Answer Set Programming for Non-Stationary Markov Decision Processes

Non-stationary domains, where unforeseen changes happen, present a challenge for agents to find an optimal policy for a sequential decision making problem. This work investigates a solution to this problem that combines Markov Decision Processes (MDP) and Reinforcement Learning (RL) with Answer Set Programming (ASP) in a method we call ASP(RL). In this method, Answer Set Programming is used to find the possible trajectories of an MDP, from where Reinforcement Learning is applied to learn the optimal policy of the problem. Results show that ASP(RL) is capable of efficiently finding the optimal solution of an MDP representing non-stationary domains

CASP Solutions for Planning in Hybrid Domains

CASP is an extension of ASP that allows for numerical constraints to be added in the rules. PDDL+ is an extension of the PDDL standard language of automated planning for modeling mixed discrete-continuous dynamics. In this paper, we present CASP solutions for dealing with PDDL+ problems, i.e., encoding from PDDL+ to CASP, and extensions to the algorithm of the EZCSP CASP solver in order to solve CASP programs arising from PDDL+ domains. An experimental analysis, performed on well-known linear and non-linear variants of PDDL+ domains, involving various configurations of the EZCSP solver, other CASP solvers, and PDDL+ planners, shows the viability of our solution.Comment: Under consideration in Theory and Practice of Logic Programming (TPLP

Answer Set Planning Under Action Costs

Recently, planning based on answer set programming has been proposed as an approach towards realizing declarative planning systems. In this paper, we present the language Kc, which extends the declarative planning language K by action costs. Kc provides the notion of admissible and optimal plans, which are plans whose overall action costs are within a given limit resp. minimum over all plans (i.e., cheapest plans). As we demonstrate, this novel language allows for expressing some nontrivial planning tasks in a declarative way. Furthermore, it can be utilized for representing planning problems under other optimality criteria, such as computing ``shortest'' plans (with the least number of steps), and refinement combinations of cheapest and fastest plans. We study complexity aspects of the language Kc and provide a transformation to logic programs, such that planning problems are solved via answer set programming. Furthermore, we report experimental results on selected problems. Our experience is encouraging that answer set planning may be a valuable approach to expressive planning systems in which intricate planning problems can be naturally specified and solved

A Multi-Engine Approach to Answer Set Programming

Answer Set Programming (ASP) is a truly-declarative programming paradigm proposed in the area of non-monotonic reasoning and logic programming, that has been recently employed in many applications. The development of efficient ASP systems is, thus, crucial. Having in mind the task of improving the solving methods for ASP, there are two usual ways to reach this goal: $(i)$ extending state-of-the-art techniques and ASP solvers, or $(ii)$ designing a new ASP solver from scratch. An alternative to these trends is to build on top of state-of-the-art solvers, and to apply machine learning techniques for choosing automatically the "best" available solver on a per-instance basis. In this paper we pursue this latter direction. We first define a set of cheap-to-compute syntactic features that characterize several aspects of ASP programs. Then, we apply classification methods that, given the features of the instances in a {\sl training} set and the solvers' performance on these instances, inductively learn algorithm selection strategies to be applied to a {\sl test} set. We report the results of a number of experiments considering solvers and different training and test sets of instances taken from the ones submitted to the "System Track" of the 3rd ASP Competition. Our analysis shows that, by applying machine learning techniques to ASP solving, it is possible to obtain very robust performance: our approach can solve more instances compared with any solver that entered the 3rd ASP Competition. (To appear in Theory and Practice of Logic Programming (TPLP).)Comment: 26 pages, 8 figure

Fages' Theorem and Answer Set Programming

We generalize a theorem by Francois Fages that describes the relationship between the completion semantics and the answer set semantics for logic programs with negation as failure. The study of this relationship is important in connection with the emergence of answer set programming. Whenever the two semantics are equivalent, answer sets can be computed by a satisfiability solver, and the use of answer set solvers such as smodels and dlv is unnecessary. A logic programming representation of the blocks world due to Ilkka Niemelae is discussed as an example

The DLV System for Knowledge Representation and Reasoning

This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to $\Delta^P_3$-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of DLV, and by deriving new complexity results we chart a complete picture of the complexity of this language and important fragments thereof. Furthermore, we illustrate the general architecture of the DLV system which has been influenced by these results. As for applications, we overview application front-ends which have been developed on top of DLV to solve specific knowledge representation tasks, and we briefly describe the main international projects investigating the potential of the system for industrial exploitation. Finally, we report about thorough experimentation and benchmarking, which has been carried out to assess the efficiency of the system. The experimental results confirm the solidity of DLV and highlight its potential for emerging application areas like knowledge management and information integration.Comment: 56 pages, 9 figures, 6 table