Simplicial Belief
🤖 AI Summary
This work addresses the limitation of existing distributed epistemic logics, which are typically grounded in simplicial complexes and thus struggle to express belief. For the first time, it formalizes belief within the simplicial complex semantics by introducing a multi-colored simplicial complex structure. By incorporating plausibility relations among states, the framework naturally accommodates multiple notions of belief. This approach significantly extends the expressive power of traditional simplicial models, offering a novel semantic foundation and modeling tool for reasoning about uncertain epistemic attitudes—such as belief—in multi-agent systems.
Application Category
📝 Abstract
Recently, much work has been carried out to study simplicial interpretations of modal logic. While notions of (distributed) knowledge have been well investigated in this context, it has been open how to model belief in simplicial models. We introduce polychromatic simplicial complexes, which naturally impose a plausibility relation on states. From this, we can define various notions of belief.
Problem
Research questions and friction points this paper is trying to address.
simplicial models
belief
modal logic
plausibility relation
polychromatic simplicial complexes
Innovation
Methods, ideas, or system contributions that make the work stand out.
polychromatic simplicial complexes
belief modeling
plausibility relation
simplicial models
modal logic
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