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Psychology
Cognitive Science

Bounded situation calculus action theories

Profile image of Yves LesperanceYves Lesperance

2016, Artificial Intelligence

Abstract

In this paper, 4 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 µcalculus 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.

Related papers

On the Progression of Situation Calculus Universal Theories with Constants
Juan Cruz Torres Navarro

2018

The progression of action theories is an important problem in knowledge representation. Progression is second-order definable and known to be first-order definable and effectively computable for restricted classes of theories. Motivated by the fact that universal theories with constants (UTCs) are expressive and natural theories whose satisfiability is decidable, in this paper we provide a thorough study of the progression of situation calculus UTCs. First, we prove that progression of a (possibly infinite) UTC is always first-order definable and results in a UTC. Though first-order definable, we show that the progression of a UTC may be infeasible, that is, it may result in an infinite UTC that is not equivalent to any finite set of first-order sentences. We then show that deciding whether there is a feasible progression of a UTC is undecidable. Moreover, we show that deciding whether a sentence (in an expressive fragment of first-order logic) is in the progression of a UTC is CONE...

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Progressing Basic Action Theories with Non-Local Effect Actions (Commonsense-2009)
Stavros Vassos

In this paper we propose a practical extension to some recent work on the progression of action theories in the situation calculus. In particular, we argue that the assumption of local-effect actions is too restrictive for realistic settings. Based on the notion of safe-range queries from database theory and just-in-time action histories, we present a new type of action theory, called range-restricted, that allows actions to have non-local effects with a restricted range. These theories can represent incomplete information in the initial database in terms of possible closures for fluents and can be progressed by directly updating the database in an algorithmic manner. We prove the correctness of our method and argue for the applicability of range-restricted theories in realistic settings.

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Abstraction in Situation Calculus Action Theories
Yves Lesperance

Proceedings of the AAAI Conference on Artificial Intelligence

We develop a general framework for agent abstraction based on the situation calculus and the ConGolog agent programming language. We assume that we have a high-level specification and a low-level specification of the agent, both represented as basic action theories. A refinement mapping specifies how each high-level action is implemented by a low-level ConGolog program and how each high-level fluent can be translated into a low-level formula. We define a notion of sound abstraction between such action theories in terms of the existence of a suitable bisimulation between their respective models. Sound abstractions have many useful properties that ensure that we can reason about the agent's actions (e.g., executability, projection, and planning) at the abstract level, and refine and concretely execute them at the low level. We also characterize the notion of complete abstraction where all actions (including exogenous ones) that the high level thinks can happen can in fact occur at...

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M.: Decidable reasoning in a modified situation calculus
Yilan Gu

2007

We consider a modified version of the situation calculus built using a two-variable fragment of the first-order logic extended with counting quantifiers. We mention several additional groups of axioms that can be introduced to capture taxonomic reasoning. We show that the regression operator in this framework can be defined similarly to regression in the Reiter's version of the situation calculus. Using this new regression operator, we show that the projection and executability problems are decidable in the modified version even if an initial knowledge base is incomplete and open. For an incomplete knowledge base and for context-dependent actions, we consider a type of progression that is sound with respect to the classical progression. We show that the new knowledge base resulting after our progression is definable in our modified situation calculus if one allows actions with local effects only. We mention possible applications to formalization of Semantic Web services.

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First-order μ -calculus over generic transition systems and applications to the situation calculus
Marco Montali

Information and Computation

In this paper, we consider µL, µL a , and µL p , three variants of the first-order µ-calculus introduced in the literature for verification of data-aware processes. In the first one, quantification on objects ranges over the whole domain; in the second one, quantification ranges over objects in the active domain of the current state only; in the latter one, objects assigned to variables are further required to persist across transitions. Each of these three logics has a distinct corresponding notion of bisimulation. In spite of the differences among these logics, we show that the three notions of bisimulation collapse for dynamic systems that are generic, which include all those systems specified in a statebased fashion using a logical formalism, such as, e.g., the situation calculus. As a result, for such dynamic systems, µL, µL a , and µL p have the same expressive power. In addition, we show that, when the dynamic system stores only a bounded number of objects in each state, a finite abstraction can be constructed which is faithful for µL (the most general variant). This yields decidability of verification. In particular, by applying such results, we show decidability of µL verification over bounded situation calculus action theories. These decidability results contrast with the undecidability of verification for first-order ltl over state-bounded generic transition systems, and notably imply that first-order ltl cannot be captured by µL.

