Related papers: Bi-capacities -- Part I: definition, M\"obius tran…
Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic…
This paper proposes that the distinctively human capacity for cumulative, adaptive, open-ended cultural evolution came about through two temporally-distinct cognitive transitions. First, the origin of Homo-specific culture over two MYA was…
We use a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to study a quantity called ``learning capacity'' which is a measure of the effective…
Making a decision is often a matter of listing and comparing positive and negative arguments. In such cases, the evaluation scale for decisions should be considered bipolar, that is, negative and positive values should be explicitly…
The aim of this paper is to introduce the notion of bipolar fuzzy soft hypervector spaces and study their basic properties. In this regard, at first some new operation and external hyperoperation are defined on bipolar fuzzy soft sets over…
We generalize the character formulas for multiplicities of irreducible constituents from group theory to semigroup theory using Rota's theory of M\"obius inversion. The technique works for a large class of semigroups including: inverse…
A potentialist system is a first-order Kripke model based on embeddings. I define the notion of bisimulation for these systems, and provide a number of examples. Given a first-order theory $T$, the system $\mathrm{Mod}(T)$ consists of all…
Human cooperation depends on how accurately we infer others' motives--how much they value fairness, generosity, or self-interest from the choices they make. We model that process in binary dictator games, which isolate moral trade-offs…
The human capacity for working together and with tools builds on cognitive abilities that, while not unique to humans, are most developed in humans both in scale and plasticity. Our capacity to engage with collaborators and with technology…
We consider capacity (fuzzy measure, non-additive probability) on a compactum as a monotone cooperative normed game. Then it is naturally to consider probability measures as elements of core of such game. We prove an analogue of…
In a noncontextual hidden variable model of quantum theory, hidden variables determine the outcomes of every measurement in a manner that is independent of how the measurement is implemented. Using a generalization of this notion to…
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…
Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world…
Perceptual multistability, observed across species and sensory modalities, offers valuable insights into numerous cognitive functions and dysfunctions. For instance, differences in temporal dynamics and information integration during…
A general theory of innovation and progress in human society is outlined, based on the combat between two opposite forces (conservatism/inertia and speculative herding "bubble" behavior). We contend that human affairs are characterized by…
Modal logics for reasoning about the power of coalitions capture the notion of effectivity functions associated with game forms. The main goal of coalition logics is to provide formal tools for modeling the dynamics of a game frame whose…
In important work on the parity of the partition function, Ono related values of the partition function to coefficients of a certain mock theta function modulo 2. In this paper, we use M\"obius inversion to give analogous results which…
Responsibility has long been a subject of study in law and philosophy. More recently, it became a focus of AI literature. The article investigates the computational complexity of two important properties of responsibility in collective…
Research ideation requires navigating trade-offs across multiple evaluative dimensions, yet most AI-assisted ideation tools leave this multi-dimensional reasoning unsupported, or reducing evaluation to unipolar scales where "more is…
The notion of a semitransitive binary action of a group $G$ on a topological space is introduced. A duality theorem is proved, establishing a bijective correspondence between semitransitive distributive binary $G$-spaces and topological…