Gaia Belardinelli

We explore logic as a method to model social phenomena, giving rise to what we term social logic. After introducing and defining this concept, we identify main examples of social logic, ranging from key precursors that have enabled researchers to start modeling complex social phenomena and concepts using the tools of logic, to more central examples of recent trends in social logic. We then reflect on logic as a modeling tool, discussing more generally why and how it is a relevant and valuable method in the social realm. Finally, we outline some promising directions for future research in social logic.

In this work, we present the first general logic of attention. Attention is a powerful cognitive ability that allows agents to focus on potentially complex information, such as logically structured propositions, higher-order beliefs, or what other agents pay attention to. This ability is a strength, as it helps to ignore what is irrelevant, but it can also introduce biases when some types of information or agents are systematically ignored. Existing dynamic epistemic logics for attention cannot model such complex attention scenarios, as they only model attention to atomic formulas. Additionally, such logics quickly become cumbersome, as their size grows exponentially in the number of agents and announced literals. Here, we introduce a logic that overcomes both limitations. First, we generalize edge-conditioned event models, which we show to be as expressive as standard event models yet exponentially more succinct (generalizing both standard event models and generalized arrow updates). Second, we extend attention to arbitrary formulas, allowing agents to also attend to other agents' beliefs or attention. Our work treats attention as a modality, like belief or awareness. We introduce attention principles that impose closure properties on that modality and that can be used in its axiomatization. Throughout, we illustrate our framework with examples of AI agents reasoning about human attention, demonstrating how such agents can discover attentional biases.

Awareness structures by Fagin, Halpern (Artif Intell 34:39–76, 1988) (FH) feature a syntactic awareness correspondence and accessibility relations modeling implicit knowledge. They are a flexible model of unawareness, and best interpreted from an outside modeler’s perspective. Unawareness structures by Heifetz et al. (J Econ Theory, 130:78–94, 2006, Games Econ Behav 62:305–324, 2008) (HMS) model awareness by a lattice of state spaces and explicit knowledge via possibility correspondences. Sublattices thereof can be interpreted as subjective views of agents. Open questions include (1) how implicit knowledge can be defined in HMS structures, and (2) in which way FH structures can be extended to model the agents’ subjective views. In this paper, we address (1) by defining implicit knowledge such that it is consistent with explicit knowledge in HMS models. We also introduce a variant of HMS models that instead of explicit knowledge, takes implicit knowledge and awareness as primitives. Further, we address (2) by introducing a category of FH models that are modally equivalent relative to sublanguages and can be interpreted as agents’ subjective views depending on their awareness. These constructions allow us to show an equivalence between HMS and FH models. As a corollary, we obtain soundness and completeness of HMS models with respect to the Logic of Propositional Awareness, based on a language featuring _both_ implicit and explicit knowledge.

When information grows abundant, attention becomes a scarce resource. As a result, agents must plan wisely how to allocate their attention in order to achieve epistemic efficiency. Here, we present a framework for multi-agent epistemic planning with attention, based on Dynamic Epistemic Logic. We identify the framework as a fragment of standard DEL, and consider its plan existence problem. While it is undecidable in the general case, we show that when attention is required for learning, all instances of the problem are decidable.