Reasoning about unpredicted change consists in explaining observations by events; we propose here an approach for explaining time-stamped observations by surprises, which are simple events consisting in the change of the truth value of a fluent. A framework for dealing with surprises is defined. Minimal sets of surprises are provided together with time intervals where each surprise has occurred, and they are characterized from a model-based diagnosis point of view. Then, a probabilistic approach of surprise minimisation is proposed.

In this chapter, we are interested in formalizing the reasoning of a single agent who can make observations on a dynamic system and considers actions to perform on it. Reasoning about action and change is among the first issues addressed within Artificial Intelligence (AI); especially, it was the subject of the seminal article by McCarthy and Hayes [1969]. Research in this area has been very productive until the late 1990s. Among other things, solutions to the various problems to be faced when dealing with action representation were put forward and a classification of action languages according to their expressive power was undertaken. Moreover, much progress towards the automatization of reasoning about action and change was made, for example through the design and the evaluation of algorithms implementing the reasoning processes of the main action languages and the investigation of the computational complexity of such processes. The reasons why an agent may wish to act in order to modify the current state of a dynamic system or to learn more about it are numerous.

When allocating indivisible items to agents, it is known that the only strategyproof mechanisms that satisfy a set of rather mild conditions are constrained serial dictatorships: given a fixed order over agents, at each step the designated agent chooses a given number of items (depending on her position in the sequence). With these rules, also known as non-interleaving picking sequences, agents who come earlier in the sequence have a larger choice of items. However, this advantage can be compensated by a higher number of items received by those who come later. How to balance priority in the sequence and number of items received is a nontrivial question. We use a previous model, parameterized by a mapping from ranks to scores, a social welfare functional, and a distribution over preference profiles. For several meaningful choices of parameters, we show that the optimal sequence can be computed in polynomial time. Last, we give a simple procedure for eliciting scoring vectors and we study the impact of the assignment from agents to positions on the ex-post social welfare.

Epistemic voting interprets votes as noisy signals about a ground truth. We consider contexts where the truth consists of a set of objective winners, knowing a lower and upper bound on its cardinality. A prototypical problem for this setting is the aggregation of multi-label annotations with prior knowledge on the size of the ground truth. We posit noise models, for which we define rules that output an optimal set of winners. We report on experiments on multi-label annotations (which we collected).

Epistemic social choice aims at unveiling a hidden ground truth given votes, which are interpreted as noisy signals about it. We consider here a simple setting where votes consist of approval ballots: each voter approves a set of alternatives which they believe can possibly be the ground truth. Based on the intuitive idea that more reliable votes contain fewer alternatives, we define several noise models that are approval voting variants of the Mallows model. The likelihood-maximizing alternative is then characterized as the winner of a weighted approval rule, where the weight of a ballot decreases with its cardinality. We have conducted an experiment on three image annotation datasets; they conclude that rules based on our noise model outperform standard approval voting; the best performance is obtained by a variant of the Condorcet noise model.

Citizens' assemblies need to represent subpopulations according to their proportions in the general population. These large committees are often constructed in an online fashion by contacting people, asking for the demographic features of the volunteers, and deciding to include them or not. This raises a trade-off between the number of people contacted (and the incurring cost) and the representativeness of the committee. We study three methods, theoretically and experimentally: a greedy algorithm that includes volunteers as long as proportionality is not violated; a non-adaptive method that includes a volunteer with a probability depending only on their features, assuming that the joint feature distribution in the volunteer pool is known; and a reinforcement learning based approach when this distribution is not known a priori but learnt online.

We provide a comprehensive analysis of the computational complexity of the outcome determination problem for the most important aggregation rules proposed in the literature on logic-based judgment aggregation. Judgment aggregation is a powerful and flexible framework for studying problems of collective decision making that has attracted interest in a range of disciplines, including Legal Theory, Philosophy, Economics, Political Science, and Artificial Intelligence. The problem of computing the outcome for a given list of individual judgments to be aggregated into a single collective judgment is the most fundamental algorithmic challenge arising in this context. Our analysis applies to several different variants of the basic framework of judgment aggregation that have been discussed in the literature, as well as to a new framework that encompasses all existing such frameworks in terms of expressive power and representational succinctness.

Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical morphology in the context of propositional logic, and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based on a semantic approach, that have an intuitive interpretation and that are formally well behaved, to perform revision, fusion and abduction. Computation and tractability are addressed, and simple examples illustrate the typical results that can be obtained.

In the context of fair allocation of indivisible items, fairness concepts often compare the satisfaction of an agent to the satisfaction she would have from items that are not allocated to her: in particular, envy-freeness requires that no agent prefers the share of someone else to her own share. We argue that these notions could also be defined relative to the knowledge that an agent has on how the items that she does not receive are distributed among other agents. We define a family of epistemic notions of envy-freeness, parameterized by a social graph, where an agent observes the share of her neighbours but not of her non-neighbours. We also define an intermediate notion between envy-freeness and proportionality, also parameterized by a social graph. These weaker notions of envy-freeness are useful when seeking a fair allocation, since envy-freeness is often too strong. We position these notions with respect to known ones, thus revealing new rich hierarchies of fairness concepts. Finally, we present a very general framework that covers all the existing and many new fairness concepts.

We consider the following problem in which a given number of items has to be chosen from a predefined set. Each item is described by a vector of attributes and for each attribute there is a desired distribution that the selected set should fit. We look for a set that fits as much as possible the desired distributions on all attributes. Examples of applications include choosing members of a representative committee, where candidates are described by attributes such as sex, age and profession, and where we look for a committee that for each attribute offers a certain representation, i.e., a single committee that contains a certain number of young and old people, certain number of men and women, certain number of people with different professions, etc. With a single attribute the problem boils down to the apportionment problem for party-list proportional representation systems (in such case the value of the single attribute is the political affiliation of a candidate). We study some properties of the associated subset selection rules, and address their computation.