this paper we show, however, that stationary expansions can be equivalently defined in terms of classical, 2-valued logic. As a byproduct, we obtain a simpler and more natural description of stationary expansions.

In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a 'feel' for the field's history and some of its recent developments. The discussion is mainly limited to logic programs under the answer set semantics. For understanding of approaches to logic programming build on well-founded semantics, general theories of argumentation, abductive reasoning, etc., the reader is referred to other publications.

Synchronous programming (Berry (1989)) is a powerful approach to programming reactive systems. Following the idea that "processes are relations extended over time" (Abramsky (1993)), we propose a simple but powerful model for timed, determinate computation, extending the closure-operator model for untimed concurrent constraint programming (CCP). In (Saraswat et al. 1994a) we had proposed a model for this called tcc--- here we extend the model of tcc to express strong time-outs: if an event A does not happen through time t, cause event B to happen at time t. Such constructs arise naturally in practice (e.g. in modeling transistors) and are supported in synchronous programming languages. The fundamental conceptual difficulty posed by these operations is that they are nonmonotonic. We provide a compositional semantics to the non-monotonic version of concurrent constraint programming (Default cc) obtained by changing the underlying logic from intuitionistic logic to Reiter's default logic...

We consider the compilation of different reasoning tasks into the evaluation problem of quantified boolean formulas (QBFs) as an approach to develop prototype reasoning systems useful, e.g., for experimental purposes.

For many years, the non-monotonic reasoning commu-nity has focussed on highly expressive logics. Such logics have tumed out to be computationally expensive, and have given little support to the practical use of non-monotonic reasoning. In this work we discuss defeasible logic, a less-expressive but more efficient non-monotonic logic. We report on two new implemented systems for defeasible logic: a query answering system employing a backward-chaining approach, and a forward-chaining implementation that computes all conclusions. Our experimental evaluation demonstrates that the systems can deal with large theories (up to hundreds of thousands of rules). We show that defea-sible logic has linear complexity, which contrasts markedly with most other non-monotonic logics and helps to explain the impressive experimental results. We believe that defea-sible logic, with its eficiency and simplicity, is a good can-didate to be used as a modelling language for practical ap-plications, including modelling of regulations and business rules. 1

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Regulations are a wide-spread and important part of government and business. They codify how products must be made and processes should be performed. Such regulations can be difficult to understand and apply. In an environment of growing complexity of, and change in, regulation, automated support for reasoning with regulations is becoming increasingly necessary. In this paper we claim that such automated support can be provided on the basis of defeasible logical rules. We highlight the support that can be provided by this logical tool, and illustrate some aspects using examples from one specific domain: university regulations. 1 Introduction Regulations are a wide-spread and important part of government and business. They codify how products must be made and processes should be performed. Such regulations can be difficult to understand and apply. Even stand-alone regulations can be self-contradictory, as a result of the incremental process of their development and the lack of a forma...

This paper relates inference in extended logic programming with nonclassical, nonmonotonic logics. We define a nonmonotonic logic, called equilibrium logic, based on the least constructive extension, N2, of the intermediate logic of "here-and-there". We show that on logic programs equilibrium logic coincides with the inference operation associated with the stable model and answer set semantics of Gelfond and Lifschitz. We thereby obtain a very simple characterisation of answer set semantics as a form of minimal model reasoning in N2, while equilibrium logic itself provides a natural generalisation of this semantics to arbitrary theories. We discuss briefly some consequences and applications of this result. 1 Introduction By contrast with the minimal model style of reasoning characteristic of several approaches to the semantics of logic programs, the stable model semantics of Gelfond and Lifschitz [8] was, from the outset, much closer in spirit to the styles of reasoning found in othe...

Defeasible reasoning is a direction in nonmonotonic reasoning that is based on the use of rules that may be defeated by other rules. It is a simple, but often more efficient approach than other nonmonotonic reasoning systems. This paper presents a family of defeasible reasoning formalisms built around Nute's defeasible logic. We describe the motivations of these formalisms and derive some basic properties and interrelationships. We also describe a query answering system that supports these formalisms and is available on the World Wide Web.

Abduction-- from observations and a theory, find using hypotheses an explanation for the observations -- gained increasing interest during the last years. This form of reasoning has wide applicability in different areas of computer science; in particular, it has been recognized as an important principle of common-sense reasoning. In this paper, we define a general abduction model for logic programming, where the inference operator (i.e., the semantics to be applied on programs), can be specified by the user. Advanced forms of logic programming have been proposed as valuable tools for knowledge representation and reasoning. We show that logic programming semantics can be more meaningful for abductive reasoning than classical inference by providing examples from the area of knowledge representation and reasoning. The main part of the paper is devoted to an extensive study of the computational complexity of the principal problems in abductive reasoning, which are: Given an inst...