Conformant Planning Research Articles

A Counter-Example Based Approach to Probabilistic Conformant Planning

A Counter-Example Based Approach to Probabilistic Conformant Planning

Complexity of multi-agent conformant planning with group knowledge

Complexity of multi-agent conformant planning with group knowledge

Conditioning in First-Order Knowledge Compilation and Lifted Probabilistic Inference

Knowledge compilation is a powerful technique for compactly representing and efficiently reasoning about logical knowledge bases. It has been successfully applied to numerous problems in artificial intelligence, such as probabilistic inference and conformant planning. Conditioning, which updates a knowledge base with observed truth values for some propositions, is one of the fundamental operations employed for reasoning. In the propositional setting, conditioning can be efficiently applied in all cases. Recently, people have explored compilation for first-order knowledge bases. The majority of this work has centered around using first-order d-DNNF circuits as the target compilation language. However, conditioning has not been studied in this setting. This paper explores how to condition a first-order d-DNNF circuit. We show that it is possible to efficiently condition these circuits on unary relations. However, we prove that conditioning on higher arity relations is #P-hard. We study the implications of these findings on the application of performing lifted inference for first-order probabilistic models.This leads to a better understanding of which types of queries lifted inference can address.

Width and Complexity of Belief Tracking in Non-Deterministic Conformant and Contingent Planning

It has been shown recently that the complexity of belief tracking in deterministic conformant and contingent planning is exponential in a width parameter that is often bounded and small. In this work, we introduce a new width notion that applies to non-deterministic conformant and contingent problems as well. We also develop a belief tracking algorithm for non-deterministic problems that is exponential in the problem width, analyze the width of non-deterministic benchmarks, compare the new notion to the previous one over deterministic problems, and present experimental results.

Planning with Incomplete Information in Quantified Answer Set Programming

AbstractWe present a general approach to planning with incomplete information in Answer Set Programming (ASP). More precisely, we consider the problems of conformant and conditional planning with sensing actions and assumptions. We represent planning problems using a simple formalism where logic programs describe the transition function between states, the initial states and the goal states. For solving planning problems, we use Quantified Answer Set Programming (QASP), an extension of ASP with existential and universal quantifiers over atoms that is analogous to Quantified Boolean Formulas (QBFs). We define the language of quantified logic programs and use it to represent the solutions different variants of conformant and conditional planning. On the practical side, we present a translation-based QASP solver that converts quantified logic programs into QBFs and then executes a QBF solver, and we evaluate experimentally the approach on conformant and conditional planning benchmarks.

A New Approach to Conformant Planning Using CNF∗

In this paper, we develop a heuristic, progression based conformant planner, called CNF, which represents belief states by a special type of CNF formulae, called CNF CNF-state. We define a transition function φCNF for computing the successor belief state resulting from the execution of an action in a belief state and prove that it is sound and complete with respect to the complete semantics defined in the literature for conformant planning. We evaluate the performance of CNF against other state-of-the-art conformant planners and identify the classes of problems where CNF is comparable with other state-of-the-art planners or scales up better than other planners. We also develop a technique called oneof relaxation which helps boost the performance of CNF. We characterize the domains where this technique can be applied and validate this idea by proposing a new set of benchmarks that is really difficult for other planners yet easy for CNF.

Non-Deterministic Conformant Planning Using a Counterexample-Guided Incremental Compilation to Classical Planning

We address the problem of non-deterministic conformant planning, i.e., finding a plan in a non-deterministic context where the environment is not observable. Our approach uses an unsound but complete reduction from non-deterministic conformant planning to classical planning to find a candidate plan; the validity of this plan is then verified by a SAT solver; if the plan is invalid, the reduction is revised to guarantee that the invalid plan will not be valid in the classical planning problem. This procedure is executed until a valid plan is found, or it is shown that there is no plan. Experiments show that this approach provides a nice trade-off between fast but unsound, and complete but slow approaches.

Splitting Epistemic Logic Programs

AbstractEpistemic logic programs constitute an extension of the stable model semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some objective literal is true in all or some stable models. As it can be imagined, the associated semantics has proved to be non-trivial, since the truth of subjective literals may interfere with the set of stable models it is supposed to query. As a consequence, no clear agreement has been reached and different semantic proposals have been made in the literature. Unfortunately, comparison among these proposals has been limited to a study of their effect on individual examples, rather than identifying general properties to be checked. In this paper, we propose an extension of the well-known splitting property for logic programs to the epistemic case. We formally define when an arbitrary semantics satisfies the epistemic splitting property and examine some of the consequences that can be derived from that, including its relation to conformant planning and to epistemic constraints. Interestingly, we prove (through counterexamples) that most of the existing approaches fail to fulfill the epistemic splitting property, except the original semantics proposed by Gelfond 1991 and a recent proposal by the authors, called Founded Autoepistemic Equilibrium Logic.

