The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful nonmonotonic formalism introduced by Teodor Przymusinski in 1994. In this paper, we specialize it to a class of theories called "super logic programs". We argue that these programs form a natural generalization of standard logic programs. In particular, they allow disjunctions and default negation of arbitrary positive objective formulas.Our main results are two new and important characterizations of the static semantics of these programs, one syntactic, and one model-theoretic. The syntactic fixed point characterization is much simpler than the fixed point construction of the static semantics for arbitrary AELB theories. The model-theoretic characterization via Kripke models allows one to construct finite representations of the inherently infinite static expansions.Both characterizations can be used as the basis of algorithms for query answering under the static semantics. We describe a query-answering interpreter for super programs that we developed based on the model-theoretic characterization and which is available on the web.

In order to be able to explicitly reason about beliefs, we've introduced a non-monotonic formalism, called the Autoepistemic Logic of Beliefs, AEB, obtained by augmenting classical propositional logic with a belief operator, β. For this language we'v

this paper we introduce the class of so called stationary extensions of a default theory. Stationary extensions include, as a special case, Reiter's original default extensions but allow us to eliminate their drawbacks that were mentioned above. Every default theory \\Delta has at least one stationary extension and among its extensions there always exists the least stationary extension E \\Delta . The (cautious) stationary semantics S (\\Delta) of a default theory \\Delta, i.e., the theory consisting of sentences which are true in all stationary extensions of \\Delta, is always well-defined, and, since it clearly coincides with the least stationary extension E \\Delta of \\Delta, it is itself a stationary extension of \\Delta. The stationary semantics of default theories is always cumulatively monotonic and it can be computed by means of a natural iterative procedure. The complexity of its computation essentially coincides with the computational complexity of satisfiability tests on the underlying first order theory and therefore it does not involve any additional complexity caused by the non-monotonicity of default logic. More precisely, for default theories consisting of

The purpose of this article is to compare three types of nonmonotonic semantics: (a) proof-theoretic semantics based on the closed world assumption, (b) model-theoretic semantics based on the notion of a minimal model, and (c) model-theoretic semantics based on the notion of a minimal Herbrand model. All of these semantics capture the nonmonotonicity of commonsense reasoning, that is, the ability to withdraw conclusions after some new information is added to the original theories, and proved to be powerful enough to handle most examples of such reasoning presented in the literature. However, since these formalizations are based on different intuitions and often produce different results, the problem of understanding the relationship between them is especially important. In the first part of the article we concentrate on the class of positive logic programs, also called definite theories. Although the three semantics usually differ for universal sentences, our main result shows that they always coincide for existential queries. This result is particularly significant in view of the fact that in many applications existential queries are of main interest. It also plays an important role in the problem of finding a suitable declarative semantics for logic programs. In the second part we investigate arbitrary universal theories and we show that subtle differences exist between the three approaches and therefore no straightforward generalization of the results from the first part can be obtained.

Article Free Access Share on Every logic program has a natural stratification and an iterated least fixed point model Author: T. C. Przymusinski University of Texas at El Paso, El Paso, TX University of Texas at El Paso, El Paso, TXView Profile Authors Info & Claims PODS '89: Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systemsMarch 1989Pages 11–21https://doi.org/10.1145/73721.73723Published:29 March 1989Publication History 123citation614DownloadsMetricsTotal Citations123Total Downloads614Last 12 Months70Last 6 weeks7 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

We describe a decidable algorithm to answer queries in circumscriptive theories, that allows the use of variable predicates. This significantly extends the results obtained in our earlier paper [P], where a similar algorithm was constructed for circumscriptive theories without variable predicates.