We study transitivity properties of edge weights in complex networks. We show that enforcing transitivity leads to a transitivity inequality which is equivalent to ultra-metric inequality. This can be used to define transitive closure on weighted undirected graphs, which can be computed using a modified Floyd-Warshall algorithm. These new concepts are extended to dissimilarity graphs and triang...

Arrow’s Impossibility Theorem states that any constitution which satisfies Transitivity, Independence of Irrelevant Alternatives (IIA) and Unanimity is a dictatorship. Wilson derived properties of constitutions satisfying Transitivity and IIA for unrestricted domains where ties are allowed. In this paper we consider the case where only strict preferences are allowed. In this case we derive a ne...

Consistency of preference relations is associated with the study of the transitivity property. In this paper, we analyze the properties to be verified by a function, T , in order to obtain the value of preference of the alternative xi over the alternative xk when we already have the values of the preference of xi over xj , and of xj over xk. As a consequence, we define T -additive transitivity ...

Sen [6] proved that by confining voters to value restricted (acyclic) domains voting paradoxes (intransitive relations) can be avoided in aggregation by majority. We generalize this result to any neutral monotone aggregation. In addition, we show that acyclicity is neither necessary nor sufficient for transitivity for neutral non-monotone aggregation: we construct a cyclic transitive domain and...

We study portfolios of parallel strategies for Boolean Satisfiability (SAT) based solving of Hamiltonian Cycle Problems (HCPs). The strategies are based on our techniques for relative SAT encoding of permutations with constraints, and exploit: 1) encodings that eliminate half of the ordering Boolean variables and two-thirds of the transitivity constraints; 2) 12 triangulation heuristics for min...

The present study aims to investigate the system of the visual transitivity by analyzing the images of American English file (2014) and Cutting edge (2005) series based on Halliday’s (1976) systemic functional linguistics and Kress and van leuween’s (1997-2006) social semiotics. The system of visual transitivity refers to a type of process which determines how represented participants are label...

In this work we study different properties of graph symmetry. The first, is vertex transitivity, which informally says, that each vertex has the same global view of the graph. We give a simple one-sided error testing algorithm for vertex transitivity in the dense-graphs model, whose query complexity is Θ̃(n). In addition, we prove that any one-sided error testing algorithm for vertex transitivit...

For groups of automorphisms of chains (linear orders) and circles which satisfy certain weak transitivity hypotheses, the Dedekind completion of the chain or circle can be reconstructed up to reversal of order or orientation from the group alone. Let 〈L,<〉 be a dense chain. Throughout, an interval means a nonempty open interval. A subgroup G ≤ Aut(〈L,<〉) is locally moving if for every interval ...

We introduce a new decision procedure for Equality Logic. The procedure improves on Bryant and Velev’s sparse method [4] from CAV’00, in which each equality predicate is encoded with a Boolean variable, and then a set of transitivity constraints are added to compensate for the loss of transitivity of equality. We suggest the Reduced Transitivity Constraints (RTC) algorithm, that unlike the spar...

We consider existential rules (aka Datalog±) as a formalism for specifying ontologies. In recent years, many classes of existential rules have been exhibited for which conjunctive query (CQ) entailment is decidable. However, most of these classes cannot express transitivity of binary relations, a frequently used modelling construct. In this paper, we address the issue of whether transitivity ca...