Existential quantification ≈ Existential quantification
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Query2box: Reasoning over Knowledge Graphs in Vector Space using Box\n Embeddings Open
Answering complex logical queries on large-scale incomplete knowledge graphs\n(KGs) is a fundamental yet challenging task. Recently, a promising approach to\nthis problem has been to embed KG entities as well as the query into a vector\nsp…
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QUERY2BOX: REASONING OVER KNOWLEDGE GRAPHS IN VECTOR SPACE USING BOX EMBEDDINGS Open
Answering complex logical queries on large-scale incomplete knowledge graphs (KGs) is a fundamental yet challenging task. Recently, a promising approach to this problem has been to embed KG entities as well as the query into a vector space…
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Only what exists can cause: An intrinsic view of free will Open
This essay addresses the implications of integrated information theory (IIT) for free will. IIT is a theory of what consciousness is and what it takes to have it. According to IIT, the presence of consciousness is accounted for by a maximu…
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Quantification and manipulation of magic states Open
Magic states can be used as a resource to circumvent the restrictions due to\nstabilizer-preserving operations, and magic-state conversion has not been\nstudied in the single-copy regime thus far. Here we solve the question of\nwhether a s…
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Deciding Hyperproperties Open
Hyperproperties, like observational determinism or symmetry, cannot be expressed as properties of individual computation traces, because they describe a relation between multiple computation traces. HyperLTL is a temporal logic that captur…
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Semantic Acyclicity on Graph Databases Open
It is known that unions of acyclic conjunctive queries (CQs) can be evaluated in linear time, as opposed to arbitrary CQs, for which the evaluation problem is NP-complete. It follows from techniques in the area of constraint-satisfaction p…
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Fractional Navier-Stokes equations Open
We consider fractional Navier-Stokes equations in a smooth bound-ed domain $Ω\subset\mathbb{R}^N$, $N≥2$. Following the geometric theory of abstract parabolic problems we give the detailed analysis concerning existence, uniqueness, regular…
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Who Needs Crossings? Hardness of Plane Graph Rigidity Open
We exactly settle the complexity of graph realization, graph rigidity, and graph global rigidity as applied to three types of graphs: "globally noncrossing" graphs, which avoid crossings in all of their configurations; matchstick graphs, w…
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Welfare Guarantees in Schelling Segregation Open
Schelling’s model is an influential model that reveals how individual perceptions and incentives can lead to residential segregation. Inspired by a recent stream of work, we study welfare guarantees and complexity in this model with respec…
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Multiagent Connected Path Planning: PSPACE-Completeness and How to Deal With It Open
In the Multiagent Connected Path Planning problem (MCPP), a team of agents moving in a graph-represented environment must plan a set of start-goal joint paths which ensures global connectivity at each time step, under some communication mo…
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On the existence of infinitely many universal tree-based networks Open
A tree-based network on a set X of n leaves is said to be universal if any rooted binary phylogenetic tree on X can be its base tree. Francis and Steel showed that there is a universal tree-based network on X in the case of n = 3, and aske…
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A Catalog of EXISTS-R-Complete Decision Problems About Nash Equilibria in Multi-Player Games Open
[Schaefer and Stefankovic, Theory of Computing Systems, 2015] provided an explicit formulation of EXISTS-R as the class capturing the complexity of deciding the Existential Theory of the Reals, and established that deciding, given a 3-play…
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On Liveness Enforcing Supervisory Policies for Arbitrary Petri Nets Open
Neither the existence nor the nonexistence of a liveness enforcing supervisory policy (LESP) for an arbitrary Petri net (PN) is semidecidable. In an attempt to identify decidable instances, we explore the decidability of certain properties…
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The Navier–Stokes regularity problem Open
There is currently no proof guaranteeing that, given a smooth initial condition, the three-dimensional Navier–Stokes equations have a unique solution that exists for all positive times. This paper reviews the key rigorous results concernin…
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‘Form’ in Conceptualising Copyright as a Property Right Open
In the UK, all works need to be recorded in some manner for copyright to subsist. While scholars acknowledge that this requirement exists, its teleological significance is not appreciated. This article argues that the need for record is a …
