We study the first-order definability of progression for situation calculus action theories with a focus on the iterability of progression. Progression, the task of updating a knowledge base according to actions' effects so that proper information is retained, is notoriously challenging as it in general requires second-order logic. Exceptions where progression is first-order like local-effect actions and normal actions impose certain syntax constraints on action theories to eliminate second-order quantifiers in the progressed knowledge base. Unfortunately, the progressed result might not satisfy the constraints again, making it impossible to apply first-order progression iteratively. In this paper, we first lift the existing result on first-order progression for normal actions by allowing disjunctions in the knowledge base. As a result, we obtain an action theory whose type is called disjunctive normal, which is iteratively first-order progressable. Second, we propose a new class of action theories, called PANACK, that strictly subsumes the disjunctive normal ones, and we show that it remains iteratively first-order progressable as well.

We investigate the synthesis of policies for high-level agent programs expressed in Golog, a language based on situation calculus that incorporates nondeterministic programming constructs. Unlike traditional approaches for program realization that assume full agent control or rely on incremental search, we address scenarios where environmental nondeterminism significantly influences program outcomes. Our synthesis problem involves deriving a policy that successfully realizes a given Golog program while ensuring the satisfaction of a temporal specification, expressed in Linear Temporal Logic on finite traces (LTLf), across all possible environmental behaviors. By leveraging an expressive class of first-order action theories, we construct a finite game arena that encapsulates program executions and tracks the satisfaction of the temporal goal. A game-theoretic approach is employed to derive such a policy. Experimental results demonstrate this approach's feasibility in domains with unbounded objects and non-local effects. This work bridges agent programming and temporal logic synthesis, providing a framework for robust agent behavior in nondeterministic environments.

Abstract Levesque and Lakemeyer proposed a logic called $$\mathcal L$$ L as a first-order logic for knowledge representation and reasoning in knowledge-based systems. A characteristic feature of this logic is that it uses a countably infinite set of what are called standard names, which are syntactically treated like constants, but which are also isomorphic to a fixed universe of discourse. Quantifiers in $$\mathcal L$$ L are then given a substitutional interpretation. This non-standard semantics not only simplifies the proofs for certain meta-theoretic properties, but is also exploited in dedicated reasoning procedures for modal extensions of $$\mathcal L$$ L that include notions of belief, actions, time, and more. However, the only sound and complete proof system provided for $$\mathcal L$$ L so far is a Hilbert-style axiom system, as well as an iterative reasoning mechanism based on resolution and clause subsumption. In this paper, we present a tableau system for $$\mathcal L$$ L , and show its soundness and completeness. Completeness is proved first by reduction to the existing axiom system, and involves the cut rule, and then via Hintikka sets, which does not require the cut rule.

In general, an agent may have incomplete and inaccurate knowledge about its environment. As well, actions may not turn out as intended or may have nondeterministic effects, and sensors may on occasion give incorrect results. We present a general, qualitative approach to reasoning about action and change in such a setting. The approach is expressed as an extension to basic action theories in the situation calculus, where an agent's epistemic state is modelled by a set of situations, where each situation is assigned a non-negative integer representing its plausibility. The agent's epistemic state is updated by modifying these plausibility values after the execution of an action, taking into account the possibility of unexpected results. To this end, we consider actions to have an intensional aspect, under the control of and determined by the agent, and an extensional aspect, not directly accessible to the agent and controlled by "nature". This leads to two distinct but related related notions of belief, an extensional "bird's eye" view which models an agent's beliefs wrt actually-executed actions, and an intensional view representing beliefs from the agent's point of view. We argue that the approach is significantly more general and comprehensive than previous accounts, and leads to a unified view of failed actions and nondeterminism with respect to physical and sensing actions.

With the advent of artificial agents in everyday life, it is important that these agents are guided by social norms and moral guidelines. Notions of obligation, permission, and the like have traditionally been studied in the field of Deontic Logic, where deontic assertions generally refer to what an agent should or should not do; that is they refer to actions. In Artificial Intelligence, the Situation Calculus is (arguably) the best known and most studied formalism for reasoning about action and change. In this paper, we integrate these two areas by incorporating deontic notions into Situation Calculus theories. We do this by considering deontic assertions as constraints, expressed as a set of conditionals, which apply to complex actions expressed as GOLOG programs. These constraints induce a ranking of "ideality" over possible future situations. This ranking in turn is used to guide an agent in its planning deliberation, towards a course of action that adheres best to the deontic constraints. We present a formalization that includes a wide class of (dyadic) deontic assertions, lets us distinguish prima facie from all-things-considered obligations, and particularly addresses contrary-to-duty scenarios. We furthermore present results on compiling the deontic constraints directly into the Situation Calculus action theory, so as to obtain an agent that respects the given norms, but works solely based on the standard reasoning and planning techniques.

