In this article we propose a Probabilistic Situation Calculus logical language to represent and reason with knowledge about dynamical worlds in which actions have uncertain effects. Two essential tasks are addressed when reasoning about change in worlds: Probabilistic Temporal Projection and Probabilistic Belief Update. Uncertain effects are modeled by dividing an action into two subparts: a deterministic input (agent produced) and a probabilistic reaction (nature produced). The probability distributions of the reactions are assumed to be known. Our logical language is an extension to Situation Calculae in the style proposed by Raymond Reiter. There are three aspects to this work. First, we extend the language to accommodate terms dealing with belief and probability. Second, we provide a operational semantics based on Randomly Timed Automata. Finally, we develop Monte-Carlo algorithms to efficiently interpret the probability and belief terms. With the framework proposed we discuss how to develop a reasoning system in Mathematica capable of performing temporal projection and belief update in the Probabilistic Situation Calculus. Finally, we present a sound basis to set rewards and observation planning. (1) Center for Logic and Computation, Departamento de Matematica, IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal. email: pmat@math.ist.utl.pt. Supported by FCT SFRH/BPD/5625/2001 and the FibLog initiative. (2) Applied Mathematics Center, Departamento de Matematica, IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal. email: apacheco@math.ist.utl.pt (3) Unfortunately J. Pinto passed away in an accident while this paper was being prepared. Formerly, he was at Bell Labs, Database Systems Research Dept., 600 Mountain Ave., New Jersey 07974, U.S.A. OBSERVATIONS AND THE P...

We present the language PC+ for probabilistic reasoning about actions, which is a generalization of the action language C+ that allows to deal with probabilistic as well as nondeterministic effects of actions. We define a formal semantics of PC+ in terms of probabilistic transitions between sets of states. Using a concept of a history and its belief state, we then show how several important problems in reasoning about actions can be concisely formulated in our formalism.

In this paper we investigate a formalism for solving planning problems based on ordered task decomposition using Answer Set Programming (ASP). Our planning methodology is an adaptation of Hierarchical Task Network (HTN) planning, an approach that has led to some very efficient planners. The ASP paradigm evolved out of the stable semantics for logic programs in recent years and is strongly related to nonmonotonic logics. It also led to various very efficient implementations (Smodels, DLV). While all previous approaches for using ASP for planning rely on action-based planning, we consider for the first time a formulation of HTN planning as described in the SHOP planning system and define a systematic translation method from SHOP’s representation of the planning problem into logic programs with negation. We show that our translation is sound and complete: answer sets of the logic program obtained by our translation correspond exactly to the solutions of the planning problem. Our approach does not rely on a particular system for computing answer sets and serves several purposes. (1) It constitutes a means

This paper is directed towards combining Pearl’s structural-model approach to causal reasoning with high-level formalisms for reasoning about actions. More precisely, we present a combination of Pearl’s structural-model approach with Poole’s independent choice logic. We show how probabilistic theories in the independent choice logic can be mapped to probabilistic causal models. This mapping provides the independent choice logic with appealing concepts of causality and explanation from the structural-model approach. We illustrate this along Halpern and Pearl’s sophisticated notions of actual cause, explanation, and partial explanation. Furthermore, this mapping also adds first-order modeling capabilities and explicit actions to the structural-model approach.

To date, there has been no work on temporal probabilistic agent reasoning on top of heterogeneous legacy databases and software modules. We will define the concept of a heterogeneous temporal probabilistic (HTP) agent. Such agents can be built on top of existing databases, data structures, and software code bases without explicitly accessing the internal code of those systems and can take actions compatible with a policy or operating principles specified by an agent developer. We will develop a formal semantics for such agents through the notion of a feasible temporal probabilistic status interpretation (FTPSI for short). Intuitively, an FTPSI specifies what all an HTP agent is permitted/forbidden/obliged to do at various times t. As changes occur in the environment, the HTP agent must compute a new FTPSI. HTP agents continuously compute FTPSI’s in order to determine what they should do and hence, the problem of computing FTPSI’s is very important. We give a sound and complete algorithm to compute FTPSI’s for a very large class of HTP agents called strict HTP agents. In a given state, many FTPSI’s may exist. These represent alternative courses of action that the HTP agent can take. We provide a notion of an optimal FTPSI that selects an FTPSI optimising an objective function and give a sound and complete algorithm to

