Related papers: General combination rules for qualitative and quan…
Quantitative Relative Judgment Aggregation (QRJA) is a new research topic in (computational) social choice. In the QRJA model, agents provide judgments on the relative quality of different candidates, and the goal is to aggregate these…
We first show that there are practical situations in for instance forensic and gambling settings, in which applying classical probability theory, that is, based on the axioms of Kolmogorov, is problematic. We then introduce and discuss…
In this article, we consider iteration principles for contraction, with the goal of identifying properties for contractions that respect conditional beliefs. Therefore, we investigate and evaluate four groups of iteration principles for…
Facing an unknown situation, a person may not be able to firmly elicit his/her preferences over different alternatives, so he/she tends to express uncertain preferences. Given a community of different persons expressing their preferences…
Forecasts support decision making in a variety of applications. Statistical models can produce accurate forecasts given abundant training data, but when data is sparse, rapidly changing, or unavailable, statistical models may not be able to…
The rules of canonical quantization normally offer good results, but sometimes they fail, e.g., leading to quantum triviality ($=$ free) for certain examples that are classically nontrivial ($\ne$ free). A new procedure, called Enhanced…
New insights into the combinatorial structure of the Mandelbrot set are given by `Correspondence' and `Translation' Principles both conjectured and partially proved by E. Lau and D. Schleicher. We provide complete proofs of these principles…
Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…
This paper addresses distributed consensus optimization problems with mixed-integer variables, with a specific focus on Boolean variables. We introduce a novel distributed algorithm that extends the Consensus Augmented Lagrangian…
Specific to Math Information Retrieval is combining text with mathematical formulae both in documents and in queries. Rigorous evaluation of query expansion and merging strategies combining math and standard textual keyword terms in a query…
Within the biological, physical, and social sciences, there are two broad quantitative traditions: statistical and mathematical modeling. Both traditions have the common pursuit of advancing our scientific knowledge, but these traditions…
Traditional logic-based belief revision research focuses on designing rules to constrain the behavior of revision operators. Frameworks have been proposed to characterize iterated revision rules, but they are often too loose, leading to…
The formalism of quantum theory in Hilbert space has been applied with success to the modeling and explanation of several cognitive phenomena, whereas traditional cognitive approaches were problematical. However, this 'quantum cognition…
The uncertainty principle bounds the uncertainties about incompatible measurements, clearly setting quantum theory apart from the classical world. Its mathematical formulation via uncertainty relations, plays an irreplaceable role in…
A correlational dialect is introduced within the quantum theory language to give a unified treatment of finite-dimensional informational/operational quantum theories, infinite-dimensional relativistic quantum theories, and quantum gravity.…
Mediation is often treated as an extension of negotiation, without taking into account the unique role that norms and facts play in legal mediation. Additionally, current approaches for updating argument acceptability in response to…
Since no fusion theory neither rule fully satisfy all needed applications, the author proposes a Unification of Fusion Theories and a combination of fusion rules in solving problems/applications. For each particular application, one selects…
We propose a new framework for integrating quantifiers with other logical connectives in a higher-categorical setting. Our method systematically incorporates key coherence conditions-including those akin to the Beck-Chevalley property-and…
I argue that the rules of unitary quantum mechanics imply that observers who will themselves be subject to measurements in a linear combination of macroscopic states (``cat" measurements) cannot make reliable predictions on the results of…
To apply the abstract quantum formalism to a particular physical system, one must specify the precise form of the relevant measurement and symmetry transformation operators. These operators are determined by a set of rules, the…