Observations and the probabilistic situation calculus

Discrete Applied Mathematics, 1992

Directed Agent) is a model for autonomous learning in probabilistic domains [desJ ardins,

2004

We present the description logic PN-ALCK α NF for reasoning about actions with sensing under qualitative and probabilistic uncertainty, which is an extension of the description logic ALCK α NF by actions with nondeterministic and probabilistic effects. We define a formal semantics of PN-ALCK α NF in terms of deterministic, nondeterministic, and probabilistic transitions between epistemic states, which are sets of possible states of the world. We introduce the notions of a conditional plan and its goodness under qualitative and probabilistic uncertainty. We then formulate the problem of conditional planning in this framework, and we present an algorithm for solving it. This algorithm is based on a reduction to reasoning in description logics, and is shown to be sound and complete in the sense that it generates all optimal plans. We also describe an application in a robotic-soccer scenario.

ACM Transactions on Computational Logic, 2009

We present the description logic PN-ALCK α NF for reasoning about actions with sensing under qualitative and probabilistic uncertainty, which is an extension of the description logic ALCK α NF by actions with nondeterministic and probabilistic effects. We define a formal semantics of PN-ALCK α NF in terms of deterministic, nondeterministic, and probabilistic transitions between epistemic states, which are sets of possible states of the world. We introduce the notions of a conditional plan and its goodness under qualitative and probabilistic uncertainty. We then formulate the problem of conditional planning in this framework, and we present an algorithm for solving it. This algorithm is based on a reduction to reasoning in description logics, and is shown to be sound and complete in the sense that it generates all optimal plans. We also describe an application in a robotic-soccer scenario.

1996

This paper shows how we can combine logical representations of actions and decision theory in such 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. As part of the consequences are a specification of the utility of (final) states. The robot adopts robot 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 uncertainty and the utility. The 'planning' problem is to find the plan with the highest expected utility. This is related to recent structured representations for POMDPs; here we use stochastic situation calculus rules to specify the state transition function and the reward/value function. Finally we show that with stochastic frame axioms, actions representations in probabilistic STRIPS are exponentially larger than using the representation proposed here.

2012 IEEE International Multi-Disciplinary Conference on Cognitive Methods in Situation Awareness and Decision Support, 2012

One of the most substantial advantages that human analysts have over machine algorithms is the ability to seamlessly integrate sensed data into a situation-based internal narrative. Replicating an analogous internal representation algorithmically has proved to be a challenging problem that is the focus of much current research. For a machine to more accurately make complex decisions over a stable, consistent and useful representation, situations must be inferred from prior experience and corroborated by incoming data. We believe that a common mathematical framework for situations that addresses varying levels of complexity and uncertainty is essential to meeting this goal. In this paper, we present work in progress on developing the mathematics for probabilistic situations.

International Journal on Artificial Intelligence Tools, 2012

Decision-making on uncertain and dynamic domains is still a challenging research area. This paper explores a solution to handle such complex decision making based on a combined logic system. We provide an explanation of our reasoning system focused on the algorithms and their implementations. The reasoning system is based on a multi-valued temporal propositional logic which we use as the foundation for the implementation of simulation/prediction and query answering tools. This system is available for users to represent knowledge and to refine these systems to debug them and to try different problem solving strategies. We provide examples to illustrate how the system can be used including a problem based on a real smart environment.