Timed Argumentation Frameworks (TAFs) allow taking into account the availability of arguments and attacks in abstract argumentation. We propose a new reasoning approach for TAFs, where a standard Dung-style AF can be associated with each timepoint. We show that, although this framework is more expressive than Dung's framework, our approach does not lead to an increase in computational complexity for most reasoning problems and classical extension-based semantics.

Abstract Though Propositional Dynamic Logic (PDL) as well as its relation to planning has been widely studied, there is as of yet no consensus as to how to handle parallelism in the framework. In this paper, we propose a parallel version of the Dynamic Logic of Propositional Assignments (${\textsf{DL-PA} } $), a simple fragment of PDL in which atomic programs are assignments of the truth value of a formula to a propositional variable. We introduce two new operators for ${\textsf{DL-PA} }$, namely parallel composition and inclusive non-deterministic composition. For the former, we suppose that two programs can be executed in parallel if they do not assign different values to the same variable. We give a polynomial translation of the resulting Dynamic Logic of Parallel Propositional Assignments (${\textsf{DL-PPA} }$) into ${\textsf{DL-PA} }$, thereby showing that complexity remains in PSpace. We then turn to planning and show how to capture executability of parallel STRIPS-like actions and solvability of planning tasks by parallel plans in ${\textsf{DL-PPA} }$, following three different semantics for parallelism: one closely following our criterion for parallelism in ${\textsf{DL-PPA} }$, and two from the literature based on interleaving.

ABSTRACT Determining whether two STRIPS planning instances are isomorphic is the simplest form of comparison between planning instances. It is also a particular case of the problem concerned with finding an isomorphism between a planning instance and a sub‐instance of another instance . One application of such a mapping is to efficiently produce a compiled form containing all solutions to from a compiled form containing all solutions to . We also introduce the notion of embedding from an instance to another instance , which allows us to deduce that has no solution‐plan if is unsolvable. In this paper, we study the complexity of these problems. We show that the first is GI‐complete and can thus be solved, in theory, in quasi‐polynomial time. While we prove the remaining problems to be NP‐complete, we propose an algorithm to build an isomorphism when possible. We report extensive experimental trials on benchmark problems that demonstrate conclusively that applying constraint propagation in preprocessing can greatly improve the efficiency of a SAT solver.

Determining whether two STRIPS planning instances are isomorphic is the simplest form of comparison between planning instances. It is also a particular case of the problem concerned with finding an isomorphism between a planning instance P and a sub-instance of another instance P'. One application of such an isomorphism is to efficiently produce a compiled form containing all solutions to P from a compiled form containing all solutions to P'. In this paper, we study the complexity of both problems. We show that the former is GI-complete, and can thus be solved, in theory, in quasi-polynomial time. While we prove the latter to be NP-complete, we propose an algorithm to build an isomorphism, when possible. We report extensive experimental trials on benchmark problems which demonstrate conclusively that applying constraint propagation in preprocessing can greatly improve the efficiency of a SAT solver.

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We present a novel approach to cognitive planning, i.e., an agent's planning aimed at changing the cognitive attitudes of another agent including her beliefs and intentions. We encode the cognitive planning problem in an epistemic logic with a semantics exploiting belief bases. We study a NP-fragment of the logic whose satisfiability problem is reduced to SAT. We provide complexity results for the cognitive planning problem. Moreover, we illustrate its potential for applications in human-machine interaction in which an artificial agent is expected to interact with a human agent through dialogue and to persuade the human to behave in a certain way.

Existing dynamic epistemic logics combine standard epistemic logic with a restricted version of dynamic logic. Instead, we here combine a restricted epistemic logic with a rich version of dynamic logic. The epistemic logic is based on `knowing-whether' operators and basically disallows disjunctions and conjunctions in their scope; it moreover captures `knowing-what'. The dynamic logic has not only all the standard program operators of Propositional Dynamic Logic, but also parallel composition as well as an operator of inclusive nondeterministic composition; its atomic programs are assignments of propositional variables. We show that the resulting dynamic epistemic logic is powerful enough to capture several kinds of sequential and parallel planning, and so both in the unbounded and in the finite horizon version.

This work deals with logical formalization and problem solving using automated solvers. We present the automatic translator TouIST that provides a simple language to generate logical formulas from a problem description. Our tool allows us to model many static or dynamic combinatorial problems and to benefit from the regular improvements of SAT, QBF or SMT solvers in order to solve these problems efficiently. In particular, we show how to use TouIST to solve different classes of planning tasks in Artificial Intelligence.

We study a simple version of multi-agent epistemic planning where the number of parallel steps has to be minimized. We prove that this extension of classical planning is in PSPACE. We propose an encoding in PDDL and present some experiments providing evidence that this encoding allows us to solve practical problems. The types of problems we can encode include problems in which one agent can teach another agent how to perform a task and communication problems where some information must not be revealed to some agents.

We introduce a dynamic logic with parallel composition and two kinds of nondeterministic composition, exclusive and inclusive. We show PSPACE completeness of both the model checking and the satisfiability problem and apply our logic to sequential and parallel classical planning where actions have conditional effects.

A realistic model of multi-agent planning must allow us to formalize notions which are absent in classical planning, such as communication and knowledge. We investigate multi-agent planning based on a simple logic of knowledge that is grounded on the visibility of propositional variables. Using such a formal logic allows us to prove the existence of a plan given the description of the individual actions. We present an encoding of multi-agent planning problems expressed in this logic into the standard planning language PDDL. The solvability of a planning task is reduced to a model checking problem in a dynamic extension of our logic, proving its complexity. Feeding the resulting problem into a PDDL planner provides a provably correct plan for the original multi-agent planning problem. We apply our method on several examples such as the gossip problem.

