We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

https://dialnet.unirioja.es/descarga/articulo/4511387.pdf

The origins of order. Self-organization and selection in evolution

The motivation and key concepts behind answer set programming---a promising approach to declarative problem solving.

Answer set programming at a glance

When I started out as a newly hatched PhD student, back in the day, one of the first articles I read and understood (or at least thought that I understood) was Ray Reiter’s classic article on default logic (Reiter, 1980).This was some years after the famous ‘non-monotonic logic’ issue of Artificial Intelligence in which that article appeared, but default logic was still one of the leading approaches, a tribute to the simplicity and power of the theory. As a result of reading the article, I became fascinated by both default logic and, more generally, non-monotonic logics. However, despite my fascination, these approaches never seemed terribly useful for the kinds of problem that I was supposed to be studying—problems like those in medical decision making—and so I eventually lost interest. In fact non-monotonic logics seemed to me, and to many people at the time I think, not to be terribly useful for anything. They were interesting, and clearly relevant to the long-term goals of Artificial Intelligence as a discipline, but not of any immediate practical importance. This verdict, delivered at the end of the 1980s, continued, I think, to be true for the next few years while researchers working in non-monotonic logics studied problems that to outsiders seemed to be ever more obscure. However, by the end of the 1990s, it was becoming clear, even to folk as short-sighted as I, that non-monotonic logics were getting to the point at which they could be used to solve practical problems. Knowledge in action shows quite how far these techniques have come. The reason that non-monotonic logics were invented was, of course, in order to use logic to reason about the world. Our knowledge of the world is typically incomplete, and so, in order to reason about it, one has to make assumptions about things one does not know. This, in turn, requires mechanisms for both making assumptions and then retracting them if and when they turn out not to be true. Non-monotonic logics are intended to handle this kind of assumption making and retracting, providing a mechanism that has the clean semantics of logic, but which has a non-monotonic set of conclusions. Much of the early work on non-monotonic logics was concerned with theoretical reasoning, that is reasoning about the beliefs of an agent—what the agent believes to be true. Theoretical reasoning is the domain of all those famous examples like ‘Typically birds fly. Tweety is a bird, so does Tweety fly?’, and the fact that so much of non-monotonic reasoning seemed to focus on theoretical reasoning was why I lost interest in it. I became much more concerned with practical reasoning—that is reasoning about what an agent should do—and non-monotonic reasoning seemed to me to have nothing interesting to say about practical reasoning. Of course I was wrong. When one tries to formulate any kind of description of the world as the basis for planning, one immediately runs into applications of non-monotonic logics, for example in keeping track of the state of a changing world. It is this use of non-monotonic logic that is at the heart of Knowledge in action. Building on the McCarthy’s situation calculus, Knowledge in action constructs a theory of action that encompasses a very large part of what an agent requires to reason about the world. As Reiter says in the final chapter,

Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems

In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.

Flows in Networks

This paper gives an overview of the open source project Potassco, the Potsdam Answer Set Solving Collection, bundling tools for Answer Set Programming developed at the University of Potsdam.

Potassco: The Potsdam Answer Set Solving Collection

Answer Set Programming (ASP) is a declarative problem solving approach, initially tailored to modeling problems in the area of Knowledge Representation and Reasoning (KRR). More recently, its attractive combination of a rich yet simple modeling language with high-performance solving capacities has sparked interest in many other areas even beyond KRR. This book presents a practical introduction to ASP, aiming at using ASP languages and systems for solving application problems. Starting from the essential formal foundations, it introduces ASP's solving technology, modeling language and methodology, while illustrating the overall solving process by practical examples. Table of Contents: List of Figures / List of Tables / Motivation / Introduction / Basic modeling / Grounding / Characterizations / Solving / Systems / Advanced modeling / Conclusions

/pdf/answer-set-solving-in-practice-vtcfq8bjfw.pdf

Answer Set Solving in Practice

We introduce a new approach to computing answer sets of logic programs, based on concepts from constraint processing (CSP) and satisfiability checking (SAT). The idea is to view inferences in answer set programming (ASP) as unit propagation on no-goods. This provides us with a uniform constraint-based framework for the different kinds of inferences in ASP. It also allows us to apply advanced techniques from the areas of CSP and SAT. We have implemented our approach in the new ASP solver clasp. Our experiments show that the approach is competitive with state-of-the-art ASP solvers.

/pdf/conflict-driven-answer-set-solving-3yapqhi9up.pdf

Conflict-driven answer set solving

Conflict-driven answer set solving: From theory to practice

We describe the conflict-driven answer set solver clasp, which is based on concepts from constraint processing (CSP) and satisfiability checking (SAT) We detail its system architecture and major features, and provide a systematic empirical evaluation of its features

Martin Gebser

Papers

Potassco: The Potsdam Answer Set Solving Collection

Answer Set Solving in Practice

Conflict-driven answer set solving

Conflict-driven answer set solving: From theory to practice

Clasp: a conflict-driven answer set solver