Related papers: Conditional Preference Orders and their Numerical …
In this paper we introduce a Conditional Answer Set Programming framework (Conditional ASP) for the definition of conditional extensions of Answer Set Programming (ASP). The approach builds on a conditional logic with typicality, and on the…
We study the problem of fair sequential decision making given voter preferences. In each round, a decision rule must choose a decision from a set of alternatives where each voter reports which of these alternatives they approve. Instead of…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
We describe a theory of finite sets, and investigate the analogue of Dedekind's theory of natural number systems (simply infinite systems) in this theory. Unlike the infinitary case, in our theory, natural number systems come in differing…
We introduce the notion of saturated sets of primes of an algebraic number field and prove an analogue of Riemann's existence theorem for the decomposition groups of infinite stably saturated sets of primes.
We consider the question of which nonconvex sets can be represented exactly as the feasible sets of mixed-integer convex optimization problems. We state the first complete characterization for the case when the number of possible integer…
An equational axiomatisation of probability functions for one-dimensional event spaces in the language of signed meadows is expanded with conditional values. Conditional values constitute a so-called signed vector meadow. In the presence of…
P representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum dynamical many-body calculations such as Bose-Einstein condensation. We introduce a…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
We consider the Cauchy problem for a degenerate fractional conservation laws driven by a noise. In particular, making use of an adapted kinetic formulation, a result of existence and uniqueness of solution is established. Moreover, a…
We provide, for any regular uncountable cardinal $\kappa$, a new argument for Pincus' result on the consistency of $\mathrm{ZF}$ with the higher dependent choice principle $\mathrm{DC}_{<\kappa}$ and the ordering principle in the presence…
We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important…
The Zellner's g-prior and its recent hierarchical extensions are the most popular default prior choices in the Bayesian variable selection context. These prior set-ups can be expressed power-priors with fixed set of imaginary data. In this…
Partial orders are a natural model for the social hierarchies that may constrain "queue-like" rank-order data. However, the computational cost of counting the linear extensions of a general partial order on a ground set with more than a few…
We consider the problem of aggregation of incomplete preferences represented by arbitrary binary relations or incomplete paired comparison matrices. For a number of indirect scoring procedures we examine whether or not they satisfy the…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
Uniform preorders are a class of combinatory representations of Set-indexed preorders that generalize Pieter Hofstra's basic relational objects. An indexed preorder is representable by a uniform preorder if and only if it has as generic…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…
In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…
Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is…