To solve ever more complex and longer tasks, mobile robots need to generate more elaborate plans and must handle dynamic environments and incomplete knowledge. We address this challenge by integrating two seemingly different approaches — PDDL-based planning for efficient plan generation and Golog for highly expressive behavior specification — in a coherent framework that supports continual planning. The latter allows to interleave plan generation and execution through assertions, which are placeholder actions that are dynamically expanded into conditional sub-plans (using classical planners) once a replanning condition is satisfied. We formalize and implement continual planning in Golog which was so far only supported in PDDL-based systems. This enables combining the execution of generated plans with regular Golog programs and execution monitoring. Experiments on autonomous mobile robots show that the approach supports expressive behavior specification combined with efficient sub-plan generation to handle dynamic environments and incomplete knowledge in a unified way.

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, range of action effects, and program constructs. So far, approaches to achieve decidability involved restrictions where action effects either had to be context-free (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 introduce two new, more general classes of action theories that allow 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 our new classes of action theories in the two-variable fragment of first-order logic, verification of CTL* properties of programs over ground actions is decidable.

We consider the realistic case of a GOLOG agent that only possesses incomplete knowledge about the state of its environment and has to resort to sensing in order to gather additional information at runtime, and where the agent is controlled by a knowledge-based program in which test conditions explicitly refer to the agent's knowledge (or lack thereof). In this paper, we propose a formalization of knowledge-based agents that extends earlier proposals by a form of non-monotonic reasoning that includes Reiter-style defaults. We present a reasoning mechanism that enables us to reduce projection queries about future states of the agent's knowledge (including nesting of epistemic modalities) to classical Default Logic, and provide a corresponding Representation Theorem. We thus obtain the theoretical foundation for an implementation where reasoning subtasks can be handed to an embedded off-the-shelf reasoner for Default Logic, and that supports a (in some respects) more expressive epistemic action language than previous solutions.

Mobile robots should perform a growing number of tasks and react to time-critical events. Thus, the ability to interrupt a task and resume it later is crucial. While interleaved execution occurs often in robotics, existing approaches do not consider the fact that interrupting a task and resuming an interrupted task often requires intermediate steps. In this paper we present an approach to interruptible task execution with resumption. We propose INTRGOLOG which extends INDIGOLOG by task interruption and resumption through introducing new constructs to determine and fulfill the requirements of tasks. Our experiments on a service robot and in simulation show that the ability to switch to another task enables a robot to react in a swift and reliable fashion to new events.

The action programming language GOLOG has been found useful for the control of autonomous agents such as mobile robots. In scenarios like these, tasks are often open-ended so that the respective control programs are non-terminating. Before deploying such programs on a robot, it is often desirable to verify that they meet certain requirements. For this purpose, Claßen and Lakemeyer recently introduced algorithms for the verification of temporal properties of GOLOG programs. However, given the expressiveness of GOLOG, their verification procedures are not guaranteed to terminate. In this paper, we show how decidability can be obtained by suitably restricting the underlying base logic, the effect axioms for primitive actions, and the use of actions within GOLOG programs. Moreover, we show that dropping any of these restrictions immediately leads to undecidability of the verification problem.

GOLOG is a high-level action programming language for controlling autonomous agents such as mobile robots. It is defined on top of a logic-based action theory expressed in the Situation Calculus. Before a program is deployed onto an actual robot and executed in the physical world, it is desirable, if not crucial, to verify that it meets certain requirements (typically expressed through temporal formulas) and thus indeed exhibits the desired behaviour. However, due to the high (first-order) expressiveness of the language, the corresponding verification problem is in general undecidable. In this paper, we extend earlier results to identify a large, non-trivial fragment of the formalism where verification is decidable. In particular, we consider properties expressed in a first-order variant of the branching-time temporal logic CTL*. Decidability is obtained by (1) resorting to the decidable first-order fragment C2as underlying base logic, (2) using a fragment of GOLOG with ground actions only, and (3) requiring the action theory to only admit local effects.

The agent programming language GOLOG and the underlying Situation Calculus have become popular means for the modelling and control of autonomous agents such as mobile robots. Although such agents' tasks are typically open-ended, little attention has been paid so far to the analysis of non-terminating GOLOG control programs. Recently we therefore introduced a logic that allows to express properties of Golog programs using operators from temporal logics while retaining the full first-order expressiveness of the Situation Calculus. Combining ideas from classical symbolic model checking with first-order theorem proving we presented a verification method for a restricted subclass of temporal properties. In this paper, we extend this work by considering arbitrary temporal formulas. Our algorithm is inspired by classical 𝒞𝒯ℒ* model checking, but introduces techniques to cope with arbitrary first-order quantification.