Decision Theory, the Situation Calculus and Conditional Plans

David Poole

Linköping Electronic Articles in Computer and Information Science, Vol 3 (1998):nr 8. June 15, 1998.

Under discussion, The Electronic Transactions on Artificial Intelligence.


This paper shows how to combine decision theory and logical representations of actions in a manner that seems natural for both. In particular, we assume an axiomatization of the domain in terms of situation calculus, using what is essentially Reiter's solution to the frame problem, in terms of the completion of the axioms defining the state change. Uncertainty is handled in terms of the independent choice logic, which allows for independent choices and a logic program that gives the consequences of the choices. The same framework handles both frame and ramification axioms. As part of the consequences are a specification of the utility of (final) states, and how (possibly noisy) sensors depend on the state. The robot adopts conditional plans, similar to the GOLOG programming language. Within this logic, we can define the expected utility of a conditional plan, based on the axiomatization of the actions, the sensors and the utility. Sensors can be noisy and actions can be stochastic. The planning problem is to find the plan with the highest expected utility. This representation is related to recent structured representations for partially observable Markov decision processes (POMDPs); here we use stochastic situation calculus rules to specify the state transition function and the reward/value function.

You can get the pdf or postscript.

One of the features of ETAI is the Online Discussion. You are welcome to participate.

There is also a complete axiomatization of the example in ICL as well as ICL interpreter that runs the code (this is both a latex file and a Sicstuc Prolog file). Or you can get the ICL code distribution.

Related Papers

D. Poole, The Independent Choice Logic for modelling multiple agents under uncertainty.

D. Poole, Abducing Through Negation As Failure: Stable models in the Independent Choice Logic.

Last updated 11 June 1998 - David Poole