Planning for extended goals in non-deterministic domains is one of the most significant and challenging planning problems. In spite

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We present the basic framework of a logic of actions and plans defined in terms of modal logic combined with a notion of dependence. The latter is used as a weak causal connection between actions and literals. In this paper we focus on the frame problem and demonstrate how it can be solved in our framework in a simple and monotonic way. We give the semantics, and associate an axiomatics and a decision procedure to it. The decision procedure is based on a sound and complete tableau method with single step rules to treat dependence. We show how it can be used to generate plans. Our solution is formally assessed by a translation of Gelfond and Lifschitz' logic A. We briefly sketch the second part of the paper, showing how we can go beyond A by some examples involving nondeterminism and ramifications.

The paper describes a transition logic, TL, and a deductive formalism for it. It shows how various important aspects (such as ramification, qualification, specificity, simultaneity, indeterminism etc.) involved in planning (or in reasoning about action and causality for that matter) can be modelled in TL in a rather natural way. (The deductive formalism for) TL extends the linear connection method proposed earlier by the author by embedding the latter into classical logic, so that classical and resource-sensitive reasoning coexist within TL. The attraction of a logical and deductive approach to planning is emphasized and the state of automated deduction briefly described. 1 Introduction Artificial Intelligence (AI, or Intellectics [Bib92a]) aims at creating artificial (or computational [PMG98]) intelligence. Were there no natural intelligence, the sentence would be meaningless to us. Hence understanding natural intelligence by necessity has always been among the goals of Intel...

Several realistic non-deterministic planning domains require plans that encode iterative trial-and-error strategies, e.g., "pick up a block until succeed". In such domains, a certain effect (e.g., action success) might never be guaranteed a priori of execution and, in principle, iterative plans might loop forever. Here, the planner should generate iterative plans whose executions always have a possibility of terminating and, when they do, they are guaranteed to achieve the goal. In this paper, we define the notion of strong cyclic plan, which formalizes in temporal logic the above informal requirements for iterative plans, define a planning algorithm based on model-checking techniques, and prove that the algorithm is guaranteed to return strong cyclic plans when they exist or to terminate with failure when they do not. We show how this approach can be extended to formalize plans that are guaranteed to achieve the goal and do not involve iterations (strong plans) and plans that have a possibility (but are not guaranteed) to achieve the goal (weak plans). The results presented in this paper constitute a formal account for "planning via model checking" in non-deterministic domains, which has never been provided before.

this paper, we pursue a monotonic approach to the frame problem and concentrate on the combinatorial problem and the overcommitment problem. We will propose a solution within the framework of propositional dynamic logic (PDL)---the modal logic of actions and of computer programs (see Pratt, 1976, 1980; Segerberg 1980; Harel, 1984). It is based on the idea of associating an operator [ff] with each action ff, the brackets being reminiscient of the box operator 2 of ordinary modal logic (see Hughes & Cresswell, 1984). The reading of a formula [ff]A is "after every terminating (halting) execution of ff, A is true." PDL provides a powerful language for describing compound actions such as sequential composition of actions ff and fi, written ff; fi, (non-deterministic) choice between ff and fi, written ff + fi, and (nondeterministic) iteration of ff, written ff

Abstract. Flexible support for crisis management can definitely be improved by making use of advanced planning capabilities. However, the complexity of the underlying domain often causes intractable efforts in modeling the domain as well as a huge search space to be explored by the system. A way to overcome these problems is to impose a structure not only according to tasks but also according to relationships between and properties of the objects involved, thereby using so-called decomposition axioms. We outline the prototype of a system that is capable of tackling planning for complex application domains. It is based on a well-founded combination of action and state abstractions. The paper presents the basic techniques and provides a formal semantic foundation of the approach. It introduces the planning system and illustrates its underlying principles by examples taken from the crisis management domain used in our ongoing project. 1

This paper is a first attempt towards a theory for reactive planning systems, i.e. systems able to plan and control execution of plans in a partially known and unpredictable environment. We start from an experimental real world application developed at IRST, discuss some of the fundamental requirements and propose a formal theory based on these requirements. The theory takes into account the following facts: (1) actions may fail, since they correspond to complex programs controlling sensors and actuators which have to work in an unpredictable environment; (2) actions need to acquire information from the real world by activating sensors and actuators; (3) actions need to generate and execute plans of actions, since the planner needs to activate different special purpose planners and to execute the resulting plans.

We introduce a method of deduction-based refinement planning where prefabricated general solutions are adapted to special problems. Refinement proceeds by stepwise transforming nonconstructive problem specifications into executable plans. For each refinement step there is a correctness proof guaranteeing the soundness of refinement and with that the generation of provably correct plans. By solving the hard deduction problems once and for all on the abstract level, planning on the concrete level becomes more efficient. With that, our approach aims at making deductive planning feasible in realistic contexts. Our approach is based on a temporal logic framework that allows for the representation of specifications and plans on the same linguistic level. Basic actions and plans are specified using a programming language the constructs of which are formulae of the logic. Abstract solutions are represented as---possibly recursive---procedures. It is this common level of representation and the fluid transition between specifications and plans our refinement process basically relies upon.

We present a systematic approach to the modular and incremental construction of provably consistent domain models for planning. It is based on a temporal logic framework that in particular allows for the introduction of abstract datatypes which can usefully be applied to mirror the computational aspects of planning problems and their solutions. A formal concept is developed that enables the construction as well as the modification of already existing domain models in a sound manner. This includes well-defined operations for the union, extension, and refinement of domain models.