Related papers: Probabilistically stable revision and comparative …
We look at preference change arising out of an interaction between two elements: the first is an initial preference ranking encoding a pre-existing attitude; the second element is new preference information signaling input from an…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
In this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
While belief functions may be seen formally as a generalization of probabilistic distributions, the question of the interactions between belief functions and probability is still an issue in practice. This question is difficult, since the…
We introduce the idea of *representation stability* (and several variations) for a sequence of representations V_n of groups G_n. A central application of the new viewpoint we introduce here is the importation of representation theory into…
We introduce a new notion of the stability of computations, which holds under post-processing and adaptive composition. We show that the notion is both necessary and sufficient to ensure generalization in the face of adaptivity, for any…
A natural notion of rationality/consistency for aggregating models is that, for all (possibly aggregated) models $A$ and $B$, if the output of model $A$ is $f(A)$ and if the output model $B$ is $f(B)$, then the output of the model obtained…
The purpose of this note is to prove the existence of a randomized mechanism, a social decision scheme (SDS), with desirable fairness, efficiency, and strategyproofness properties unmatched by all known SDSs. In particular, we disprove a…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
By probabilistic logic I mean a normative theory of belief that explains how a body of evidence affects one's degree of belief in a possible hypothesis. A new axiomatization of such a theory is presented which avoids a finite additivity…
The research on non-prioritized revision studies revision operators which do not accept all new beliefs. In this paper, we contribute to this line of research by introducing the concept of dynamic-limited revision, which are revisions…
Quasi-probabilities appear across diverse areas of physics, but their conceptual foundations remain unclear: they are often treated merely as computational tools, and operations like conditioning and Bayes' theorem become ambiguous. We…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Belief revision has been studied mainly with respect to background logics that are monotonic in character. In this paper we study belief revision when the underlying logic is non-monotonic instead--an inherently interesting problem that is…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…
Stability is a central property in learning and statistics promising the output of an algorithm $A$ does not change substantially when applied to similar datasets $S$ and $S'$. It is an elementary fact that any sufficiently stable algorithm…
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…
We establish an operational rigidity result for a broad class of probability rules in infinite-dimensional settings, applicable under normality and steering assumptions. Starting from a topological generalization of generalized…
The AGM recovery postulate says: assume a set of propositions X; assume that it is consistent and that it is closed under logical consequences; remove a belief P from the set minimally, but make sure that the resultant set is again some set…