Temporal planning with fuzzy constraints and preferences

Krystian Jobczyk 1
1 Equipe MAD - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : Temporal planning forms conceptually a part of temporal reasoning and it belongs to research area of Artificial Intelligence and it may be seen as an extension of classical planning by temporal aspects of acting. Temporal planing is usually complemented by considering preferences or different types of temporal constraints imposed on execution of actions. There exist many approaches to this issue. One one hand, there are different paradigms to temporal planning, such as: planning via search in graphs (STRIPS), planning via satisfiability or planning in terms of Markov processes. These approaches are mutually incompatible. In addition, temporal planning requires a subject-specification as it is rather defined in a methodological way. On the other hand, temporal constraints are represented and modeled in different ways dependently on their quantitative or qualitative nature. In particular, Allen’s relations between temporal intervals – an important class of temporal constraints – do not have any quantitative aspects and cannot be considered in computational contexts. According to this situation, this PhD-thesis is aimed at the proposing a depth-analysis of temporal planning with fuzzy constraints which contains some remedies on these difficulties. Namely, two approaches to the representation and modeling of these issues are put forward. In the first one (chapter 2, chapter 3) – fuzzy Allen’s relations as fuzzy temporal constraints are represented by norms of convolutions in a Banach space of Lebesgue integrable functions. It allows us immerse Allen’s relations in the computational contexts of temporal planning (based on STRIPS and on DavisPutnam procedure) and to elucidate their quantitative nature. This approach is developed in a context of Multi-Agent Problem as a subject basis of this approach. In the second one (chapter 4, chapter 5) – fuzzy temporal constrains with fuzziness introduced by preferences are represented in a logical terms of Preferential Halpern-Shoham Logic. It allows us to adopt these result in a construction of the plan controller. This approach is developed in a context of Temporal Traveling Salesman Problem as a subject basis of this approach. Finally, an attempt to reconcile these two lines of representation of fuzzy temporal constraints was also proposed.
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Krystian Jobczyk. Temporal planning with fuzzy constraints and preferences. Artificial Intelligence [cs.AI]. Normandie Université, 2017. English. ⟨NNT : 2017NORMC259⟩. ⟨tel-01729288⟩

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