Related papers: The Blackwell relation defines no lattice
A quantum analogue of the famous Blackwell Theorem in classical statistics has recently been proposed. Given two quantum channels A and B, a set of payoff functions have been proven to have values for B at least as high as they are for A if…
A given question can be defined in terms of the set of statements or assertions that answer it. Application of logical inference to these sets of assertions allows one to derive the logic of inquiry among questions. There are interesting…
Relational lattice is a formal mathematical model for Relational algebra. It reduces the set of six classic relational algebra operators to two: natural join and inner union. We continue to investigate Relational lattice properties with…
Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type…
A notion of interpretation between arbitrary logics is introduced, and the poset Log of all logics ordered under interpretability is studied. It is shown that in Log infima of arbitrarily large sets exist, but binary suprema in general do…
We construct a weakly compact convex subset of $\ell^2$ with nonempty interior that has an isolated maximal element, with respect to the lattice order $\ell _+^2$. Moreover, the maximal point cannot be supported by any strictly positive…
We consider a simple model of higher order, functional computation over the booleans. Then, we enrich the model in order to encompass non-termination and unrecoverable errors, taken separately or jointly. We show that the models so defined…
We show that all finite lattices, including non-distributive lattices, arise as stable matching lattices when all agents have path-independent choice functions. This result answers an open question of Blair~\cite{blair1988lattice}. In the…
This article discusses completeness of Boolean Algebra as First Order Theory in Goedel's meaning. If Theory is complete then any possible transformation is equivalent to some transformation using axioms, predicates etc. defined for this…
Birkhoff's representation theorem for finite distributive lattices states that any finite distributive lattice is isomorphic to the lattice of order ideals (lower sets) of the partial order of the join-irreducible elements of the lattice.…
We provide proofs for the fact that certain orders have no descending chains and no antichains.
We show that the set of all measures on any measurable space is a complete lattice, i.e. every collection of measures has both a greatest lower bound and a least upper bound.
The union-closed sets conjecture, also known as Frankl's conjecture, is a well-studied problem with various formulations. In terms of lattices, the conjecture states that every finite lattice $L$ with more than one element contains a…
In this paper, we devise non-distributive relatives of Exactly True Logic (ETL) by Pietz and Riveccio and its dual (NFL) Non-Falsity Logic by Shramko, Zaitsev and Belikov. We consider two pre-orders which are algebraic counterparts of the…
Employing the lattice theory on majorization, we investigate the universal quantum uncertainty relation for any number observables and general measurement. We find: 1. The least bounds of the universal uncertainty relations can only be…
A general formulation of the basic conflict of the information problem is given, encapsulated in a "black hole theorem." This is framed in a more general context than the usual one of quantum field theory on a background, and is based on…
In a totally ordered set the notion of sorting a finite sequence is defined through a suitable permutation of the sequence's indices. In this paper we prove a simple formula that explicitly describes how the elements of a sequence are…
This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…
In a finite volume system, we prove a no-go theorem on a Leibniz rule with a care of locality argument on latttice. The new possibility on the Leibniz rule solutions on lattice is discussed. Although the new solution admits a local…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…