23,218 research outputs found

    Bounded Situation Calculus Action Theories

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    In this paper, we investigate bounded action theories in the situation calculus. A bounded action theory is one which entails that, in every situation, the number of object tuples in the extension of fluents is bounded by a given constant, although such extensions are in general different across the infinitely many situations. We argue that such theories are common in applications, either because facts do not persist indefinitely or because the agent eventually forgets some facts, as new ones are learnt. We discuss various classes of bounded action theories. Then we show that verification of a powerful first-order variant of the mu-calculus is decidable for such theories. Notably, this variant supports a controlled form of quantification across situations. We also show that through verification, we can actually check whether an arbitrary action theory maintains boundedness.Comment: 51 page

    On First-Order Ό-Calculus over Situation Calculus Action Theories

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    In this paper we study verification of situation calculus action theories against first-order mu-calculus with quantification across situations. Specifically, we consider mu-La and mu-Lp, the two variants of mu-calculus introduced in the literature for verification of data-aware processes. The former requires that quantification ranges over objects in the current active domain, while the latter additionally requires that objects assigned to variables persist across situations. Each of these two logics has a distinct corresponding notion of bisimulation. In spite of the differences we show that the two notions of bisimulation collapse for dynamic systems that are generic, which include all those systems specified through a situation calculus action theory. Then, by exploiting this result, we show that for bounded situation calculus action theories, mu-La and mu-Lp have exactly the same expressive power. Finally, we prove decidability of verification of mu-La properties over bounded action theories, using finite faithful abstractions. Differently from the mu-Lp case, these abstractions must depend on the number of quantified variables in the mu-La formula

    Progression and Verification of Situation Calculus Agents with Bounded Beliefs

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    We investigate agents that have incomplete information and make decisions based on their beliefs expressed as situation calculus bounded action theories. Such theories have an infinite object domain, but the number of objects that belong to fluents at each time point is bounded by a given constant. Recently, it has been shown that verifying temporal properties over such theories is decidable. We take a first-person view and use the theory to capture what the agent believes about the domain of interest and the actions affecting it. In this paper, we study verification of temporal properties over online executions. These are executions resulting from agents performing only actions that are feasible according to their beliefs. To do so, we first examine progression, which captures belief state update resulting from actions in the situation calculus. We show that, for bounded action theories, progression, and hence belief states, can always be represented as a bounded first-order logic theory. Then, based on this result, we prove decidability of temporal verification over online executions for bounded action theories. © 2015 The Author(s

    Bounded Situation Calculus Action Theories and Decidable Verification

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    Abstract We define a notion of bounded action theory in the situation calculus, where the theory entails that in all situations, the number of ground fluent atoms is bounded by a constant. Such theories can still have an infinite domain and an infinite set of states. We argue that such theories are fairly common in applications, either because facts do not persist indefinitely or because one eventually forgets some facts, as one learns new ones. We discuss various ways of obtaining bounded action theories. The main result of the paper is that verification of an expressive class of first-order ”-calculus temporal properties in such theories is in fact decidable

    LTL Verification of Online Executions with Sensing in Bounded Situation Calculus

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    Abstract. We look at agents reasoning about actions from a firstperson perspective. The agent has a representation of world as situation calculus action theory. It can perform sensing actions to acquire information. The agent acts “online”, i.e., it performs an action only if it is certain that the action can be executed, and collects sensing results from the actual world. When the agent reasons about its future actions, it indeed considers that it is acting online; however only possible sensing values are available. The kind of reasoning about actions we consider for the agent is verifying a first-order (FO) variant (without quantification across situations) of linear time temporal logic (LTL). We mainly focus on bounded action theories, where the number of facts that are true in any situation is bounded. The main results of this paper are: (i) possible sensing values can be based on consistency if the initial situation description is FO; (ii) for bounded action theories, progression over histories that include sensing results is always FO; (iii) for bounded theories, verifying our FO LTL against online executions with sensing is decidable.

    Decidable Verification of Golog Programs over Non-Local Effect Actions: Extended Version

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    The Golog action programming language is a powerful means to express high-level behaviours in terms of programs over actions defined in a Situation Calculus theory. In particular for physical systems, verifying that the program satisfies certain desired temporal properties is often crucial, but undecidable in general, the latter being due to the language’s high expressiveness in terms of first-order quantification and program constructs. So far, approaches to achieve decidability involved restrictions where action effects either had to be contextfree (i.e. not depend on the current state), local (i.e. only affect objects mentioned in the action’s parameters), or at least bounded (i.e. only affect a finite number of objects). In this paper, we present a new, more general class of action theories (called acyclic) that allows for context-sensitive, non-local, unbounded effects, i.e. actions that may affect an unbounded number of possibly unnamed objects in a state-dependent fashion. We contribute to the further exploration of the boundary between decidability and undecidability for Golog, showing that for acyclic theories in the two-variable fragment of first-order logic, verification of CTL properties of programs over ground actions is decidable

    Noncommutative Yang-Mills-Higgs actions from derivation-based differential calculus

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    Derivations of a noncommutative algebra can be used to construct differential calculi, the so-called derivation-based differential calculi. We apply this framework to a version of the Moyal algebra M{\cal{M}}. We show that the differential calculus, generated by the maximal subalgebra of the derivation algebra of M{\cal{M}} that can be related to infinitesimal symplectomorphisms, gives rise to a natural construction of Yang-Mills-Higgs models on M{\cal{M}} and a natural interpretation of the covariant coordinates as Higgs fields. We also compare in detail the main mathematical properties characterizing the present situation to those specific of two other noncommutative geometries, namely the finite dimensional matrix algebra Mn(C)M_n({\mathbb{C}}) and the algebra of matrix valued functions C∞(M)⊗Mn(C)C^\infty(M)\otimes M_n({\mathbb{C}}). The UV/IR mixing problem of the resulting Yang-Mills-Higgs models is also discussed.Comment: 23 pages, 2 figures. Improved and enlarged version. Some references have been added and updated. Two subsections and a discussion on the appearence of Higgs fiels in noncommutative gauge theories have been adde

    Abstraction of Agents Executing Online and their Abilities in the Situation Calculus

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    We develop a general framework for abstracting online behavior of an agent that may acquire new knowledge during execution (e.g., by sensing), in the situation calculus and ConGolog. We assume that we have both a high-level action theory and a low-level one that represent the agent's behavior at different levels of detail. In this setting, we define ability to perform a task/achieve a goal, and then show that under some reasonable assumptions, if the agent has a strategy by which she is able to achieve a goal at the high level, then we can refine it into a low-level strategy to do so

    Hierarchical agent supervision

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    Agent supervision is a form of control/customization where a supervisor restricts the behavior of an agent to enforce certain requirements, while leaving the agent as much autonomy as possible. To facilitate supervision, it is often of interest to consider hierarchical models where a high level abstracts over low-level behavior details. We study hierarchical agent supervision in the context of the situation calculus and the ConGolog agent programming language, where we have a rich first-order representation of the agent state. We define the constraints that ensure that the controllability of in-dividual actions at the high level in fact captures the controllability of their implementation at the low level. On the basis of this, we show that we can obtain the maximally permissive supervisor by first considering only the high-level model and obtaining a high- level supervisor and then refining its actions locally, thus greatly simplifying the supervisor synthesis task
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