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Reasoning About Action and Change

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Abstract

This chapter presents the state of research concerning the formalisation of an agent reasoning about a dynamic system which can be partially observed and acted upon. We first define the basic concepts of the area: system states, ontic and epistemic actions, observations; then the basic reasoning processes: prediction, progression, regression, postdiction, filtering, abduction, and extrapolation. We then recall the classical action representation problems and show how these problems are solved in some standard frameworks. For space reasons, we focus on these major settings: the situation calculus, STRIPS and some propositional action languages, dynamic logic, and dynamic Bayesian networks. We finally address a special case of progression, namely belief update.

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Notes

  1. 1.

    There are many other uncertainty models that should be mentioned but will not be, for space reasons - they include ordinal models, where belief states and action effects are modeled as pre-orders over \({\mathscr {S}}\), possibilistic models that are similar in spirit to them, non-Bayesian probabilistic models, where a belief state is a family of probability distributions, etc. (see chapter “Representations of Uncertainty in Artificial Intelligence: Probability and Possibility” of this volume).

  2. 2.

    A system is Markovian if the transition of the system to any given state depends only on the current state and not on the previous ones.

  3. 3.

    In the probabilistic model, there may not exist a unique probability distribution b on \({\mathscr {S}}\) satisfying \(b'(s') = \sum _{s \in {\mathscr {S}}} b(s).p(s'|s,\alpha )\), \(b'(s')\) with \(p(s'|s,\alpha )\) being known for all s, \(s'\) and \(\alpha \).

  4. 4.

    A more complex abduction problem consists in reasoning not only on the event which took place, but also on the system states at time points t and \(t+1\), on which one wishes to obtain more precise beliefs.

  5. 5.

    If the rifle is loaded in the situation s then the fluent “Alive” is abnormal (i.e., non persistent) when the action “Shoot” takes place in s and the person will not be alive any more in the resulting situation.

  6. 6.

    If the fluent is not abnormal with respect to an action then it keeps its value after the execution of this action.

  7. 7.

    A pathological case is when the conditions of rules leading to complementary literals are conjointly satisfied in s; in such a case, the progression is undefined; this can reflect an error when specifying the representation of the action, or the fact that s is impossible (and in this case corresponds to an implicit static law).

  8. 8.

    If they were equivalent, then the encoding of action “Shoot” by Loaded \(\mapsto \lnot \) Alive in the Yale Shooting Problem would be equivalent to Alive \(\mapsto \lnot \) Loaded, meaning that shooting on a living person results on the gun being magically unloaded (and the person staying alive...).

  9. 9.

    As shown in (Friedman and Halpern 1999), revision remains relevant even if the initial belief state and the new formula do not refer to the same time point, as long as there is a syntactical distinction (via some time-stamping) between a fluent at a time point and the same fluent at another time point: what matters for revision is not that the world is static, but that the propositions that are used to describe the world are static. This also explains that belief extrapolation also corresponds to a revision process (Dupin de Saint-Cyr and Lang 2011).

  10. 10.

    If U6 and U7 are used instead of U9 then the theorem gives us a faithful preorder that is only partial.

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Authors and Affiliations

  1. IRIT-CNRS, Université Paul Sabatier, Toulouse, France

    Florence Dupin de Saint-Cyr & Andreas Herzig

  2. CNRS, Université Paris-Dauphine, PSL Research University, LAMSADE, Paris, France

    Jérôme Lang

  3. CRIL-CNRS, Université d’Artois and Institut Universitaire de France, Lens, France

    Pierre Marquis

Authors
  1. Florence Dupin de Saint-Cyr
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  2. Andreas Herzig
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  4. Pierre Marquis
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Correspondence to Florence Dupin de Saint-Cyr .

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Editors and Affiliations

  1. CRIL-CNRS, Université d'Artois and Institut Universitaire de France, Lens, France

    Pierre Marquis

  2. Aix Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France

    Odile Papini

  3. IRIT, CNRS and Université Paul Sabatier, Toulouse, France

    Henri Prade

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Dupin de Saint-Cyr, F., Herzig, A., Lang, J., Marquis, P. (2020). Reasoning About Action and Change. In: Marquis, P., Papini, O., Prade, H. (eds) A Guided Tour of Artificial Intelligence Research. Springer, Cham. https://doi.org/10.1007/978-3-030-06164-7_15

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