Computing Superior Counter-Examples for Conformant Planning

In a counter-example based approach to conformant planning, choosing the right counter-example can improve performance. We formalise this observation by introducing the notion of “superiority” of a counter-example over another one, that holds whenever the superior counter-example exhibits more tags than the latter. We provide a theoretical explanation that supports the strategy of searching for maximally superior counter-examples, and we show how this strategy can be implemented. The empirical experiments validate our approach.

CPCES: A planning framework to solve conformant planning problems through a counterexample guided refinement

We introduce cpces, a novel planner for the problem of deterministic conformant planning. cpces solves the problem by producing candidate plans based on a sample of the initial belief state, searching for counter-examples to these plans, and assigning these counter-examples to the sample, until a valid plan has been produced or the problem has been proved unfeasible. On top of providing a means to compute a conformant plan, the sample can also be understood as a justification for the plan being found, or relevant reasons why a plan cannot be found. We study the theoretical properties that cpces enjoys—correctness, completeness, and optimality—and how the several variants of cpces we describe differ in behaviour. Moreover, we establish a theoretical connection between the cpces framework and well-known concepts from the literature such as tags and width. With this connection we prove the worst case complexity for some variants of cpces.Finally, we show how cpces can be used in a more incremental fashion by learning sequencing of actions from the previous plan being found. Such a technique mimics the use of macro-operators, widely used in automated planning to speedup resolution.Our theoretical analysis is accompanied with a thorough experimental evaluation of the (many) possible incarnations of cpces. This not only proves our theoretical findings from an empirical perspective, but also shows that cpces is able to handle problems that have been traditionally hard to solve by the existing conformant planners, whilst remaining competitive over “easier” conformant planning problems. Importantly, cpces is able to prove many unsolvable conformant planning problems as such, extending substantially the reach of conformant planners.

A Logic for Multi-Agent Conformant Planning Over Transition Systems

Reasoning about actions and information is one of the most active areas of research in artificial intelligence. In this article, we study the reasoning about actions and information in multi-agent conformant planning, which is an essential branch of artificial intelligence. We introduce a semantic-driven formalism to capture the information change during the execution of actions. We then propose a dynamic epistemic logic for multi-agent conformant planning. Moreover, we give an alternative Kripke semantics and provide a complete axiomatization.

A dynamic epistemic framework for reasoning about conformant probabilistic plans

In this paper, we introduce a probabilistic dynamic epistemic logical framework that can be applied for reasoning and verifying conformant probabilistic plans in a single agent setting. In conformant probabilistic planning (CPP), we are looking for a linear plan such that the probability of achieving the goal after executing the plan is no less than a given threshold probability δ. Our logical framework can trace the change of the belief state of the agent during the execution of the plan and verify the conformant plans. Moreover, with this logic, we can enrich the CPP framework by formulating the goal as a formula in our language with action modalities and probabilistic beliefs. As for the main technical results, we provide a complete axiomatization of the logic and show the decidability of its validity problem.

Sampling Strategies for Conformant Planning

We present a generalisation of CPCES, a conformant planner that uses two procedures: candidate plan generation and sampling of the initial belief state. The new CPCES better distinguishes these two procedures and therefore provides a clearer framework for the resolution of conformant planning problems. We study CPCES theoretically by analysing the sampling phase through the lens of tags, width and basis. The benefit of this new interpretation is twofold: firstly it allows us to bound the maximum number of iterations required by CPCES, and second it allows us to individuate sampling strategies that guarantee the discovery of subsets of minimal bases. An experimental analysis reported in the paper shows that the greedy sampling (the original version of CPCES) is the more effective strategy, coverage wise. However, when either the quality of the plans or the size of the resulting samples is important a more sophisticated sampling is more effective.

Landmark-based heuristic online contingent planning

In contingent planning problems, agents have partial information about their state and use sensing actions to learn the value of some variables. When sensing and actuation are separated, plans for such problems can often be viewed as a tree of sensing actions, separated by conformant plans consisting of non-sensing actions that enable the execution of the next sensing action. We propose a heuristic, online method for contingent planning which focuses on identifying the next useful sensing action. We select the next sensing action based on a landmark heuristic, adapted from classical planning. We discuss landmarks for plan trees, providing several alternative definitions and discussing their merits. The key part of our planner is the novel landmarks-based heuristic, together with a projection method that uses classical planning to solve the intermediate conformant planning problems. The resulting heuristic contingent planner solves many more problems than state-of-the-art, translation-based online contingent planners, and in most cases, much faster, up to 3 times faster on simple problems, and 200 times faster on non-simple domains.

