Related papers: Every hierarchy of beliefs is a type
Belief change is a fundamental problem in AI: Agents constantly have to update their beliefs to accommodate new observations. In recent years, there has been much work on axiomatic characterizations of belief change. We claim that a better…
We consider a team formation setting where agents have varying levels of expertise in a global set of required skills, and teams are ranked with respect to how well the expertise of teammates complement each other. We model this setting as…
We present a game semantics for intuitionistic type theory. Specifically, we propose categories with families of a new variant of games and strategies for both extensional and intensional variants of the type theory with dependent function,…
Necessary and sufficient conditions for a measure to be an extreme point of the set of measures (on an abstract measurable space) with prescribed generalized moments are given, as well as an application to extremal problems over such moment…
Feferman proved in 1962 that any arithmetical theorem is a consequence of a suitable transfinite iteration of full uniform reflection of $\mathsf{PA}$. This result is commonly known as Feferman's completeness theorem. The purpose of this…
Information theory is a powerful framework for quantifying complexity, uncertainty, and dynamical structure in time-series data, with widespread applicability across disciplines such as physics, finance, and neuroscience. However, the…
The computer-mechanization of an ambitious explicit ethical theory, Gewirth's Principle of Generic Consistency, is used to showcase an approach for representing and reasoning with ethical theories exhibiting complex logical features like…
We regard Forcing Notions P adding real numbers and the algebras of P-measurable sets. As for Cohen- and Random-Forcing we can show that each analytic set is P-measurable using Solovay's Unfolding Trick for infinite games. To show this we…
We present for mental processes the program of mathematical mapping which has been successfully realized for physical processes. We emphasize that our project is not about mathematical simulation of brain's functioning as a complex physical…
We prove that a countable simple unidimensional theory that eliminates hyperimaginaries is supersimple. This solves a problem of Shelah in the more general context of simple theories under weak assumptions.
We prove the conjecture that any Grothendieck $(\infty,1)$-topos can be presented by a Quillen model category that interprets homotopy type theory with strict univalent universes. Thus, homotopy type theory can be used as a formal language…
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…
This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…
This paper provides an analysis of different formal representations of beliefs in epistemic game theory. The aim is to attempt a synthesis of different structures of beliefs in the presence of indeterminate probabilities. Special attention…
While non-contextual hidden-variable theories are proved to be impossible, contextual ones are possible. In a contextual hidden-variable theory, an observable is called a beable if the hidden-variable assigns its value in a given…
The Hausdorff hyperspace of a metric space consists of all its non-empty bounded closed sets and it is equipped with the Pompeiu--Hausdorff set distance. We present a simpler novel proof that the Hausdorff hyperspace of a complete space is…
Insightful interdisciplinary collaboration is essential to the principled governance of technology. When such efforts address the interaction between computation and society, they often focus on modeling, the process by which computer…
We consider time-delay systems with a finite number of delays in the state space $L^\infty\times\mathbb{R}^n$. In this framework, we show that forward completeness implies the bounded reachability sets property, while this implication was…
Let $ M (X)$ be the ring of all real measurable functions on a measurable space $(X, \mathscr{A})$. In this article, we show that every ideal of $M(X)$ is a $Z^{\circ}$-ideal. Also, we give several characterizations of maximal ideals of…
At the beginning of a dynamic game, players may have exogenous theories about how the opponents are going to play. Suppose that these theories are commonly known. Then, players will refine their first-order beliefs, and challenge their own…