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An action language for multi-agent domains
Son Tran

Artificial Intelligence, 2021

In multi-agent domains, the actions performed by an agent may not only modify the world and the agent's knowledge and beliefs about the world, but may also change the knowledge and beliefs of other agents about the world and their own knowledge and beliefs about other agents' knowledge and beliefs about the world. Similarly, the goals of an agent in a multi-agent domain may involve manipulating the knowledge and beliefs of other agents' and, again, not just their knowledge 1 about the world, but also their knowledge about other agents' knowledge about the world. The goal of this paper is to investigate an action language, called mA * , that provides the necessary features to address the above aspects in representing and reasoning about actions and change in multi-agent domains. The language, as designed, can also serve as a specification language for epistemic planning, thereby addressing an important issue in the development of multi-agent epistemic planning systems. The mA * action language is a generalization of the single-agent action languages, extensively studied in the literature, to the case of multi-agent domains. The language allows the representation of different types of actions that an agent can perform in a domain where many other agents might be present-such as world-altering actions, sensing actions, and communication actions. The action language also allows the specification of agents' dynamic awareness of action occurrences-which has implications on what agents' know about the world and other agents' knowledge about the world. These features are embedded in a language that is simple, yet powerful enough to address a large variety of knowledge manipulation scenarios in multi-agent domains. The semantics of mA * relies on the notion of state, which is described by a pointed Kripke model and is used to encode the agents' knowledge and the real state of the world. The semantics is defined by a transition function that maps pairs of actions and states into sets of states. The paper presents a number of properties of the action theories, including properties that guarantee finiteness of the set of initial states and their practical realization in a system. Finally, the paper relates mA * to other relevant formalisms in the area of reasoning about actions in multi-agent domains.

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Reasoning about Actions and Planning in LTL Action Theories
Moshe Vardi

2002

In this paper, we study reasoning about actions and planning with incomplete information in a setting where the dynamic system is specified by adopting Linear Temporal Logic (ltl). Specifically, we study: (i) reasoning about action effects (i.e., projection, historical queries, etc.), in such a setting; (ii) when actions can be legally executed, assuming a non-prescriptive approach, where executing an action is possible in a given situation unless forbidden by the system specification; (iii) the problem of finding conformant plans for temporally extended goals that consist of arbitrary ltl formulas, thus allowing for expressing sophisticated dynamic requirements. For each of these problems we establish techniques and characterize the computational complexity. For the last two problems we make use of a second-order variant of ltl.

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Progressing Basic Action Theories with Non-Local Effect Actions (PLS-2009 short paper)
Stavros Vassos

In this paper we propose a practical extension to some recent work on the progression of action theories in the situation calculus. Based on the notion of safe-range queries from database theory and just-in-time action histories, we present a new type of action theory, called range-restricted, that allows actions to have non-local e ects with a restricted range. These theories can represent incomplete information in terms of possible closures for fluents and can be progressed by directly updating the database in an algorithmic manner.

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Reasoning about large taxonomies of actions in the situation calculus
Yilan Gu

Citeseer

We design a representation based on the situation calculus that facilitates development, maintenance and elaboration of very large taxonomies of actions. It leads to a modular basic action theories (BATs) for reasoning about actions more compact than Reiter's current representation ...

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Progressing Basic Action Theories with NonLocal Effect Actions
Sebastian Sardina

In this paper we propose a practical extension to some recent work on the progression of action theories in the situation calculus. In particular, we argue that the assumption of local-effect actions is too restrictive for realistic settings. Based on the notion of safe-range queries from database theory and just-in-time action histories, we present a new type of action theory, called range-restricted, that allows actions to have non-local effects with a restricted range. These theories can represent incomplete information in the initial database in terms of possible closures for fluents and can be progressed by directly updating the database in an algorithmic manner. We prove the correctness of our method and argue for the applicability of range-restricted theories in realistic settings.

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Related topics

  • Cognitive Science
  • Mathematics
  • Computer Science
  • Artificial Intelligence
  • Language and Linguistics
  • Situation Calculus
  • Reasoning About Action
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