Robust planning with incomplete domain models

Most current planners assume complete domain models and focus on generating correct plans. Unfortunately, domain modeling is a laborious and error-prone task, thus real world agents have to plan with incomplete domain models. While domain experts cannot guarantee completeness, often they are able to circumscribe the incompleteness of the model by providing annotations as to which parts of the domain model may be incomplete. In this paper, we study planning problems with incomplete domain models where the annotations specify possible preconditions and effects of actions. We show that the problem of assessing the quality of a plan, or its plan robustness, is #P-complete, establishing its equivalence with the weighted model counting problems. We present two approaches to synthesizing robust plans. While the method based on the compilation to conformant probabilistic planning is much intuitive, its performance appears to be limited to only small problem instances. Our second approach based on stochastic heuristic search works well for much larger problems. It aims to use the robustness measure directly for estimating heuristic distance, which is then used to guide the search. Our planning system, PISA, outperforms a state-of-the-art planner handling incomplete domain models in most of the tested domains, both in terms of plan quality and planning time. Finally, we also present an extension of PISA called CPISA that is able to exploit the available of past successful plan traces to both improve the robustness of the synthesized plans and reduce the domain modeling burden.

A logic of goal-directed knowing how

In this paper, we propose a decidable single-agent modal logic for reasoning about goal-directed “knowing how”, based on ideas from linguistics, philosophy, modal logic, and automated planning in AI. We first define a modal language to express “I know how to guarantee \(\varphi \) given \(\psi \)” with a semantics based not on standard epistemic models but on labeled transition systems that represent the agent’s knowledge of his own abilities. The semantics is inspired by conformant planning in AI. A sound and complete proof system is given to capture valid reasoning patterns, which highlights the compositional nature of “knowing how”. The logical language is further extended to handle knowing how to achieve a goal while maintaining other conditions.

A Dynamic Epistemic Framework for Conformant Planning

In this paper, we introduce a lightweight dynamic epistemic logical framework for automated planning under initial uncertainty. We reduce plan verification and conformant planning to model checking problems of our logic. We show that the model checking problem of the iteration-free fragment is PSPACE-complete. By using two non-standard (but equivalent) semantics, we give novel model checking algorithms to the full language and the iteration-free language.

Conformant planning as a case study of incremental QBF solving

We consider planning with uncertainty in the initial state as a case study of incremental quantified Boolean formula (QBF) solving. We report on experiments with a workflow to incrementally encode a planning instance into a sequence of QBFs. To solve this sequence of successively constructed QBFs, we use our general-purpose incremental QBF solver DepQBF. Since the generated QBFs have many clauses and variables in common, our approach avoids redundancy both in the encoding phase as well as in the solving phase. We also present experiments with incremental preprocessing techniques that are based on blocked clause elimination (QBCE). QBCE allows to eliminate certain clauses from a QBF in a satisfiability preserving way. We implemented the QBCE-based techniques in DepQBF in three variants: as preprocessing, as inprocessing (which extends preprocessing by taking into account variable assignments that were fixed by the QBF solver), and as a novel dynamic approach where QBCE is tightly integrated in the solving process. For DepQBF, experimental results show that incremental QBF solving with incremental QBCE outperforms incremental QBF solving without QBCE, which in turn outperforms nonincremental QBF solving. For the first time we report on incremental QBF solving with incremental QBCE as inprocessing. Our results are the first empirical study of incremental QBF solving in the context of planning and motivate its use in other application domains.

The language of epistemic specifications (refined) including a prototype solver

Abstract In this article, we present a new version of the language of Epistemic Specifications. The goal is to simplify and improve the intuitive and formal semantics of the language. We describe an algorithm for computing solutions of programs written in this new version of the language. The new semantics is illustrated by a number of examples, including an Epistemic Specifications-based framework for conformant planning. In addition, we introduce the notion of an epistemic logic program with sorts . This extends recent efforts to define a logic programming language that includes the means for explicitly specifying the domains of predicate parameters. An algorithm and its implementation as a solver for epistemic logic programs with sorts is also discussed.

A generic approach to planning in the presence of incomplete information: Theory and implementation

This paper proposes a generic approach to planning in the presence of incomplete information. The approach builds on an abstract notion of a belief state representation, along with an associated set of basic operations. These operations facilitate the development of a sound and complete transition function, for reasoning about effects of actions in the presence of incomplete information, and a set of abstract algorithms for planning. The paper demonstrates how the abstract definitions and algorithms can be instantiated in three concrete representations—minimal-DNF, minimal-CNF, and prime implicates—resulting in three highly competitive conformant planners: Dnf, Cnf, and PIP. The paper relates the notion of a representation to that of ordered binary decision diagrams, a well-known belief state representation employed by many conformant planners, and several target compilation languages that have been presented in the literature. The paper also includes an experimental evaluation of the planners Dnf, Cnf, and PIP and proposes a new set of conformant planning benchmarks that are challenging for state-of-the-art conformant planners.