A calculus of events is presented in which domain constraints, concurrent events, and events with non-deterministic effects can be represented. The paper offers a non-monotonic solution to the frame problem for this formalism that combines two of the techniques developed for the situation calculus, namely causal and state-based minimisation. A theorem is presented which guarantees that temporal projection will not interfere with minimisation in this solution, even in domains with ramifications, concurrency, and non-determinism. Finally, the paper shows how the formalism can be extended to cope with continuous change, whilst preserving the conditions for the theorem to apply. 1 Introduction The frame problem was first described by McCarthy and Hayes in the Sixties [23], and has occupied the thoughts of AI researchers ever since. In a nutshell, the problem is this: if we deploy classical logic in a straightforward way to describe the effects of actions, we have to represent explicitl...

While historically the Fluent Calculus arose from approaches to the Frame Problem using non-classical, linear logics, an alternative is to view it as a development of the Situation Calculus with the aim of coping with the inferential aspect of the Frame Problem. Starting off from the concept of successor state axioms as a solution to the representational aspect, we show how by gradual improvement regarding the inferential aspect, but without losing the representational merits, one finally arrives at a novel version of the Fluent Calculus. We illustrate that under the provision that actions have no so-called open effects, any Situation Calculus specification can be transformed into an essentially equivalent Fluent Calculus specification. Our hope is that this alternative access to the Fluent Calculus both clarifies its role in relation to the most popular axiomatization paradigm and helps enhancing its acceptance.

This paper describes ILP-PLAN, a framework for solving AI planning problems represented as integer linear programs. ILP-PLAN extends the planning as satisfiability framework to handle plans with resources, action costs, and complex objective functions. We show that challenging planning problems can be effectively solved using both traditional branchand -bound IP solvers and efficient new integer local search algorithms. ILP-PLAN can find better quality solutions for a set of hard benchmark logistics planning problems than had been found by any earlier system. 1 Introduction In recent years the AI community witnessed the unexpected success of satisfiability testing as a method for solving state-space planning problems (Weld 1999). Kautz and Selman (1996) demonstrated that in certain computationally challenging domains, the approach of axiomatizing problems in propositional logic and solving them with general randomized SAT algorithms (SATPLAN) was competitive with or superior to the ...

: Agents interacting with an incompletely known dynamic world need to be able to reason about the effects of their actions, and to gain further information about that world using sensors of some sort. Unfortunately, sensor information is inherently noisy, and in general serves only to increase the agent's degree of confidence in various propositions. Building on a general logical theory of action formalized in the situation calculus, developed by Reiter and others, we propose a simple axiomatization of the effect on an agent's state of belief of taking a reading from a noisy sensor. By exploiting Reiter's solution to the frame problem, we automatically obtain that these sensor actions leave the rest of the world unaffected, and further, that non-sensor actions change the state of belief of the agent in appropriate ways. Keywords: situation calculus, theories of action, knowledge, degree of belief. Declaration: This paper has not already been accepted by and is not currently under rev...

Agents interacting with an incompletely known world need to be able to reason about the effects of their actions, and to gain further information about that world they need to use sensors of some sort. Unfortunately, both the effects of actions and the information returned from sensors are subject to error. To cope with such uncertainties, the agent can maintain probabilistic beliefs about the state of the world. With probabilistic beliefs the agent will be able to quantify the likelihood of the various outcomes of its actions and is better able to utilize the information gathered from its error-prone actions and sensors. In this paper, we present a model in which we can reason about an agent's probabilistic degrees of belief and the manner in which these beliefs change as various actions are executed. We build on a general logical theory of action developed by Reiter and others, formalized in the situation calculus. We propose a simple axiomatization that captures an agent's state of ...

We propose a new approach to the use of circumscription for representing knowledge. Nested abnormality theories are similar to simple abnormality theories introduced by McCarthy, except that their axioms may have a nested structure, with each level corresponding to another application of the circumscription operator. The new style of applying circumscription sometimes leads to more economical and elegant formalizations. Mathematical properties of nested abnormality theories may be easier to investigate. These advantages are demonstrated by recasting several familiar applications of circumscription in the new format, including some examples of inheritance hierarchies, the domain closure assumption and causal minimization. Nested abnormality theories provide also a convenient representation for the explanation closure approach to the frame problem developed by Schubert.

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We address the problem of formalizing the evolution of a database under the effect of an arbitrary sequence of update transactions. We do so by appealing to a first order representation language called the situation calculus, which is a standard approach in artificial intelligence to the formalization of planning problems. We formalize database transactions in exactly the same way as actions in the artificial intelligence planning domain. This leads to a database version of the frame problem in artificial intelligence. We provide a solution to the frame problem for a special, but substantial, class of update transactions. We next briefly describe some of the results obtained within this axiomatization. Specifically, we provide procedures for determining whether a given sequence of update transactions is legal, and for query evaluation in an updated database. These procedures have the nice property that they appeal to theorem-proving only with respect to the initial database state. We a...

We continue our exploration of a theory of database updates (Reiter [21, 23]) based upon the situation calculus. The basic idea is to take seriously the fact that databases evolve in time, so that updatable relations should be endowed with an explicit state argument representing the current database state. Database transactions are treated as functions whose effect is to map the current database state into a successor state. The formalism is identical to that arising in the artificial intelligence planning literature and indeed, borrows shamelessly from those ideas. Within this setting, we consider several topics, specifically: 1. A logic programming implementation of query evaluation. 2. The treatment of database views. 3. State constraints and the ramification problem. 4. The evaluation of historical queries. 5. An approach to indeterminate transactions. 1 Introduction Elsewhere (Reiter [21, 23]), we have described how one may represent databases and their update transactions with...

Most agents can acquire information about their environments as they operate. A good plan for such an agent is one that not only achieves the goal, but is also executable, i.e., ensures that the agent has enough information at every step to know what to do next. In this paper, we present a formal account of what it means for an agenttoknow how to execute a plan and to be able to achieve a goal. Such a theory is a prerequisite for producing specifications of planners for agents that can acquire information at run time. It is also essential to account for cooperation among agents. Our account is more general than previous proposals, correctly handles programs containing loops, and incorporates a solution to the frame problem. It can also be used to prove programs containing sensing actions correct.