We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated (or revised) knowledge base. This problem amounts to evaluating the counterfactual p > q over T . Besides the general case, also subcases are considered, in particular where T is a conjunction of Horn clauses, or where the size of p is bounded by a constant.

this paper, including transaction logs and historical queries, the complexity of query evaluation, actualized transactions, logic programming approaches to updates, database views and state constraints. / This paper consolidates and expands on a variety of results, some of which have been described elsewhere (Reiter [46, 45, 44])

Closed-world inference is the process of determining that a logical sentence is false based on its absence from a knowledge base, or the inability to derive it. This process is essential for planning with incomplete information. We describe a novel method for closed-world inference and update over the first-order theories of action used by planning algorithms such as NONLIN, TWEAK, and UCPOP. We show the method to be sound and efficient, but incomplete. In our experiments, closed-world inference consistently averaged about 2 milliseconds, while updates averaged approximately 1.2 milliseconds. We incorporated the method into the XII planner, which supports our Internet Softbot (software robot). The method cut the number of actions executed by the Softbot bya factor of one hundred, and resulted in a corresponding speedup to XII. 1

: Revision and update operators add new information to some old information represented by a logical theory. Katsuno and Mendelzon show that both revision and update operators can be characterized as accomplishing a minimal change in the old information to accommodate the new information. Arbitration operators add two or more weighted informations together where the weights indicate the relative importance of the informations rather than a strict priority. This paper shows that arbitration operators can be also characterized as accomplishing a minimal change. The operator of model-fitting is also defined and analyzed in the paper. 1 Introduction Arbitration is the process of settling a conflict between two or more persons. Arbitration occurs in many situations. For example, settling a labor dispute by an outsider, reaching a verdict in a trial, evaluating several alternative research hypotheses, negotiating an international peace agreement, or setting the price of a product in a compe...

: Katsuno and Mendelzon divide theory change, the problem of adding new information to a logical theory, into two types: revision and update. We propose a third type of theory change: arbitration. The key idea is the following: the new information is considered neither better nor worse than the old information represented by the logical theory. The new information is simply one voice against a set of others already incorporated into the logical theory. From this follows that arbitration should be commutative. First we define arbitration by a set of postulates and then describe a model-theoretic characterization of arbitration for the case of propositional logical theories. We also study weighted arbitration where different models of a theory can have different weights. 1 Introduction The problem of updating logical theories is a common fundamental concern to databases, to Artificial Intelligence [McC68, Rei92], and to belief revision [Mak85, Gar88]. It is well-known that giving semant...

Recently the field of theory update has seen some improvement, in what concerns model updating, by allowing updates to be specified by so-called revision programs. The updating of theory models is governed by their update rules and also by inertia applied to those literals not directly affected by the update program. Though this is important, it remains necessary to tackle as well the updating of programs specifying theories. Some results have been obtained on the issue of updating a logic program which encodes a set of models, to obtain a new program whose models are the desired updates of the initial models. But here the program only plays the rôle of a means to encode the models. A logic program encodes much more than a set of models: it encodes knowledge in the form of the relationships between the elements of those models. In this paper we advocate that the principle of inertia is advantageously applied to the rules of the initial program rather than to the individual literals in...

We propose a general framework in which to study belief change. We begin by defining belief in terms of knowledge and plausibility: an agent believes ' if he knows that ' is true in all the worlds he considers most plausible. We then consider some properties defining the interaction between knowledge and plausibility, and show how these properties affect the properties of belief. In particular, we show that by assuming two of the most natural properties, belief becomes a KD45 operator. Finally, we add time to the picture. This gives us a framework in which we can talk about knowledge, plausibility (and hence belief), and time, which extends the framework of Halpern and Fagin [HF89] for modeling knowledge in multi-agent systems. We show that our framework is quite expressive and lets us model in a natural way a number of different scenarios for belief change. For example, we show how we can capture an analogue to prior probabilities, which can be updated by "conditioning". In a related ...

We study the problem of combining updates ---a special instance of theory change--- and counterfactual conditionals in propositional knowledgebases. Intuitively, an update means that the world described by the knowledgebase has changed. This is opposed to revisions ---another instance of theory change--- where our knowledge about a static world changes. A counterfactual implication is a statement of the form `If A were the case, then B would also be the case', where the negation of A may be derivable from our current knowledge. We present a decidable logic, called VCU 2 , that has both update and counterfactual implication as connectives in the object language. Our update operator is a generalization of operators previously proposed and studied in the literature. We show that our operator satisfies certain postulates set forth for any reasonable update. The logic VCU 2 is an extension of D. K. Lewis' logic VCU for counterfactual conditionals. The semantics of VCU 2 is that of a m...

In this work we address the problem of dealing with data inconsistencies while integrating data sets derived from multiple autonomous relational databases. The fundamental assumption in the classical relational model is that data is consistent and hence no support is provided for dealing with inconsistent data. Due to this limitation of the classical relational model, the semantics for detecting, representing, and manipulating inconsistent data have to be explicitly encoded in the applications by the application developer.

Closed world reasoning is the process of inferring that a logical sentence is false based on its absence from a knowledge base, or the inability to derive it. Previous work on circumscription, autoepistemic logic, and database theory has explored logical axiomatizations of closed world reasoning, and investigated computational tractability for propositional theories. Work in planning has traditionally made the closed world assumption but has avoided closed world reasoning. We take a middle position, and describe a tractable method for closed world reasoning over the schematized theories of action used by planning algorithms such as nonlin, tweak, and ucpop. We show the method to be both sound and tractable, and incorporate it into the xii planner (Golden et al. 1994). Experiments utilizing our softbot (software robot) demonstrate that the method can substantially improve its performance by eliminating redundant information gathering. 1 INTRODUCTION AND MOTIVATION Classical planners s...