In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten- sions of the language of definite logic programs by classical (strong) negation, disjunc- tion, and some modal operators and show how each of the added features extends the representational power of the language.

Although there are many arguments that logic is an appropriate tool for artificial intelligence, there has been a perceived problem with the monotonicity of classical logic. This paper elaborates on the idea that reasoning should be viewed as theory formation where logic tells us the consequences of our assumptions. The two activities of predicting what is expected to be true and explaining observations are considered in a simple theory formation framework. Properties of each activity are discussed, along with a number of proposals as to what should be predicted or accepted as reasonable explanations. An architecture is proposed to combine explanation and prediction into one coherent framework. Algorithms used to implement the system as well as examples from a running implementation are given. Key words: defaults, conjectures, explanation, prediction, abduction, dialectics, logic, nonmonotonicity, theory formation Explanation and Prediction 2 1 Introduction One way to do research i...

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Disjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning. This paper focuses on stable model semantics, currently the most widely acknowledged semantics for disjunctive logic programs. After presenting a new notion of unfounded sets for disjunctive logic programs, we provide two declarative characterizations of stable models in terms of unfounded sets. One shows that the set of stable models coincides with the family of unfounded-free models (i.e., a model is stable iff it contains no unfounded atoms). The other proves that stable models can be defined equivalently by a property of their false literals, as a model is stable iff the set of its false literals coincides with its greatest unfounded set. We then generalize the well-founded WP operator to disjunctive logic programs, give a fixpoint semantics for disjunctive stable models and present an algorithm for computing the stable models of function-free programs. The algor...

Research on nonmonotonic and default reasoning has identified several important criteria for preferring alternative default inferences. The theories of reasoning based on each of these criteria may uniformly be viewed as theories of rational inference, in which the reasoner selects maximally preferred states of belief. Though researchers have noted some cases of apparent conflict between the preferences supported by different theories, it has been hoped that these special theories of reasoning may be combined into a universal logic of nonmonotonic reasoning. We show that the different categories of preferences conflict more than has been realized, and adapt formal results from social choice theory to prove that every universal theory of default reasoning will violate at least one reasonable principle of rational reasoning. Our results can be interpreted as demonstrating that, within the preferential framework, we cannot expect much improvement on the rigid lexicographic priority mechanisms that have been proposed for conflict resolution.

The paper considers the fundamental notions of many- valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite valued logics. Key words: mathematical fuzzy logic, algebraic semantics, continuous t-norms, left-continuous t-norms, Pavelka-style fuzzy logic, fuzzy set theory, non-monotonic fuzzy reasoning 1 Basic ideas 1.1 From classical to many-valued logic Logical systems in general are based on some formalized language which includes a notion of well formed formula, and then are determined either semantically or syntactically. That a logical system is semantically determined means that one has a notion of interpretation or model 1 in the sense that w.r.t. each such interpretation every well formed formula has some (truth) value or represents a function into

How should what one knows about an individual affect default conclusions about that individual? This paper contrasts two views of "knowledge" in default reasoning systems. The first is the traditional view that one knows the logical consequences of one's knowledge base. It is shown how, under this interpretation, having to know an exception is too strong for default reasoning. It is argued that we need to distinguish "background" and "contingent" knowledge in order to be able to handle specificity, and that this is a natural distinction. The second view of knowledge is what is contingently known about the world under consideration. Using this view of knowledge, a notion of conditioning that seems like a minimal property of a default is defined. Finally, a qualitative version of the lottery paradox is given; if we want to be able to say that individuals that are typical in every respect do not exist, we should not expect to conclude the conjunction of our default conclusions. This paper...

We suggest a new approach for the study of the nonmonotonicity of human commonsense reasoning. The two main premises that underlie this work are that commonsense reasoning is an inductive phenomenon, and that missing information in the interaction of the agent with the environment may be as informative for future interactions as observed information. This intuition is formalized and the problem of reasoning from incomplete information is presented as a problem of learning attribute functions over a generalized domain. We consider examples that illustrate various aspects of the non-monotonic reasoning phenomena, which have been used over the years as "bench-marks" for various formalisms, and translate them into Learning to Reason problems. We demonstrate that these have concise representations over the generalized domain and prove that these representations can be learned efficiently. The framework developed suggests an "operational " approach to studying reasoning that is nevertheless ...

In this paper we consider constrained and rational default logics. We provide two characterizations of constrained extensions. One of them is used to derive complexity results for decision problems involving constrained extensions. In particular, we show that the problem of membership of a formula in at least one (in all) constrained extension(s) of a default theory is \Sigma P 2 -complete (\Pi P 2 -complete). We establish the relationship between constrained and rational default logics. We prove that rational extensions determine constrained extensions and that for seminormal default theories there is a one-to-one correspondence between these objects. We also show that the definition of a constrained extension can be extended to cover the case of default theories which may contain justification-free defaults.

We describe the elds of disjunctive logic programming and disjunctive deductive databases from the time of their inception to the current time. Contributions with respect to semantics, implementations and applications are surveyed.