In this paper, we review some recent work on declarative logic programming languages based on stable models/answer sets semantics of logic programs. These languages, gathered together under the name of A-Prolog, can be used to represent various types of knowledge about the world. By way of example we demonstrate how the corresponding representations together with inference mechanisms associated with A-Prolog can be used to solve various programming tasks.
In this paper, we suggest an architecture for a software agent which operates a physical device and is capable of making observations and of testing and repairing the device's components. We present simplfied definitions of the notions of symptom, candidate diagnosis, and diagnosis which are based on the theory of action language AL. The definitions allow one to give a simple account of the agent's behavior in which many of the agent's tasks are reduced to computing stable models of logic programs.
The nonmonotonic causal logic defined in this paper can be used to represent properties of actions, including actions with conditional and indirect effects, nondeterministic actions, and concurrently executed actions. It has been applied to several challenge problems in the theory of commonsense knowledge. We study the relationship between this formalism and other work on nonmonotonic reasoning and knowledge representation, and discuss its implementation, called the Causal Calculator.
To perform nontrivial reasoning an intelligent agent situated in a changing domain needs the knowledge of causal laws that describe the effects of actions that change the domain, and the ability to observe and record occurrences of these actions and the truth values of fluents at particular moments of time. One of the central problems of knowledge representation is the discovery of methods of representing this kind of information in a form allowing various types of reasoning about the dynamic world and at the same time tolerant of future updates. The goal of this chapter is to demonstrate how recent advances in logic programming can be used to address this problem.Paolo Ferraris and Vladimir Lifschitz, Mathematical foundations of answer set programming, in We Will Show Them! Essays in Honour of Dov Gabbay, Vol 1, College Publications, 2005.
Answer set programming (ASP) is a form of declarative logic programming oriented towards difficult combinatorial search problems. ASP has been applied, for instance, to developing a decision support system for the Space Shuttle (Nogeira et al, 2001) and to graph-theoretic problems arising in zoology and linguistics (Brooks et al, 2005). This is an expository paper about the design of provably correct ASP programs and about the mathematical theory it is based on. Our description of ASP may be useful as a complement to the monograph (Baral, 2003) and to the manuals on the software systems SMODELS and DLV.
The aim of this paper is to demonstrate that A-Prolog is a powerful language for the construction of reasoning systems. In fact, A-Prolog allows to specify the initial situation, the domain model, the control knowledge, and the reasoning modules. Moreover, it is efficient enough to be used for practical tasks and can be nicely integrated with programming languages such as Java. An extension of A-Prolog (CR-Prolog) allows to further improve the quality of reasoning by specifying requirements that the solutions should satisfy if at all possible. The features of A-Prolog and CR-Prolog are demonstrated by describing in detail the design of USA-Advisor, an A-Prolog based decision support system for the Space Shuttle flight controllers.Vladimir Lifschitz and Wanwan Ren, A modular action description language, in Proceedings of the National Conference on Artificial Intelligence (AAAI), 2006.
"Toy worlds" involving actions, such as the blocks world and the Missionaries and Cannibals puzzle, are often used by researchers in the areas of commonsense reasoning and planning to illustrate and test their ideas. We would like to create a database of general-purpose knowledge about actions that encodes common features of many action domains of this kind, in the same way as abstract algebra and topology represent common features of specific number systems. This paper is a report on the first stage of this project--the design of an action description language in which this database will be written. The new language is an extension of the action language C+. Its main distinctive feature is the possibility of referring to other action descriptions in the definition of a new action domain.
The definition of a stable model has provided a declarative semantics for Prolog programs with negation as failure and has led to the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming (including disjunctive rules, choice rules and conditional literals) and, unlike the original definition, refers neither to grounding nor to fixpoints. Rather, it is based on a syntactic transformation, which turns a logic program into a formula of second-order logic that is very similar to the formula familiar from the definition of circumscription.
Introduction. Syntax and semantics of A-Prolog. Creating a knowledge base. Reasoning with defaults. Answer set programming. Reasoning in dynamic domains. The Prolog interpreter.Vladimir Lifschitz, Lecture notes on mathematical logic.
These notes provide an elementary, but mathematically solid, introduction to propositional and first-order logic. They contain many exercises.