We focus on the aspect of sensing in reasoning about actions under qualitative and probabilistic uncertainty. We extend an A-related action language by actions with nondeterministic and probabilistic effects, and define a formal semantics in terms of deterministic, nondeterministic, and probabilistic transitions between epistemic states. We then introduce the notions of a conditional plan and its goodness in this framework, and we formulate the conditional planning problem. We present an algorithm for solving it, which is proved to be sound and complete in the sense that it produces all optimal plans. We also report on a first prototype implementation of this algorithm. An application in a robotic-soccer scenario underlines the usefulness of our formalism in realistic applications.

In this paper we introduce a formalism for solving Hierarchical Task Network (HTN) Planning using Answer Set Programming (ASP). The ASP paradigm evolved out of the stable semantics for logic programs in recent years and is strongly related to nonmonotonic logics. We consider the formulation of HTN planning as described in the SHOP planning system and dene a systematic translation method from SHOP's representation of the planning problem into logic programs with negation. We show that our translation is sound and complete: answer sets of the logic program obtained by our translation correspond exactly to the solutions of the planning problem. Our approach does not rely on a particular system for computing answer sets. It can therefore serve as a means to evaluate ASP systems by using well-established benchmarks from the planning community. We tested our method on various such benchmarks and used smodels and DLV for computing answer sets. We compared our method to (1) similar approaches based on non-HTN planning and (2) SHOP, a dedicated planning system. We show that our approach outperforms non-HTN methods and that its performance is closer to that of SHOP, when we are using ASP systems which allow for nonground programs.

In this paper we present a new stochastic nondeterministic high-level action language ### which is a stochastic extension of Action Language #. We describe the syntax and semantics of ### and show it has an equivalent expressive power to Hidden Markov Models (HMMs). The main advantage of ### is its smooth conversion of propositions and probability, and use of a well-established stochastic model. We show two simple examples in the nuclear reactor domain and propose a normalisation technique for declarative probability assignments which match our intuition.

Mobile robots generally have only incomplete knowledge about their world. This knowledge is augmented through sensing actions. There have been several approaches in reasoning about actions that deal with sensing and knowledge. One important approach, which has been successfully realized on a robotic soccer team, is based on autoepistemic description logics. In this paper, we present a probabilistic generalization of this approach and define a formal semantics through probabilistic transitions between epistemic states. We then present the language PK-PDDL for reasoning about actions with sensing, knowledge, and probabilities, which is given a formal semantics in the above description logic. Furthermore, we formulate the problem of conditional planning under probabilistic uncertainty in this framework, and give an algorithm for optimally solving it, which is based on a reduction to reasoning in description logics.

Reasoning in the presence of imprecision and vagueness is inevitable in many real-world applications including those in robotics and intelligent agents. Although, reasoning about actions is a major component in these real-world applications, current actions languages for reasoning about actions lack the ability to represent and reason about actions in the presence of imprecision and vagueness that stem from effects of actions in these real-world applications. In this paper we present a new action language called fuzzy action language, AF, that allows the representation and reasoning about actions with vague (fuzzy) effects. In addition we define the notions of fuzzy planning and fuzzy plan in the fuzzy action language AF. Furthermore, we describe a fuzzy planner based on the fuzzy action language AF that is developed by translating a fuzzy action theory, FT, inAF into a normal logic program with answer set semantics, Π, where trajectories in FT are equivalent to the answer sets of Π. In addition, we formally prove the correctness of our translation. Furthermore, we show that fuzzy planning problems can be encoded as a SAT problem.