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.

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In this paper we investigate updates of knowledge bases represented by logic programs. In order to represent negative information, we use generalized logic programs which allow default negation not only in rule bodies but also in their heads.We start by introducing the notion of an update P \Phi U of one logic program P by another logic program U . Subsequently, we provide a precise semantic characterization of P \Phi U , and study some basic properties of program updates. In particular, we show that our update programs generalize the notion of interpretation update. We then extend this notion to compositional sequences of logic programs updates P1 \Phi P2 \Phi : : : , defining a dynamic program update, and thereby introducing the paradigm of dynamic logic programming. This paradigm significantly facilitates modularization of logic programming, and thus modularization of non-monotonic reasoning as a whole. Specifically, suppose that we are given a set of logic program modules, each de...

In this paper, we have combined techniques from epistemic and dynamic logic to arrive at a logic for describing multi-agent information change. The key concept of dynamic semantics is that the meaning of an assertion is the way in which the assertion changes the information of the hearer. Thus a dynamic epistemic semantics consist in a explicit formal definition of the information change potential of a sentence. We used these ideas to arrive at the system of Dynamic Epistemic Semantics, which is semantics for a language describing information change in a multi-agent setting. This semantics proved useful for analyzing the Muddy Children paradox, and also for giving a semantics for knowledge programs, since it enabled us to model knowledge change by giving an explicit semantics to the triggers of the information change (the latter being the assertions made, or the messages sent). We feel that this is an important extension, since standard approaches to for example the Muddy Children (e.g. Fagin et al. 1995) generally use static epistemic logics like S5 to describe the situation before and after a certain epistemic event, leaving the transition between `before' and `after' to considerations in the meta-language.

Belief revision leads to temporal nonmonotonicity, i.e., the set of beliefs does not grow monotonically with time. Default reasoning leads to logical nonmonotonicity, i.e., the set of consequences does not grow monotonically with the set of premises. The connection between these forms of nonmonotonicity will be studied in this paper focusing on syntaxbased approaches. It is shown that a general form of syntax-based belief revision corresponds to a special kind of partial meet revision in the sense of the theory of epistemic change, which in turn is expressively equivalent to some variants of logics for default reasoning. Additionally, the computational complexity of the membership problem in revised belief sets and of the equivalent problem of derivability in default logics is analyzed, which turns out to be located at the lower end of the polynomial hierarchy. 1 INTRODUCTION Belief revision is the process of incorporating new information into a knowledge base while preserving consist...

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...

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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])

Most of the work conducted so far in the eld of logic programming has focused on representing static knowledge, i.e. knowledge that does not evolve with time. To overcome this limitation, in a recent paper, the authors introduced dynamic logic programming. There, they studied and dened the declarative and operational semantics of sequences of logic programs (or dynamic logic programs). Each program in the sequence contains knowledge about some given state, where dierent states may, for example, represent dierent time periods or dierent sets of priorities. But how, in concrete situations, is a sequence of logic programs built? For instance, in the domain of actions, what are the appropriate sequences of programs that represent the performed actions and their eects? Whereas dynamic logic programming provides a way for, given the sequence, determining what should follow, it does not provide a good practical language for the specication of the sequence of updates which may be condi...