A formal description of tactical plan recognition Frank Mulder a,b, * , Frans Voorbraak c a Section Communications Research & Semiotics, Faculty of General Sciences, University Maastricht, Grote Gracht 82, P.O. Box 616, 6200 MD Maastricht, The Netherlands b Thales Nederland B.V., Zuidelijke havenweg 40, P.O. Box 42-7550 GD Hengelo(Ov), The Netherlands c Academisch Medisch Centrum, University of Amsterdam, Meibergdreef 15, 1105 AZ Amsterdam, The Netherlands Received 26 July 2001; received in revised form 20 August 2002; accepted 21 August 2002 Abstract Plan recognition can roughly be described as the problem of finding the plan(s) underlying the observed behaviour of agent(s). Of course, usually, the observed behaviour and available background knowledge does not determine the underlying plan, and therefore one can typically at best generate (reasonable) plan hypotheses. Traditionally, plan recognition has been studied, formalized and implemented in areas like story understanding and user modelling. In this paper, we propose a formal definition of tactical plan recognition, i.e. the recognition of enemy plans. We will focus on military applications, where this task of tactical plan recognition is crucial, but this task is relevant for every application where one has to deal with intelligent adversial agents. Tactical plan recognition differs from traditional plan recognition in a number of ways. For example, an enemy will often try to avoid making his plans known. We will not pay much explicit attention to this feature. We will focus on another important characteristic feature of tactical plan recognition, namely that the identity of the observed enemy objects, for which plans are to be recognized, may be unknown. A consequence of this is that it is typically not known which observations originate from the same objects. Our formalization of plan recognition is based on classical abduction. The concepts of classical abduction can readily be applied to plan recognizers for identified observations, as has been done by Lin and Goebel [18] and Bauer and Paul [7]. However, for tactical plan recognition some adaptations have to be made. Here the plan recognizer will not only have to generate plan hypotheses, but also assignment hypotheses, which correspond to formal links of objects to observations. A choice for an assignment is es- sentially a decision concerning the question which observations originate from the same objects. For observations with stochastic variables the probability of an assignment hypothesis is calculated, rather than the probability of the plan hypotheses. For this, ReidÕs multiple hypothesis tracking formula can be adapted to calculate the assignment hypothesis probability. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Tactical plan recognition; Multiple hypothesis tracking; Abduction 1. Introduction Recognizing the plan(s) underlying the observed be- havior of agent(s) is an important problem in many contexts. Traditionally, automatic plan recognition has been applied in areas like story understanding and user modelling. In this paper, we propose a formal definition of tactical plan recognition, i.e. the recognition of enemy plans. We will focus on military applications, where tactical plan recognition plays a crucial role, but obvi- ously this task is relevant whenever one has to deal with adversial agents. Tactical plan recognition differs from traditional plan recognition in a number of ways. For example, an enemy will often try to avoid making his plans known. One could try to explicitly capture this adversial be- havior in a game-theoretical setting, but we will assume that it is tackled implicitly. For example, the considered plan templates should take into account that the enemy tries to reduce the probability of detection. This paper concentrates on another important characteristic feature of tactical plan recognition, namely that the identity of * Corresponding author. Address: Thales Nederland B.V., Zuidelijke havenweg 40, P.O. Box 42-7550 GD Hengelo(Ov), The Netherlands. Fax: +31-74-2484077. E-mail addresses: frank.mulder@nl.thalesgroup.com (F. Mulder), f.p.voorbraak@amc.uva.nl (F. Voorbraak). 1566-2535/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII:S1566-2535(02)00102-1 Information Fusion 4 (2003) 47–61 www.elsevier.com/locate/inffus