the close connection between enforcing arguments and belief revision. Our analysis of enforcing arguments proceeds by (i) axiomatizing it as an operation in propositional logic and providing a representation result in terms of rankings on sets of interpretations, (ii) showing that it stands in close relationship to belief revision, and (iii) using it as a gateway towards a principled treatment of enforcement in abstract argumentation.

Belief merging is a central operation within the field of belief change and addresses the problem of combining multiple, possibly mutually inconsistent knowledge bases into a single, consistent one. A current research trend in belief change is concerned with representation theorems tailored to fragments of logic, in particular Horn logic. Hereby, the goal is to guarantee that the result of the change operations stays within the fragment under consideration. While several such results have been obtained for Horn revision and Horn contraction, merging of Horn theories has been neglected so far. In this article, we provide a novel representation theorem for Horn merging by strengthening the standard merging postulates. Moreover, we present concrete Horn merging operators satisfying all postulates.

Merging is one of the central operations in the field of belief change, which is concerned with aggregating the opinions of individuals. Representation theorems provide a family of merging operators satisfying some natural desiderata for merging beliefs. However, little is known about how these operators can be further distinguished. In the field of social choice, on the other hand, numerous properties have been proposed in order to classify voting rules. In this work, we adapt these properties to the context of merging and investigate how they relate to the standard postulates. Our results thus lead to a more fine-grained classification of merging operators and shed light on the question of which particular merging operator is best suited in a concrete application domain.