Related papers: Properties of Selector Proofs
Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence…
When making simultaneous decisions, our preference for the outcomes on one subset can depend on the outcomes on a disjoint subset. In referendum elections, this gives rise to the separability problem, where a voter must predict the outcome…
The famous G\"odel incompleteness theorem states that for every consistent sufficiently rich formal theory T there exist true statements that are unprovable in T. Such statements would be natural candidates for being added as axioms, but…
We prove that in a countable theory T fully stable over a predicate P, any complete set A has the existence property. This means that A can be extended to a model of T without changing the P-part. In particular, T has the Gaifman property:…
Motivated by a problem of scheduling unit-length jobs with weak preferences over time-slots, the random assignment problem (also called the house allocation problem) is considered on a uniform preference domain. For the subdomain in which…
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…
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
In this short note we relate some known properties of propositional calculus to purely algebraic considerations of a Boolean algebra. Classes of formulas of propositional calculus are considered as elements of a Boolean algebra. As such…
The oracle property of model selection procedures has attracted a large volume of favorable publications in the literature, but also faced criticisms of being ineffective and misleading in applications. In this paper, we introduce a class…
By Solovay's celebrated completeness result on formal provability we know that the provability logic $\mathrm GL$ describes exactly all provable structural properties for any sound and strong enough arithmetical theory with a decidable…
A set-theoretic property called Property S is introduced as a generalization of the well-known Property B. Property S is named for A.Schrijver who first used it to formulate an equivalent of the boolean prime ideal theorem. It was…
We consider different choice procedures such as scoring rules, rules, using majority relation, value function and tournament matrix, which are used in social and multi-criteria choice problems. We focus on the study of the properties that…
In this paper we define and examine the power of the {\em conditional-sampling} oracle in the context of distribution-property testing. The conditional-sampling oracle for a discrete distribution $\mu$ takes as input a subset $S \subset…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
Although regular conditional distributions (r.c.d.) are well-defined and widely used measure-theoretic objects, they can violate our intuition from the classical definition of a conditional probability given an event. For that purpose, the…
We show that the sequentially $(S_r)$ condition for simplicial complexes is a topological property. Along the way, we present an elementary proof for the fact that the Serre's condition $(S_r)$ is a topological property.
Mathematical proofs are a cornerstone of control theory, and it is important to get them right. Deduction systems can help with this by mechanically checking the proofs. However, the structure and level of detail at which a proof is…
Algorithmic theories of randomness can be related to theories of probabilistic sequence prediction through the notion of a predictor, defined as a function which supplies lower bounds on initial-segment probabilities of infinite sequences.…
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…
In this paper, we analyze properties of prime number sequences produced by the alternating sum of higher-order subsequences of the primes. We also introduce a new sieve which will generate these prime number sequences via the systematic…