We propose a novel formalism, called Frame Logic (abbr., F-logic), that accounts in a clean and declarative fashion for most of the structural aspects of object-oriented and frame-based languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, encapsulation, and others. In a sense, F-logic stands in the same relationship to the objectoriented paradigm as classical predicate calculus stands to relational programming. F-logic has a model-theoretic semantics and a sound and complete resolution-based proof theory. A small number of fundamental concepts that come from object-oriented programming have direct representation in F-logic; other, secondary aspects of this paradigm are easily modeled as well. The paper also discusses semantic issues pertaining to programming with a deductive object-oriented language based on a subset of F-logic.

We present a novel language for querying object-oriented databases. The language is built around the idea of extended path expressions that substantially generalize [ZAN83], and on an adaptation of the first-order formalization of object-oriented languages from [KW89, KLW90, KW92]. The language incorporates features not found in earlier proposals; it is easier to use and has greater expressive power. Some of the salient features of our language are: ffl Precise model-theoretic semantics. ffl A very expressive form of path expressions that not only can do joins, selections and unnesting, but can also be used to explore the database schema. ffl Views can be defined and manipulated in a much more uniform way than in other proposals. ffl Database schema can be explored in the very same language that is used to retrieve data. Unlike in relational languages, the user needs not know anything about the system tables that store schema information. ffl The notions of a type and type-correctness have precise meaning. It accommodates a wide variety of queries that might be deemed well- or ill-typed under different circumstances. In particular, we show that there is more than one way of settling the issue of type correctness. For expository purposes and due to space limitation, we chose to make a number of simplifying assumptions and left some features out. A more complete account can be found in [KSK92].

We propose a database logic which accounts in a clean declarative fashion for most of the “object-oriented” features such as object identity, complex objects, inheritance, methods, etc. Furthermore, database schema is part of the object language, which allows the user to browse schema and data using the same declarative formalism. The proposed logic has a formal semantics and a sound and complete resolution-based proof procedure, which makes it also computationally attractive.

Most known computational approaches to reasoning have problems when facing inconsistency, so they assume that a given logical system is consistent. Unfortunately, the latter is difficult to verify and very often is not true. It may happen that addition of data to a large system makes it inconsistent, and hence destroys the vast amount of meaningful information. We present a logic, called APC (annotated predicate calculus; cf. annotated logic programs of [3], that treats any set of clauses, either consistent or not, in a uniform way. In this logic, consequences of a contradiction are not nearly as damaging as in the standard predicate calculus, and meaningful information can still be extracted from an inconsistent set of formulae. APC has a resolution-based sound and complete proof procedure. We also introduce a novel notion of "epistemic entailment" and show its importance for investigating inconsistency in predicate calculus as well as its application to nonmonotonic reasoning. Most importantly, our claim that a logical theory is an adequate model of human perception of inconsistency, is actually backed by rigorous arguments.

Abstract not found

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.

This paper exhibits some problematic cases of defeasible or nonmonotonic reasoning that tend to be handled incorrectly by all of the theories of defeasible and nonmonotonic reasoning in the current literature. The paper focuses particularly on default logic, circumscription, and the author's own argument-based approach to defeasible reasoning. A proposal is made for how to deal with these problematic cases. The paper closes with a demonstration that the proposed solution is able to differentiate, in a congenial way, between cases having the structure of the lottery paradox and cases having the structure of the paradox of the preface. The algorithm proposed for computing justificational status has been implemented in the automated defeasible reasoner OSCAR. 1. Introduction The purpose of this paper is to exhibit some problematic cases of defeasible or nonmonotonic reasoning that tend to be handled incorrectly by all of the theories of defeasible and nonmonotonic reasoning in the curr...

Logics for knowledge representation suffer from overspecialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several logics and, when necessary, combine the representations. In general, such an approach results in a very difficult problem of combination. However, if we can choose the logics from a uniform framework then the problem of combining them is greatly simplified. In this paper, we develop such a framework for defeasible logics. It supports all defeasible logics that satisfy a strong negation principle. We use logic meta-programs as the basis for the framework.

We present a formal model of argumentation based on situation calculus which captures both the logical and the procedural aspects of argumentation processes. The logic is used to determine what is accepted by each agent participating in the discussion and by the group as a whole, on the basis of the speech acts performed during argumentation. Argumentation protocols, also called rules of order, describe declaratively which speech acts are legal in a particular state of the argumentation. We first discuss argumentation with fixed rules of order. Our model tolerates protocol violations but makes it possible to object to illegal actions. In realistic settings the rules of order themselves can at any time become the topic of the debate. We show how meta level argumentation of this kind can be modelled in what we call dynamic argument systems. To illustrate the notions introduced in the paper we present a reconstruction of Rescher's theory of formal disputation and a dynamic argument system with three levels which we use to discuss a murder case. 1

Abstract not found