Deterministic planning in incompletely known domains with local effects

Conformant planning has been traditionally studied in the form of classical planning extended with a mechanism for expressing unknown facts and/or disjunctive knowledge. Despite a sizable body of research, most approaches do not attempt to move beyond essentially propositional planning. We address this shortcoming by defining conformant planning in terms of the situation calculus semantics and use recent advances in the fields of first-order knowledge base progression and query answering to develop a sound and complete conformant planning algorithm capable of handling knowledge defined in an expressive fragment of first-order logic. We implement a prototype planner and evaluate its performance on several existing domains.

Deterministic planning in incompletely known domains with local effects

Conformant planning has been traditionally studied in the form of classical planning extended with a mechanism for expressing unknown facts and/or disjunctive knowledge. Despite a sizable body of research, most approaches do not attempt to move beyond essentially propositional planning. We address this shortcoming by defining conformant planning in terms of the situation calculus semantics and use recent advances in the fields of first-order knowledge base progression and query answering to develop a sound and complete conformant planning algorithm capable of handling knowledge defined in an expressive fragment of first-order logic. We implement a prototype planner and evaluate its performance on several existing domains.

On the Splitting Property for Epistemic Logic Programs (Extended Abstract)

Epistemic 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. However, its 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. In this paper, we review an extension of the well-known splitting property for logic programs to the epistemic case. This "epistemic splitting property" is defined as a general condition that can be checked on any arbitrary epistemic semantics. Its satisfaction has desirable consequences both in the representation of conformant planning problems and in the encoding of the so-called subjective constraints.

Splitting Epistemic Logic Programs

Epistemic 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.

Intelligent Belief State Sampling for Conformant Planning

We propose a new method for conformant planning based on two ideas. First given a small sample of the initial belief state we reduce conformant planning for this sample to a classical planning problem, giving us a candidate solution. Second we exploit regression as a way to compactly represent necessary conditions for such a solution to be valid for the non-deterministic setting. If necessary, we use the resulting formula to extract a counter-example to populate our next sampling. Our experiments show that this approach is competitive on a class of problems that are hard for traditional planners, and also returns generally shorter plans. We are also able to demonstrate unsatisfiability of some problems.