An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter.

Knowledge representation and reasoning is the foundation of artificial intelligence, declarative programming, and the design of knowledge-intensive software systems capable of performing intelligent tasks. Using logical and probabilistic formalisms based on answer set programming (ASP) and action languages, this book shows how knowledge-intensive systems can be given knowledge about the world and how it can be used to solve non-trivial computational problems. The authors maintain a balance between mathematical analysis and practical design of intelligent agents. All the concepts, such as answering queries, planning, diagnostics, and probabilistic reasoning, are illustrated by programs of ASP. The text can be used for AI-related undergraduate and graduate classes and by researchers who would like to learn more about ASP and knowledge representation.

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A nswer set programming (ASP) is a knowledge representation and reasoning (KR) paradigm. It has rich highlevel representation languages that allow recursive definitions, aggregates, weight constraints, optimization statements, default negation, and external atoms. With such expressive languages, ASP can be used to declaratively represent knowledge (for example, mathematical models of problems, behaviour of dynamic systems, beliefs and actions of agents) and solve combinatorial search problems (for example, planning, diagnosis, phylogeny reconstruction) and knowledge-intensive problems (for example, query answering, explanation generation). The idea is to represent a problem as a "program" whose models (called "answer sets" Lifschitz 1988, 1991]

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This paper describes an architecture for robots that combines the complementary strengths of probabilistic graphical models and declarative programming to represent and reason with logic-based and probabilistic descriptions of uncertainty and domain knowledge. An action language is extended to support non-boolean fluents and nondeterministic causal laws. This action language is used to describe tightly-coupled transition diagrams at two levels of granularity, with a fine-resolution transition diagram defined as a refinement of a coarse-resolution transition diagram of the domain. The coarse-resolution system description, and a history that includes (prioritized) defaults, are translated into an Answer Set Prolog (ASP) program. For any given goal, inference in the ASP program provides a plan of abstract actions. To implement each such abstract action, the robot automatically zooms to the part of the fine-resolution transition diagram relevant to this action. A probabilistic representation of the uncertainty in sensing and actuation is then included in this zoomed fine-resolution system description, and used to construct a partially observable Markov decision process (POMDP). The policy obtained by solving the POMDP is invoked repeatedly to implement the abstract action as a sequence of concrete actions, with the corresponding observations being recorded in the coarse-resolution history and used for subsequent reasoning. The architecture is evaluated in simulation and on a mobile robot moving objects in an indoor domain, to show that it supports reasoning with violation of defaults, noisy observations and unreliable actions, in complex domains. 1 We use the terms "robot" and "agent" interchangeably in this paper. 1 arXiv:1508.03891v4 [cs.RO] 21 Sep 2018 probability reason optimally (or near optimally) about the effects of numerically quantifiable uncertainty in sensing and action. There have been many attempts to combine the benefits of these two classes of systems, including work on joint (i.e., logic-based and probabilistic) representations of state and action, and algorithms for planning and decisionmaking in such formalisms. These approaches provide significant expressive power, but they also impose a significant computational burden. More efficient (and often approximate) reasoning algorithms for such unified probabilisticlogical paradigms are being developed. However, practical robot systems that combine abstract task-level planning with probabilistic reasoning, link, rather than unify, their logic-based and probabilistic representations, primarily because roboticists often need to trade expressivity or correctness guarantees for computational speed. Information close to the sensorimotor level is often represented probabilistically to quantitatively model and reason about the uncertainty in sensing and actuation, with the robot's beliefs including statements such as "the robotics book is on the shelf with probability 0.9". At the same time, logic-based systems are used to reason with (more) abstract commonsen...