The challenge of finding compromises between agent proposals is fundamental to AI sub-fields such as argumentation [27], mediation [22], and negotiation [20]. Building on this tradition, Elkind et al. [9] introduced a process for coalition formation that seeks majority-supported proposals preferable to the status quo, using a metric space where each agent has an ideal point. The crucial step in this iterative process involves identifying compromise proposals around which agent coalitions can unite. How to effectively find such compromise proposals, however, remains an open question. We address this gap by formalizing a holistic model that encompasses agent bounded rationality and uncertainty and developing AI models to generate such compromise proposals. We focus on the domain of collaboratively writing text documents-e.g., to enable the democratic creation of a community constitution. We apply NLP (Natural Language Processing [7]) techniques and utilize LLMs (Large Language Models [35]) to create a semantic metric space for text and develop algorithms to suggest suitable compromise points. To evaluate the effectiveness of our algorithms, we simulate various coalition formation processes and demonstrate the potential of AIto facilitate large-scale democratic text editing, such as collaboratively drafting a constitution-an area where traditional tools are limited.
The principle of minimal change in belief revision theory requires that, when accepting new information, one keeps one's belief state as close to the initial belief state as possible. This is precisely what the method known as minimal revision does. However, unlike less conservative belief revision methods, minimal revision falls short in learning power: It cannot learn everything that can be learned by other learning methods. We begin by showing that, despite this limitation, minimal revision is still a successful learning method in a wide range of situations. Firstly, it can learn any problem that is finitely identifiable. Secondly, it can learn with positive and negative data, as long as one considers finitely many possibilities. We then characterize the prior plausibility assignments (over finitely many possibilities) that enable one to learn via minimal revision, and do the same for conditioning and lexicographic upgrade. Finally, we show that not all of our results still hold when learning from possibly erroneous information.
Impure simplicial complexes are a powerful tool to model multi-agent epistemic situations where agents may die, but it is difficult to define a satisfactory semantics for the ordinary propositional modal language on such models, since many conceptually dubious expressions involving dead agents can be expressed in this language. In this paper, we introduce a term-modal language with assignment operators, in which such conceptually dubious expressions are syntactically excluded. We define both simplicial semantics and first-order Kripke semantics for this language, characterize their respective expressivity through notions of bisimulation, and show that the two semantics are equivalent when we consider a special class of first order Kripke models called local epistemic models. We also offer a complete axiomatization for the epistemic logic based on this language, and show that our language has a notion of assignment normal form. Finally, we discuss the behavior of a kind of intensional distributed knowledge that can be naturally expressed in our language.
Simulation and refinement are variations of the bisimulation relation, where in the former we keep only atoms and forth, and in the latter only atoms and back. Quantifying over simulations and refinements captures the effects of information change in a multi-agent system. In the case of quantification over refinements, we are looking at all the ways the agents in a system can become more informed. Similarly, in the case of quantification over simulations, we are dealing with all the ways the agents can become less informed, or in other words, could have been less informed, as we are at liberty how to interpret time in dynamic epistemic logic. While quantification over refinements has been well explored in the literature, quantification over simulations has received considerably less attention. In this paper, we explore the relationship between refinements and simulations. To this end, we also employ the notion of mutual factual ignorance that allows us to capture the state of a model before agents have learnt any factual information. In particular, we consider the extensions of multi-modal logic with the simulation and refinement modalities, as well as modalities for mutual factual ignorance. We provide reduction-based axiomatizations for several of the resulting logics that are built extending one another in a modular fashion.
We introduce a new logic of graded distributed belief that allows us to express the fact that a group of agents distributively believe that a certain fact holds with at least strength k. We interpret our logic by means of computationally grounded semantics relying on the concept of belief base. The strength of the group's distributed belief is directly computed from the group's belief base after having merged its members' individual belief bases. We illustrate our logic with an intuitive example, formalizing the notion of epistemic disagreement. We also provide a sound and complete Hilbert-style axiomatization, decidability result obtained via filtration, and a tableaux-based decision procedure that allows us to state PSPACE-completeness for our logic.
This paper examines the conditions under which Bayesian conditioning aligns with Maximum Entropy. Specifically, I address cases in which newly learned information does not correspond to an event in the probability space defined on the sample space of outcomes. To facilitate Bayesian conditioning in such cases, one must therefore extend the probability space so that the new information becomes an event in this expanded space. Skyrms (1985) argues that Bayesian conditioning in an extended probability space on a product space of outcomes aligns precisely with the solution from Maximum Entropy. In contrast, Seidenfeld (1986) uses Friedman and Shimony's (1971) result to criticize Skyrms' approach as trivial, suggesting that alignment holds only under a degenerate probability model. Here, I argue that Friedman and Shimony's result must either (1) be a benign consequence of Skyrms' approach, or (2) pose a universal challenge to any method of extending spaces. Accepting (2) would imply that Bayesian conditioning is incapable of accommodating information beyond the probability space defined on the original outcome space.