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The Erdös--Hajnal Conjecture for Long Holes and Antiholes Open
Erd\\H{o}s and Hajnal conjectured that, for every graph $H$, there exists a\nconstant $c_H$ such that every graph $G$ on $n$ vertices which does not contain\nany induced copy of $H$ has a clique or a stable set of size $n^{c_H}$. We\nprove…
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An Effective Syntax for Bounded Relational Queries Open
A query Q is boundedly evaluable under a set A of access constraints if for all datasets D that satisfy A, there exists a fraction DQ of D such that Q(D) = Q(DQ), and the sizeof DQ and time for identifying DQ are both independent of the si…
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Certain Answers Meet Zero-One Laws Open
Query answering over incomplete data invariably relies on the standard notion of certain answers which gives a very coarse classification of query answers into those that are certain and those that are not. Here we propose to refine it by …
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Simple dynamics on graphs Open
Can the interaction graph of a finite dynamical system force this system to have a “complex” dynamics? In other words, given a finite interval of integers A, which are the signed digraphs G such that every finite dynamical system f:An→An w…
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A Single Approach to Decide Chase Termination on Linear Existential Rules Open
Existential rules, long known as tuple-generating dependencies in database theory, have been intensively studied in the last decade as a powerful formalism to represent ontological knowledge in the context of ontology-based query answering…
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Erdős–Hajnal for graphs with no 5‐hole Open
The Erdős–Hajnal conjecture says that for every graph there exists such that every graph not containing as an induced subgraph has a clique or stable set of cardinality at least . We prove that this is true when is a cycle of length five. …
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A rectifiability result for finite-perimeter sets in Carnot groups Open
In the setting of Carnot groups, we are concerned with the rectifiability problem for subsets that have finite sub-Riemannian perimeter. We introduce a new notion of rectifiability that is, possibly, weaker than the one introduced by Franc…
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Generalized Drazin inverses in a ring Open
An element a in a ring R has generalized Drazin inverse if and only if there exists b ? comm2(a) such that b = b2a,a-a2b ? Rqnil. We prove that a ? R has generalized Drazin inverse if and only if there exists p3 = p ? comm2(a) such that a …
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COMPUTABILITY, ORDERS, AND SOLVABLE GROUPS Open
The main objective of this paper is the following two results. (1) There exists a computable bi-orderable group that does not have a computable bi-ordering; (2) there exists a bi-orderable, two-generated computably presented solvable group…
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EFX Exists for Three Agents Open
We study the problem of distributing a set of indivisible items among agents with additive valuations in a $\mathit{fair}$ manner. The fairness notion under consideration is Envy-freeness up to any item (EFX). Despite significant efforts b…
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Trees and linear anticomplete pairs Open
We prove a conjecture of Liebenau, Pilipczuk, and the last two authors, that for every forest $H$ there exists $\epsilon>0$, such that if $G$ has $n\ge 2$ vertices and does not contain $H$ as an induced subgraph, and has maximum degree les…
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Bundled Fragments of First-Order Modal Logic: (Un)Decidability Open
Quantified modal logic is notorious for being undecidable, with very few known decidable fragments such as the monodic ones. For instance, even the two-variable fragment over unary predicates is undecidable. In this paper, we study a parti…
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Bounded Query Rewriting Using Views Open
A query Q has a bounded rewriting using a set of views if there exists a query Q′ expressed in the same language as Q, such that given a dataset D, Q(D) can be computed by Q′ that accesses only cached views and a small fraction DQ of D. We…
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ON THE ORDER OF METRIC APPROXIMATION OF MAXIMAL LINKED SYSTEMS AND CAPACITARIAN DIMENSIONS Open
It is shown that in any metric compact space X there exists a countable closed subset F whose upper capacitarian dimension dimBF is equal to any preassigned non-negative number not exceeding the upper capacitarian dimension of X. A similar…
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Six variations on a theme: almost planar graphs Open
A graph is apex if it can be made planar by deleting a vertex, that is, there exists [math] such that [math] is planar. We also define several related notions; a graph is edge apex if there exists [math] such that [math] is planar, and con…