this paper, we argue that no such set of postulates will be adequate for every application. In particular, we make a fundamental distinction between two kinds of modifications to a knowledge base. The first one, update, consists of bringing the knowledge base up to date when the world described by it changes. For example, most database updates are of this variety, e.g. "increase Joe's salary by 5%". Another example is the incorporation into the knowledge base of changes caused in the world by the actions of a robot (Ginsberg and Smith 1987, Winslett 1988, Winslett 1990) . We show that the AGM postulates must be drastically modified to describe update. The second type of modification, revision, is used when we are obtaining new information about a static world. For example, we may be trying to diagnose a faulty circuit and want to incorporate into the knowledge base the results of successive tests, where newer results may contradict old ones. We claim the AGM postulates describe only revision.

I present several computational complexity results for propositional STRIPS planning, i.e., STRIPS planning restricted to ground formulas. Different planning problems can be defined by restricting the type of formulas, placing limits on the number of pre- and postconditions, by restricting negation in pre- and postconditions, and by requiring optimal plans. For these types of restrictions, I show when planning is tractable (polynomial) and intractable (NPhard) . In general, it is PSPACE-complete to determine if a given planning instance has any solutions. Extremely severe restrictions on both the operators and the formulas are required to guarantee polynomial time or even NP-completeness. For example, when only ground literals are permitted, determining plan existence is PSPACE-complete even if operators are limited to two preconditions and two postconditions. When definite Horn ground formulas are permitted, determining plan existence is PSPACE-complete even if operators are limited t...

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.

The idea of ordering plays a basic role in commonsense reasoning for addressing three interrelated tasks: inconsistency handling, belief revision and plausible inference. We study the behavior of non-monotonic inferences induced by various methods for priority-based handling of inconsistent sets of classical formulas. One of them is based on a lexicographic ordering of maximal consistent subsets, and refines Brewka's preferred sub-theories. This new approach leads to a non-monotonic inference which satisfies the "rationality " property while solving the problem of blocking of property inheritance. It differs from and improves previous equivalent approaches such as Gardenfors and Makinson's expectation-based inference, Pearl's System Z and possibilistic logic. 1

The ramification problem in the context of commonsense reasoning about actions and change names the challenge to accommodate actions whose execution causes indirect effects. Not being part of the respective action specification, such effects are consequences of general laws describing dependencies between components of the world description. We present a general approach to this problem which incorporates causality, formalized by directed relations between two single effects stating that, under specific circumstances, the occurrence of the first causes the second. Moreover, necessity of exploiting causal information in this way or a similar is argued by elaborating the limitations of common paradigms employed to handle ramifications, namely, the principle of categorization and the policy of minimal change. Our abstract solution is exemplarily integrated into a specific calculus based on the logic programming paradigm. To apper in: Artificial Intelligence Journal On leave from FG Inte...

Most of the solutions proposed to the Yale shooting problem have either introduced new nonmonotonic reasoning methods (generally involving temporal priorities) or completely reformulated the domain axioms to represent causality explicitly. This paper presents a new solution based on the idea that since the abnormality predicate takes a situational argument, it is important for the meanings of the situations to be held constant across the various models being compared. This is accomplished by a simple change in circumscription policy: when Ab is circumscribed, Result (rather than Holds) is allowed to vary. In addition, we need an axiom ensuring that every consistent situation is included in the domain of discourse. Ordinary circumscription will then produce the intuitively correct answer. Beyond its conceptual simplicity, the solution proposed here has additional advantages over the previous approaches. Unlike the approach that uses temporal priorities, it can support reasoning backward...

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...

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

We present a computationally effective approach to representing and reasoning about actions with many qualifications. The approach involves treating actions as qualified not by specific facts that may or may not hold when the action is executed, but instead as potentially qualified by general constraints describing the domain being investigated. Specifically, we suggest that the result of the action be computed without considering these qualifying domain constraints, and take the action to be qualified if and only if any of the constraints is violated after the computation is complete. Our approach is presented using the framework developed in [6], where we discussed a solution to the frame and ramification problems based on the notion of possible worlds, and compared the computational requirements of that solution to the needs of more conventional ones. In the present paper, we show that the domain constraint approach to qualification, coupled with the possible worlds approach describ...