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically computability and set theory, to analyze the grounded extension, a widely-used model of maximally skeptical reasoning, defined as the least fixed-point of a natural defense operator. Without additional constraints, finding this fixed-point requires transfinite iterations. We identify the exact ordinal number corresponding to the length of this iterative process and determine the complexity of deciding grounded acceptance, showing it to be maximally complex. This shows a marked distinction from the finite case where the grounded extension is polynomial-time computable, thus simpler than other reasoning problems explored in formal argumentation.
We study cautious reasoning in finite sequential games played by agents with perfect recall. Our contribution lies in formulating a definition of prudent rationalizability (Heifetz et al. 2021, BEJTE) as an iterative reduction procedure of beliefs. To this end, we represent the players' beliefs by systems of conditional non-standard probability measures. The key novelty is the notion of c-strong belief, a non-standard, "cautious" version of strong belief (Battigalli and Siniscalchi 2002, JET). Our formulation of prudent rationalizability embodies a "best rationalization principle" similar to the one that underlies the solution concept of strong rationalizability. The main results show the equivalence between the proposed definition with the one originally put forth by Heifetz et al. (2021) in terms of conditional beliefs represented by standard probabilities. In particular, it is shown that prudent rationalizability can be algorithmically characterized by iterated admissibility. Finally, our formulation can be extended to sequential games with unawareness.
We study the design of mechanisms under asymmetric awareness and information. While the mechanism designer cannot necessarily commit to a particular social choice function in the face of unawareness, she can at least commit to properties of social choice functions such as efficiency given ex post awareness. Assuming quasi-linear utilities and private values, we show that we can implement in conditional dominant strategies a social choice function that is utilitarian ex post efficient under pooled awareness without the need of the social planner being fully aware ex ante. To this end, we develop novel dynamic versions of Vickrey-Clarke-Groves mechanisms in which true types are revealed and subsequently elaborated at endogenous higher awareness levels. We explore how asymmetric awareness affects budget balance and participation constraints. We show that ex ante unforeseen contingencies are no excuse for deficits. Finally, we propose a dynamic elaboration reverse second price auction for efficient procurement of complex incompletely specified projects with budget balance and participation constraints.
Work on the development of optimal fault-tolerant Agreement protocols using the logic of knowledge has concentrated on the "full information" approach to information exchange, which is costly with respect to message size. Alpturer, Halpern, and van der Meyden (PODC 2023) introduced the notion of optimality with respect to a limited information exchange, and studied the Eventual Agreement problem in the sending omissions failure model. The present paper studies the Simultaneous Agreement problem for the crash failures model, and a number of limited information exchanges from the literature. In particular, the paper considers information exchanges from a FloodSet protocol (Lynch, Distributed Algorithms 1996), a variant of this in which agents also count the number of failures (Castañeda et al, NETYS 2017), and a variant in which agents associate each agent with a value (Raynal, PRDC 2002). A new information exchange is also introduced that enables decisions to be made at worst one round later than the optimal protocol of Dwork and Moses (I C 88), but with lower computation cost and space requirements. By determining implementations of a knowledge based program, protocols are derived that are optimal amongst protocols for each of these information exchanges.
We discuss winning possibilities of players in various variants of cops and robber game played on large random graphs, a testbed for various kinds of network queries, search problems in particular. We explore the use of logic frameworks to investigate such results; in particular, we show that whenever a winning condition for either player can be expressed as a certain kind of formula in first-order logic, that player almost always wins. In the process, we obtain more insight into the logic-game connection from the zero-one law perspective.
Distributed knowledge is a key concept in the standard epistemic logic of knowledge-that. In this paper, we propose a corresponding notion of distributed knowledge-how and study its logic. Our framework generalizes two existing traditions in the logic of know-how: the individual-based multi-step framework and the coalition-based single-step framework. In particular, we assume a group can accomplish more than what its individuals can jointly do. The distributed knowledge-how is based on the distributed knowledge-that of a group whose multi-step strategies derive from distributed actions that subgroups can collectively perform. As the main result, we obtain a sound and strongly complete proof system for our logic of distributed knowledge-how, which closely resembles the logic of distributed knowledge-that in both the axioms and the proof method of completeness.
In this paper, we generalize epistemic logic so that it can help reason about ways of combining common knowledge and distributed knowledge such as "common distributed knowledge", "distributed common knowledge", "distributed common distributed knowledge" and so on. Moreover, we study the logic of its dynamic update by arbitrary reading events. We axiomatize these logics and prove their soundness and completeness.
Aumann's famous Agreeing to Disagree Theorem states that if a group of agents share a common prior, update their beliefs by Bayesian conditioning based on private information, and have common knowledge of their posterior beliefs regarding some event, these posteriors must be identical. There is an elegant generalization of this theorem by Monderer and Samet, later refined by Neeman: if a group of agents share a common prior, update their beliefs using Bayesian conditioning on private information, and have common p-belief of their posteriors, these posteriors must be close (i.e., they cannot differ by more than 1 - p). Here, common p-belief generalizes the concept of common knowledge to probabilistic beliefs: agents commonly p-believe an event E if everyone believes E to at least degree p, everyone believes to at least degree p that everyone believes E to at least degree p, and so on. This paper further extends the Monderer-Samet-Neeman Agreement Theorem from classical probability measures to plausibility measures – a very general framework introduced by Halpern that unifies many formal models of belief. To facilitate this extension, we provide a new proof of the Monderer-Samet-Neeman theorem in the classical setting. Building upon both the original proof and our new proof, we offer two different generalizations of the theorem to plausibility-based structures. We then apply these generalized results to several non-classical belief models, including conditional probability structures and lexicographic probability structures. Moreover, we show that whenever our generalized theorems do not apply, the Monderer-Samet-Neeman Agreement Theorem fails. These findings suggest that our results successfully identify the minimal conditions required for a belief model to satisfy the Monderer-Samet-Neeman Agreement Theorem.
