Nondeterministic Effects Research Articles

Applying the mu-calculus in planning and reasoning about action

Planning algorithms have traditionally been geared towards achievement goals in single-agent environments. Such algorithms essentially produce plans to reach one of a specified set of states. More general approaches for planning based on temporal logic (TL) are emerging. Current approaches tend to use linear TL, and can handle sets of sequences of states. However, they assume deterministic actions with all changes effected solely by one agent. By contrast, we use a branching model of time that can express concurrent actions by multiple agents and the environment, leading to nondeterministic effects of an agent's actions. For this reason, we view plans not as sequences of actions, but as decision graphs describing the agent's actions in different situations. Thus, although we consider single-agent decision graphs, our approach is better suited to multiagent systems. We also consider an expressive formalism, which allows a wider variety of goals, including achievement and maintenance goals. Achievement corresponds to traditional planning, but maintenance is more powerful than traditional maintenance goals, and may require nonterminating plans. To formalize decision graphs requires a means to ‘alternate’ the agent's and the environment's choices. From logics of program, we introduce the prepositional mu-calculus;, which has operators for least and greatest fixpoints. We give a semantics, a fixpoint characterization, and an algorithm to compute decision graphs.

Planning with graded nondeterministic actions: A possibilistic approach

This article proposes a framework for planning under uncertainty given a partially known initial state and a set of actions having nondeterministic (disjunctive) effects, some being more possible (normal) than the others. The problem, henceforth called possibilistic planning problem, is represented in an extension of the STRIPS formalism in which the initial state of the world and the graded nondeterministic effects of actions are described by possibility distributions. Two notions of solution plans are introduced: γ-acceptable plans that lead to a goal state with a certainty greater than a given threshold γ, and optimally safe plans that lead to a goal state with maximal certainty. It is shown that the search of a γ-acceptable plan amounts to solve a derived planning problem that has only pure (nongraded) nondeterministic actions. A sound and complete partial order planning algorithm, called NDP, has been developed for such classical nondeterministic planning problems. The generation of γ-acceptable and optimally safe plans is achieved by two sound and complete planning algorithms: POSPLAN that relies on NDP, and POSPLAN* that can be seen as a hierarchical version of POSPLAN. The possibilistic planning framework is illustrated throughout the article by an example in the agronomic domain. © 1997 John Wiley & Sons, Inc.

Planning with graded nondeterministic actions: A possibilistic approach

This article proposes a framework for planning under uncertainty given a partially known initial state and a set of actions having nondeterministic (disjunctive) effects, some being more possible (normal) than the others. The problem, henceforth called possibilistic planning problem, is represented in an extension of the STRIPS formalism in which the initial state of the world and the graded nondeterministic effects of actions are described by possibility distributions. Two notions of solution plans are introduced: γ-acceptable plans that lead to a goal state with a certainty greater than a given threshold γ, and optimally safe plans that lead to a goal state with maximal certainty. It is shown that the search of a γ-acceptable plan amounts to solve a derived planning problem that has only pure (nongraded) nondeterministic actions. A sound and complete partial order planning algorithm, called NDP, has been developed for such classical nondeterministic planning problems. The generation of γ-acceptable and optimally safe plans is achieved by two sound and complete planning algorithms: POSPLAN that relies on NDP, and POSPLAN* that can be seen as a hierarchical version of POSPLAN. The possibilistic planning framework is illustrated throughout the article by an example in the agronomic domain. © 1997 John Wiley & Sons, Inc.

On the relation between situation calculus and event calculus

In this paper we make a detailed comparison of the Situation Calculus and the Event Calculus, two logic-based temporal reasoning formalisms. We concentrate on differences between the calculi, considering the similarities sufficiently indicated in the recent literature. We illustrate the inability of Event Calculus to handle counterfactual reasoning problems, and that of Situation Calculus to deal with counterfactual statements in the presence of actions with nondeterministic effects. We present a new calculus which extends both Situation and Event Calculus. In this new calculus we define a natural and clear relation between situations and time points, which differs from those used in previous comparisons. We show the relation of this new calculus to both original calculi. We compare the original calculi using the new calculus as an analysis tool.

