Related papers: Consistency Spaces
Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. They have been used to reason about beliefs, lies, and group epistemic behaviour inspired by social…
We recover the rays in the tensor product of Hilbert spaces within a larger class of so called `states of compoundness', structured as a complete lattice with the `state of separation' as its top element. At the base of the construction…
Conceived and developed by Christopher Alexander through his life's work: The Nature of Order, wholeness is defined as a mathematical structure of physical space in our surroundings. Yet, there was no mathematics, as Alexander admitted…
In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented…
Attribute and size reductions are key issues in formal concept analysis. In this paper, we consider a special kind of equivalence relation to reduce concept lattices, which will be called local congruence. This equivalence relation is based…
The inherent difficulty in talking about quantum decoherence in the context of quantum cosmology is that decoherence requires subsystems, and cosmology is the study of the whole Universe. Consistent histories gave a possible answer to this…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
The aim of the present paper is to extend the concept of a congruence from lattices to posets. We use an approach different from that used by the first author and V. Sn\'a\v{s}el. By using our definition we show that congruence classes are…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…
The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft…
We design and conduct a simple experiment to study whether neural networks can perform several steps of approximate reasoning in a fixed dimensional latent space. The set of rewrites (i.e. transformations) that can be successfully performed…
We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…
We consider the question that the spectrum and arithmetic of locally symmetric spaces defined by congruent arithmetical lattices should mutually determine each other. We frame these questions in the context of automorphic representations.
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…
We show that the process of spontaneous symmetry breaking can trap a field theoretic system in a highly non-trivial state containing a lattice of domain walls. In one large compact space dimension, a lattice is inevitably formed. In two…
This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…
Every countable structure has a sentence of the infinitary logic $\mathcal{L}_{\omega_1 \omega}$ which characterizes that structure up to isomorphism among countable structures. Such a sentence is called a Scott sentence, and can be thought…
With a complete residuated lattice $L$ as the truth value table, we extend the definition of sobriety of classical convex spaces to the framework of $L$-convex spaces. We provide a specific construction for the sobrification of an…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…