The Classification of Magic SET Squares

A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations and reflections of the square. Under these transformations, there are 21 types of magic SET squares. We calculate the number of squares of each type. In addition, we discuss a game of SET tic-tac-toe.

Conclusion

This chapter returns to the high-level assumptions that motivated the writing of this book which include: (1) the field of strategy in the current day and age has become more relevant (not less); (2) strategic management should be practiced by more people (not fewer, and certainly not solely by those at the top of the organization; (3) strategy’s functional domain should be broadened (not narrowed); and (4) anyone with career ambition in the business world needs to become a strategist. It also discusses the option of combining multiple tools and offers advice on how this can be done. We note that there is no magic set of combinations that always works. Part of the learning experience in becoming a good strategist is learning when and how to apply certain tools in combination. As with many things in life, practice makes perfect. The chapter concludes with discussing the next frontier in strategic management.

Enhancing Magic Sets with an Application to Ontological Reasoning

Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the rewriting may introduce new recursive definitions, which can involve even negation and aggregations, and may slow down program evaluation. This paper enhances the magic set technique by preventing the creation of (new) recursive definitions in the rewritten program. It turns out that the new version of magic sets is closed for Datalog programs with stratified negation and aggregations, which is very convenient to obtain efficient computation of the stable model of the rewritten program. Moreover, the rewritten program is further optimized by the elimination of subsumed rules and by the efficient handling of the cases where binding propagation is lost. The research was stimulated by a challenge on the exploitation of Datalog/dlv for efficient reasoning on large ontologies. All proposed techniques have been hence implemented in the dlv system, and tested for ontological reasoning, confirming their effectiveness.

Caribou Song by T. Highway

Highway, Tomson. Illus. John Rombough. Caribou Song. Markham, ON.: Fifth House, 2013. Print.While Tomson Highway’s English text remains consistent with the 2001 publication of this title illustrated by Brian Deines, this new version has been translated into a colloquial dialect of Cree rather than the original high Cree. It has been revitalized by John Rombough, a Chipewyan Dene artist from the Northwest Territories. His stylistic and intensely coloured illustrations make this a very different viewing experience from that of the softer and more realistic illustrations by Deines. Rombough’s illustrations are infused with great energy, which is especially intriguing since the broad black lines contain only static shapes of colour layered on the variously tinted pages. There is magic here that is highly reminiscent of stain glass artistry and, like the stained glass pieces, engage the viewer into active participation in the storytelling experience.The story, too, contains magic. Set in Northern Manitoba, the tale follows the adventures of two young brothers, Joe and Cody, who call the caribou with their accordion (kitoochigan) and singing. The caribou respond with great vigor, enabling the boys’ parents’ traditional hunt. There is much laughter between the boys but danger as well as the migrating animals enthusiastically stream between them. Thankfully the spirit voice of the caribou leads the boys to safety, much to the relief of their parents and the boys themselves.Many years ago, when speaking with Tomson about the translation of the first edition he expressed sorrow that it was in the more formal Cree language; he felt that it was not the dialect that was easily accessible by the very people he wished to reach with this book. I hope this translation satisfies and ratifies this aspiration for those who read Cree. It certainly satisfies the artistic appreciation of this reviewer. The 2001 version was the first book in a trilogy about Joe, Cody, their family and the traditional culture and life of the Cree in Northern Manitoba. Is this edition also the first in a trilogy? One can always hope.Highly recommended: 4 out of 4 stars Reviewer: Gail de VosGail de Vos, an adjunct instructor, teaches courses on Canadian children's literature, Young Adult Literature and Comic Books and Graphic Novels at the School of Library and Information Studies for the University of Alberta and is the author of nine books on storytelling and folklore. She is a professional storyteller and has taught the storytelling course at SLIS for over two decades.

Complexity of super-coherence problems in ASP

Adapting techniques from database theory in order to optimize Answer Set Programming (ASP) systems, and in particular the grounding components of ASP systems, is an important topic in ASP. In recent years, the Magic Set method has received some interest in this setting, and a variant of it, called Dynamic Magic Set, has been proposed for ASP. However, this technique has a caveat, because it is not correct (in the sense of being query-equivalent) for all ASP programs. In a recent work, a large fragment of ASP programs, referred to assuper-coherent programs, has been identified, for which Dynamic Magic Set is correct. The fragment contains all programs which possess at least one answer set, no matter which set of facts is added to them. Two open question remained: How complex is it to determine whether a given program is super-coherent? Does the restriction to super-coherent programs limit the problems that can be solved? Especially the first question turned out to be quite difficult to answer precisely. In this paper, we formally prove that deciding whether a propositional program is super-coherent is Π3P-complete in the disjunctive case, while it is Π2P-complete for normal programs. The hardness proofs are the difficult part in this endeavor: We proceed by characterizing the reductions by the models and reduct models which the ASP programs should have, and then provide instantiations that meet the given specifications. Concerning the second question, we show that all relevant ASP reasoning tasks can be transformed into tasks over super-coherent programs, although this transformation is more of theoretical than practical interest.

Disjunctive ASP with functions: Decidable queries and effective computation

Querying over disjunctive ASP with functions is a highly undecidable task in general. In this paper we focus on disjunctive logic programs with stratified negation and functions under the stable model semantics (ASPfs). We show that query answering in this setting is decidable, if the query is finitely recursive (ASPfsfr). Our proof yields also an effective method for query evaluation. It is done by extending the magic set technique to ASPfsfr. We show that the magic-set rewritten program is query equivalent to the original one (under both brave and cautious reasoning). Moreover, we prove that the rewritten program is also finitely ground, implying that it is decidable. Importantly, finitely ground programs are evaluable using existing ASP solvers, making the class of ASPfsfr queries usable in practice.

Optimization of bound disjunctive queries with constraints

This paper presents a technique for the optimization of bound queries over disjunctive deductive databases with constraints. The proposed approach is an extension of the well-known Magic-Set technique and is well-suited for being integrated in current bottom-up (stable) model inference engines. More specifically, it is based on the exploitation of binding propagation techniques which reduce the size of the data relevant to answer the query and, consequently, reduces both the complexity of computing a single model and the number of models to be considered. The motivation of this work stems from the observation that traditional binding propagation optimization techniques for bottom-up model generator systems, simulating the goal driven evaluation of top-down engines, are only suitable for positive (disjunctive) queries, while hard problems are expressed using unstratified negation. The main contribution of the paper consists in the extension of a previous technique, defined for positive disjunctive queries, to queries containing both disjunctive heads and constraints (a simple and expressive form of unstratified negation). As the usual way of expressing declaratively hard problems is based on the guess-and-check technique, where the guess part is expressed by means of disjunctive rules and the check part is expressed by means of constraints, the technique proposed here is highly relevant for the optimization of queries expressing hard problems. The value of the technique has been proved by several experiments.