Related papers: Belief in Simplicial Complexes
The mathematical representation of uncertainty has led to a proliferation of preference structures, such as interval-valued fuzzy sets, intuitionistic fuzzy sets, and various granular models. While these extensions are often studied…
A primary motivation for reasoning under uncertainty is to derive decisions in the face of inconclusive evidence. However, Shafer's theory of belief functions, which explicitly represents the underconstrained nature of many reasoning…
In the philosophical literature, symmetries of physical theories are most often interpreted within the general doctrine called 'Sophistication'. Roughly speaking, it says that models related by symmetries can peacefully co-exist while…
The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. As biological systems are generally not…
When we work with information from multiple sources, the formalism each employs to handle uncertainty may not be uniform. In order to be able to combine these knowledge bases of different formats, we need to first establish a common basis…
Many economic theory models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness…
We consider simplicial sets equipped with a notion of smallness, and observe that this slight "topological" extension of the "algebraic" simplicial language allows a concise reformulation of a number of classical notions in topology, e.g.…
We construct a model structure on the category of ordered simplicial complexes, Quillen equivalent to the standard model structure on simplicial sets. This shows that simplicial complexes, which are fully combinatorial in nature, provide a…
We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible…
Plausibility models are Kripke models that agents use to reason about knowledge and belief, both of themselves and of each other. Such models are used to interpret the notions of conditional belief, degrees of belief, and safe belief. The…
This paper develops a new approach to computational argumentation that is informed by philosophical and linguistic views. Namely, it takes into account two ideas that have received little attention in the literature on computational…
The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, ?consistent betting behavior' arguments are well-known. To those not already convinced of the unique fitness and…
We investigate the position that foundational theories should be modelled on ordinary computability. In this context, we investigate the metamathematics of $\Sigma$ formulas. We consider theories whose axioms are implications between…
This paper proposes a belief-based framework for social norms in environments where individuals choose a single action. Relaxing the assumption that the appropriateness standard is common knowledge, the framework allows individuals to be…
We extend the notion of belief function to the case where the underlying structure is no more the Boolean lattice of subsets of some universal set, but any lattice, which we will endow with a minimal set of properties according to our…
The notion of argumentation and the one of belief stand in a problematic relation to one another. On the one hand, argumentation is crucial for belief formation: as the outcome of a process of arguing, an agent might come to (justifiably)…
This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and…
Conditioning is crucial in applied science when inference involving time series is involved. Belief calculus is an effective way of handling such inference in the presence of epistemic uncertainty -- unfortunately, different approaches to…
As large language models (LLMs) continue to demonstrate remarkable abilities across various domains, computer scientists are developing methods to understand their cognitive processes, particularly concerning how (and if) LLMs internally…
Explaining autonomous and intelligent systems is critical in order to improve trust in their decisions. Counterfactuals have emerged as one of the most compelling forms of explanation. They address ``why not'' questions by revealing how…