In recent years, epistemic logics have been extended with operators K_ax for knowledge of (the value of) a variable x (by an agent a). We study dynamic versions of these logics, enriched with modalities for semi-public data-exchange events (e.g., public announcements, data-sharing within a subgroup, or changing the value of a variable). To obtain a complete axiomatization of data-exchange events, in the presence of equality x = y and K_ax, one needs to extend the logic further: first, with an operator for distributed knowledge K_Ax of the value (by a group of agents A); next, with a conditional version of this: distributed knowledge K^P_A x (of the value by a group) given some hypothetical condition (expressed by some proposition P); then, with definite descriptions x^P_A , denoting the 'hypothetical' value of x according to A's (distributed) knowledge given condition P. In order to deal with common knowledge in the presence of semi-public data exchanges, we also need to add a novel conditional version of the recent concept of common distributed knowledge. We investigate the resulting logic, giving examples and presenting a complete axiomatization and a decidability proof.
The Skating System, which originated from the scrutineering system in dance sport tournaments, can be formulated as a voting system: We introduce and formalize the Skating System Single (SkS, for short), a new voting system embedded into the framework of computational social choice. Although SkS has similarities with Bucklin voting, it differs from it because it is subject to additional constraints when determining the election winners. Through an analysis of the axiomatic properties of SkS and of its vulnerability to manipulative and electoral control attacks, we compare SkS with Bucklin voting and provide insights into its potential strengths and weaknesses. In particular, we show that SkS satisfies nondictatorship as well as the majority criterion, positive responsiveness, monotonicity, and citizens' sovereignty but violates the Condorcet criterion, strong monotonicity, independence of clones, consistency, participation, resoluteness, and strategy-proofness. Further, we study manipulation, i.e., where (groups of) voters vote strategically to improve the outcome of an election in their favor, showing that the constructive coalitional weighted manipulation problem for SkS is NP-complete, while the destructive variant can be solved in polynomial time. Lastly, we initiate the study of electoral control, where an external agent attempts to change the election outcome by interfering with the structure of the election. Here, we show NP-completeness for constructive and destructive control by deleting candidates as well as for constructive control by adding voters, whereas we show that the problem of destructive control by adding voters can be solved in polynomial time.
Hedonic games -- at the interface of cooperative game theory and computational social choice -- are coalition formation games in which the players have preferences over the coalitions they can join. Kerkmann et al. [13] introduced altruistic hedonic games where the players' utilities depend not only on their own but also on their friends' valuations of coalitions. The complexity of the verification problem for core stability has remained open in four variants of altruistic hedonic games: namely, for the variants with average- and minimum-based "equal-treatment" and "altruistic-treatment" preferences. We solve these four open questions by proving the corresponding problems coNP-complete; our reductions rely on rather intricate gadgets in the related networks of friends.
Methods for probability updating, of which Bayesian conditionalization is the most well-known and widely used, are modeling tools that aim to represent the process of modifying an initial epistemic state, typically represented by a prior probability function P, which is adjusted in light of new information. Notably, updating methods and conditional sentences seem to intuitively share a deep connection, as is evident in the case of conditionalization. The present work contributes to this line of research and aims at shedding new light on the relationship between updating methods and conditional connectives. Departing from previous literature that often focused on a specific type of conditional or a particular updating method, our goal is to prove general results concerning the connection between conditionals and their probabilities. This will allow us to characterize the probabilities of certain conditional connectives and to understand what class of updating procedures can be represented using specific conditional connectives. Broadly, we adopt a general perspective that encompasses a large class of conditionals and a wide range of updating methods, enabling us to prove some general results concerning their interrelation.
Intentions are crucial for our practical reasoning. The rational intention obeys some simple logical principles, such as agglomeration and consistency, among others, motivating the search for a proper logic of intention. However, such a logic should be weak enough not to force the closure under entailment; otherwise, we cannot distinguish between intended consequences of agents' choices and their unintended side-effects. In this paper we argue that we should avoid not only the closure under entailment, but the weaker closure under equivalence as well. To achieve this, we develop a hyperintensional logic of intention, where what an agent intends is constrained by the agent's decision problem. The proposed system combines some elements of inquisitive and topic-sensitive theories of intensional modals. Along the way, we also show that the existing closest relatives of our framework overgenerate validities by validating some instances of closure under equivalence. Finally, we provide a sound and strongly complete axiomatization for this logic.
