Symmetry breaking is a technique for speeding up propositional satisfiability testing byadding constraints to the theory that restrict the search space while preserving satisfiability.In this work, we extend symmetry breaking to the problem of model finding in weighted and unweighted relational theories, a class of problems that includes MAP inference in Markov Logic and similar statistical-relational languages. We introduce term symmetries, which are induced by an evidence set and extend to symmetries over a relational theory. We provide the important special case of term equivalent symmetries, showing that such symmetries can be found in low-degree polynomial time. We show how to break an exponential number of these symmetries with added constraints whose number is linear in the size of the domain. We demonstrate the effectiveness of these techniques through experiments in two relational domains. We also discuss the connections between relational symmetry breaking and work on lifted inference in statistical-relational reasoning.
Symmetry-breaking is a technique for efficiently solving SAT instances that contain high degrees of symmetry among the variables of the instance. When satisfiability problems are represented as a relational schema, symmetries between objects in the domain can be detected directly from evidence, that is, variables known to have a particular setting prior to solving. These symmetries between domain objects are called term symmetries. In this work, we present two novel extensions to the technique of term equivalent symmetry breaking which allow the detection and exploitation of conditional or hidden symmetries, those relationships between domain objects that are obscured until the instance is partially solved. We give promising preliminary experimental results for this technique, and discuss how the techniques could be extended for use in probabilistic domains.
It's a valuable historical document that depicts the events leading up to the Norman conquest of England by William the Conqueror in 1066. But more than 950 years later, social media jokers are trying to imagine the Bayeux Tapestry in the present-day with a series of tongue-in-cheek memes today. The joke pictures were posted online after it was revealed French officials are considering loaning the treasured piece of medieval art to Britain for the first time. Among the captions are'pictorals, else it did not occur', 'does anyone knoweth the wifi code' and'hast thou been injured in an accident at work?'. One made reference to Darth Vader and Luke Skywalker in Star Wars Episode V: The Empire Strikes Back, with the quote: 'Luketh, I am thy father'.
Intuitively, the concept of similarity is the notion to measure an inexact matching between two entities of the same reference set. The notions of similarity and its close relative dissimilarity are widely used in many fields of Artificial Intelligence. Yet they have many different and often partial definitions or properties, usually restricted to one field of application and thus incompatible with other uses. This paper contributes to the design and understanding of similarity and dissimilarity measures for Artificial Intelligence. A formal dual definition for each concept is proposed, joined with a set of fundamental properties. The behavior of the properties under several transformations is studied and revealed as an important matter to bear in mind. We also develop several practical examples that work out the proposed approach.