Radiation protection in interventional radiology.

Introduction Furthermore, this information is usually displayed at the operator’s console where it cannot be seen In recent years there has been an increase in by the interventionalist undertaking the examinthe number, type and complexity of interventional ation. Unfortunately, total elapsed fluoroscopy radiology procedures. The impetus behind this time does not correlate very well with maximum rapid and continuing expansion has been the desire skin entrance dose. The latter quantity being for improved, more cost-effective medicine, in dependent on the automatic dose-rate control setwhich the patient can look forward to an improved ting selected, patient’s size, focus–skin distance and prognosis. Often patients having interventional the period of time that the area of skin was radiology procedures are treated as either outirradiated. Equipment developments are required patients or day cases, whereas the alternative surgito enable the interventionalist to be provided with cal technique would require hospitalization. This an on-line display which provides a better indiexpansion in interventional radiology has occurred cation of the potential onset of deterministic effects. in many countries worldwide, irrespective of the Extended fluoroscopy times, sometimes coupled type of system for health care delivery, because of with higher than average fluoroscopy currents can the many benefits. lead to an increased risk of non-deterministic In the main, interventional procedures are characeffects such as leukaemia in which the probability terized by having extended fluoroscopy times, and of the effect is proportional to the dose. The risk sometimes requiring many radiographic images to of inducing a hypothetical cancer at some time in be taken. As a consequence, developments in interthe future from interventional radiology correlates ventional radiology have a number of profound reasonably well with dose–area product. radiation protection implications for both patients Dose–area product is a quantity which may be and staff. In particular, the application of the conmeasured using a large area ionization chamber cept of justification to these procedures is different placed at the output port of the X-ray tube or than to other radiological examinations, as both inferred from a knowledge of X-ray technique deterministic and non-deterministic effects on the factors and the field size. Measurement of dose– patient have to be considered. area product is also recommended in the National Patient Dosimetry Protocol [1]. Patient dose The maximum skin entrance dose can be deduced from the dose–area product if the field For the patient, long fluoroscopy times lead to size and focus–skin distance are known. higher radiation doses, sometimes limited to a Instrumentation that is able to accomplish this is small area of the patient’s skin surface. This in in an early developmental stage. The display of turn leads to the potential for deterministic effects, total dose–area product and the estimated maxisuch as skin erythema, to be seen in patients who mum skin entrance dose on the interventionalist’s have had interventional radiology procedures. television monitor would provide information Physicians treating patients who have had an about the two types of radiation effect. interventional radiology procedure need to be It is also important to minimize patient doses aware of this possibility. whenever possible. One method of trying to achieve The potential induction of deterministic effects patient dose reductions would be to provide the in the skin is compounded by the lack of approinterventionalist with online dose rate information. priate patient dosimetry information available to The interventionalist could then select techniques the interventionalist during the procedure. At prewhich resulted in a lower patient dose, if desired. sent, fluoroscopy units used for interventional radiology are only required to be fitted with an Staff dose indication of total elapsed fluoroscopy time.

A circumscriptive calculus of events

A calculus of events is presented in which domain constraints, concurrent events, and events with nondeterministic effects can be represented. The paper offers a nonmonotonic 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 nondeterminism. Finally, the paper shows how the formalism can be extended to cope with continuous change, whilst preserving the conditions for the theorem to apply.

Tracking and track fitting

We generalize in several directions a previously published Runge-Kutta method for track fitting. We point out that the same basic idea applies to any equation of motion and any general method for numerical integration. For comparison we also discuss the quintic spline fit. In particular we extend the previous Runge-Kutta method to the case when energy loss (due to ionization) is important, treating this as a deterministic problem. In a second paper we will return to the treatment of non-deterministic effects, i.e. multiple Coulomb scattering and fluctuations in energy loss.