Jens Claßen

GOLOG and PDDL: what is the relative expressiveness?

Action formalisms such as GOLOG or FLUX have been developed primarily for representing and reasoning about change in a logical framework. For this reason, expressivity was the main goal in the development of these formalisms. In another line of research, efficiency of planning methods was the topmost goal resulting in the basic STRIPS language, which has only moderate expressivity. The planning language PDDL developed since 1998 is an extension of basic STRIPS with many expressive features. Now the interesting question is how PDDL compares to GOLOG or other action languages from an expressivity point of view. We will show that a GOLOG fragment, which we call Restricted Basic Action Theories, is as expressive as the ADL fragment of PDDL. To prove this equivalence we use the compilation framework. From a practical point of view, this result can be used for employing efficient planners inside a GOLOG interpreter.

Platas—Integrating Planning and the Action Language Golog

Action programming languages like Golog allow to define complex behaviors for agents on the basis of action representations in terms of expressive (first-order) logical formalisms, making them suitable for realistic scenarios of agents with only partial world knowledge. Often these scenarios include sub-tasks that require sequential planning. While in principle it is possible to express and execute such planning sub-tasks directly in Golog, the system can performance-wise not compete with state-of-the-art planners. In this paper, we report on our efforts to integrate efficient planning and expressive action programming in the Platas project. The theoretical foundation is laid by a mapping between the planning language Pddl and the Situation Calculus, which is underlying Golog, together with a study of how these formalisms relate in terms of expressivity. The practical benefit is demonstrated by an evaluation of embedding a Pddl planner into Golog, showing a drastic increase in performance while retaining the full expressiveness of Golog.

Verifying CTL* properties of GOLOG programs over local-effect actions

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 C2 as underlying base logic, (2) using a fragment of GOLOG with ground actions only, and (3) requiring the action theory to only admit local effects.

Decidable Verification of Decision-Theoretic Golog

The Golog agent programming language is a powerful means to express high-level behaviours in terms of programs over actions defined in a Situation Calculus theory. Its variant DTGolog includes decision-theoretic aspects in the form of stochastic (probabilistic) actions and reward functions. In particular for physical systems such as robots, verifying that a 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. Recent results for classical Golog show that by suitably restricting these aspects, the verification problem becomes decidable for a non-trivial fragment that retains a large degree of expressiveness. In this paper, we lift these results to the decision-theoretic case by providing an abstraction mechanism for reducing the infinite-state Markov Decision Process induced by the DTGolog program to a finite-state representation, which then can be fed into a state-of-the-art probabilistic model checker.