The gossip problem, in which information (secrets) must be shared among a certain number of agents using the minimum number of calls, is of interest in the conception of communication networks and protocols. We extend the gossip problem to arbitrary epistemic depths. For example, we may require not only that all agents know all secrets but also that all agents know that all agents know all secrets. We give optimal protocols for the generalised gossip problem, in the case of two-way communications, one-way communications and parallel communication. In the presence of negative goals testing the existence of a successful protocol is NP-complete.

The frameworks dedicated to the representation of quantitative temporal constraint satisfaction problems, as rich as they are in terms of expressiveness, define difficult requests - typically NP-complete decision problems. It is therefore adventurous to use them for an online resolution. Hence the idea to compile the original problem into a form that could be easily solved. Difference Decision Diagrams (DDDs) have been proposed by [1] as a possible way to cope with this difficulty, following a compilation-based approach. In this article, we draw a compilation map that evaluates the relative capabilities of these languages (TCSP, STP, DTP and DDD) in terms of algorithmic efficiency, succinctness and expressiveness.

This paper describes a polynomially-solvable class of temporal planning problems. Polynomiality follows from two assumptions. Firstly, by supposing that each sub-goal fluent can be established by at most one action, we can quickly determine which actions are necessary in any plan. Secondly, the monotonicity of sub-goal fluents allows us to express planning as an instance of STP≠ (Simple Temporal Problem with difference constraints). This class includes temporally-expressive problems requiring the concurrent execution of actions, with potential applications in the chemical, pharmaceutical and construction industries. We also show that any (temporal) planning problem has a monotone relaxation which can lead to the polynomial-time detection of its unsolvability in certain cases. Indeed we show that our relaxation is orthogonal to relaxations based on the ignore-deletes approach used in classical planning since it preserves deletes and can also exploit temporal information.

Relaxation is ubiquitous in the practical resolution of combinatorial problems. If a valid relaxation of an instance has no solution then the original instance has no solution. A tractable relaxation can be built and solved in polynomial time. The most obvious application is the efficient detection of certain unsolvable instances. We review existing relaxation techniques in temporal planning and propose an alternative relaxation inspired by a tractable class of temporal planning problems. Our approach is orthogonal to relaxations based on the ignore-all-deletes approach used in non-temporal planning. We show that our relaxation can even be applied to non-temporal problems, and can also be used to extend a tractable class of temporal planning problems.

To correctly model certain real‐world planning problems, it is essential to take into account time. This is the case for problems requiring the concurrent execution of actions (known as temporally expressive problems). In this paper, we define and study the notion of temporally cyclic problems, that is problems involving sets of cyclically dependent actions. We characterize those temporal planning languages, which can express temporally cyclic problems. We also present a polynomial‐time algorithm, which transforms a temporally cyclic problem into an equivalent acyclic problem. Applying our transformation allows any temporal planner to solve temporally cyclic problems without explicitly managing cyclicity. We first present our results for temporal PDDL (Planning Domain Description Language) 2.1 and then extend them to a language that allows conditions over arbitrary intervals and effects at arbitrary instants.

An important aspect of any automatic planner is the language in which the user expresses problem instances. A rich language is an advantage for the user, whereas a simple language is an advantage for the programmer who must write a program to solve all planning problems expressible in the language. Considering the temporal planning language PDDL 2.1 as a low-level language, we show how to automatically compile a much richer language into PDDL 2.1. The worst-case complexity of this transformation is quadratic. Our high-level language allows the user to declare time-points and impose simple temporal constraints between them. Conditions and effects can be imposed at time-points, over intervals and over sliding intervals within fixed intervals. Non-instantaneous transitions can also be modelled.

In order to correctly model certain real-world planning problems, it is essential to take into account time. This is the case for problems requiring the concurrent execution of actions (known as temporally-expressive problems). However, we show in this paper that certain existing planners which solve this type of problem are, in fact, incomplete. They cannot guarantee to find a solution to a problem involving sets of cyclically-dependent actions (which we call temporally-cyclic problems). We characterize those temporal planning languages which can express temporally-cyclic problems. We also present a polynomial-time algorithm which transforms a temporally-cyclic problem into an equivalent acyclic problem. Applying our transformation restores the completeness of these temporal planners.

One of the major challenges for planning is to take into account the time dimension. In this paper, we present a simple approach to deal with temporally expressive problems, that is problems for which all possible solutions require concurrency of actions. Our planner TLP-GP mixes some of the advantages of GRAPHPLAN search with a constraint-based and flexible temporal formalism. Its language is consistent with PDDL 2.1 and extends its expressivity. Experimental trials on new temporally expressive benchmarks show the efficiency of our approach and demonstrate the practical possibility of solving temporally expressive problems which up until now were unsolvable by existing techniques.

This article describes an algorithm which solves temporally-expressive planning problems, that is problems for which all possible solutions require concurrency of actions. The planner TLP-GP which implements this algorithm constructs a simplified planning graph until the goals are attained, as in classic atemporal planners. It then establishes temporal constraints between actions and searches backward for a solution-plan in the planning graph using a disjunctive temporal constraint solver. If the search fails, the graph is extended to the next level and the search is restarted. This method can solve problems in a language whose expressivity is greater than PDDL 2.1. Preconditions can be required and effects can take place on any temporal interval relative to the start-time of an action. This algorithm can also take into account, in a very natural way, exogenous events as well as temporally extended goals. We also propose several different means of extending expressivity even further. TLP-GP is complete for the temporally-expressive sublanguages of PDDL 2.1.We compared our planner with two state-of-the-art temporally-expressive planners such as LPGP and VHPOP. These experimental trials not only show the efficiency of our approach but also demonstrate the practical possibility of solving temporally expressive problems which up until now were unsolvable by existing techniques.