Related papers: Difference hierarchies and duality with an applica…

We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…

The emerging field of Diverse Intelligence seeks to identify, formalize, and understand commonalities in behavioral competencies across a wide range of implementations. Especially interesting are simple systems that provide unexpected…

We consider a model where an agent is must choose between alternatives that each provide only an imprecise description of the world (e.g. linguistic expressions). The set of alternatives is closed under logical conjunction and disjunction,…

We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…

The concept of Central sets, introduced by Furstenberg through the framework of topological dynamics, has played a pivotal role in combinatorial number theory. Furstenberg's Central Sets Theorem highlighted their rich combinatorial…

Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…

The fundamental algebraic concepts of quantum mechanics, as expressed by many authors, are reviewed and translated into the framework of the relatively new non-distributive system of Boolean fractions (also called conditional events or…

Considering patterns as sets of their instances, a difference operator over patterns computes a finite set of two given patterns, which represents the difference between the dividend pattern and the divisor pattern. A complement of a…

This paper proposes a nonparametric Bayesian method for exploratory data analysis and feature construction in continuous time series. Our method focuses on understanding shared features in a set of time series that exhibit significant…

In this work we build a quantum logic that allows us to refer to physical magnitudes pertaining to different contexts from a fixed one without the contradictions with quantum mechanics expressed in no-go theorems. This logic arises from…

Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and…

Label hierarchies are often available apriori as part of biological taxonomy or language datasets WordNet. Several works exploit these to learn hierarchy aware features in order to improve the classifier to make semantically meaningful…

The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain…

We extend the theory of unified correspondence to a very broad class of logics with algebraic semantics given by varieties of normal lattice expansions (LEs), also known as `lattices with operators'. Specifically, we introduce a very…

It is a common belief that the order of a Boolean network is mainly determined by its attractors, including fixed points and cycles. Using semi-tensor product (STP) of matrices and the algebraic state-space representation (ASSR) of Boolean…

A lattice is a partially ordered set supporting a meet (or join) operation that returns the largest lower bound (smallest upper bound) of two elements. Just like graphs, lattices are a fundamental structure that occurs across domains…

A class or taxonomic hierarchy is often manually constructed, and part of our knowledge about the world. In this paper, we propose a novel algorithm for automatically acquiring a class hierarchy from a classifier which is often a large…

This paper presents a graded hierarchy or chain of binary operations on the reals and the complex numbers. The operations are related distributively in the sense that any one of them distributes over the next lower operation in the chain.…

Our main goal is to develop a representation for finite distributive nearlattices through certain ordered structures. This representation generalizes the well-known representation given by Birkhoff for finite distributive lattices through…

From the work of Bauer and Lesnick, it is known that there is no functor from the category of pointwise finite-dimensional persistence modules to the category of barcodes and overlap matchings. In this work, we introduce sub-barcodes and…