Forgetting in Answer Set Programming – A Survey

Theory and Practice of Logic Programming ◽

10.1017/s1471068421000570 ◽

2021 ◽

pp. 1-43

Author(s):

RICARDO GONÇALVES ◽

MATTHIAS KNORR ◽

JOÃO LEITE

Keyword(s):

Computational Complexity ◽

Knowledge Base ◽

Answer Set Programming ◽

Complete Picture ◽

Variable Elimination ◽

Application Requirements ◽

Answer Set

Abstract Forgetting – or variable elimination – is an operation that allows the removal, from a knowledge base, of middle variables no longer deemed relevant. In recent years, many different approaches for forgetting in Answer Set Programming have been proposed, in the form of specific operators, or classes of such operators, commonly following different principles and obeying different properties. Each such approach was developed to address some particular view on forgetting, aimed at obeying a specific set of properties deemed desirable in such view, but a comprehensive and uniform overview of all the existing operators and properties is missing. In this article, we thoroughly examine existing properties and (classes of) operators for forgetting in Answer Set Programming, drawing a complete picture of the landscape of these classes of forgetting operators, which includes many novel results on relations between properties and operators, including considerations on concrete operators to compute results of forgetting and computational complexity. Our goal is to provide guidance to help users in choosing the operator most adequate for their application requirements.

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Complex optimization in answer set programming

Theory and Practice of Logic Programming ◽

10.1017/s1471068411000329 ◽

2011 ◽

Vol 11 (4-5) ◽

pp. 821-839 ◽

Cited By ~ 26

Author(s):

MARTIN GEBSER ◽

ROLAND KAMINSKI ◽

TORSTEN SCHAUB

Keyword(s):

Computational Complexity ◽

Answer Set Programming ◽

Pareto Efficiency ◽

Modeling Techniques ◽

Complex Optimization ◽

Answer Sets ◽

Implementation Technique ◽

Preference Handling ◽

Answer Set ◽

Qualitative Preferences

AbstractPreference handling and optimization are indispensable means for addressing nontrivial applications in Answer Set Programming (ASP). However, their implementation becomes difficult whenever they bring about a significant increase in computational complexity. As a consequence, existing ASP systems do not offer complex optimization capacities, supporting, for instance, inclusion-based minimization or Pareto efficiency. Rather, such complex criteria are typically addressed by resorting to dedicated modeling techniques, likesaturation. Unlike the ease of common ASP modeling, however, these techniques are rather involved and hardly usable by ASP laymen. We address this problem by developing a general implementation technique by means of meta-prpogramming, thus reusing existing ASP systems to capture various forms of qualitative preferences among answer sets. In this way, complex preferences and optimization capacities become readily available for ASP applications.

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When you must forget: Beyond strong persistence when forgetting in answer set programming

Theory and Practice of Logic Programming ◽

10.1017/s1471068417000382 ◽

2017 ◽

Vol 17 (5-6) ◽

pp. 837-854

Author(s):

RICARDO GONÇALVES ◽

MATTHIAS KNORR ◽

JOÃO LEITE ◽

STEFAN WOLTRAN

Keyword(s):

Computational Complexity ◽

Answer Set Programming ◽

Correct Result ◽

Open Question ◽

Shed Light ◽

Answer Set

AbstractAmong the myriad of desirable properties discussed in the context of forgetting in Answer Set Programming, strong persistence naturally captures its essence. Recently, it has been shown that it is not always possible to forget a set of atoms from a program while obeying this property, and a precise criterion regarding what can be forgotten has been presented, accompanied by a class of forgetting operators that return the correct result when forgetting is possible. However, it is an open question what to do when we have to forget a set of atoms, but cannot without violating this property. In this paper, we address this issue and investigate three natural alternatives to forget when forgetting without violating strong persistence is not possible, which turn out to correspond to the different possible relaxations of the characterization of strong persistence. Additionally, we discuss their preferable usage, shed light on the relation between forgetting and notions of relativized equivalence established earlier in the context of Answer Set Programming, and present a detailed study on their computational complexity.

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Manipulation of Articulated Objects Using Dual-arm Robots via Answer Set Programming

Theory and Practice of Logic Programming ◽

10.1017/s1471068420000459 ◽

2020 ◽

pp. 1-30

Author(s):

RICCARDO BERTOLUCCI ◽

ALESSIO CAPITANELLI ◽

CARMINE DODARO ◽

NICOLA LEONE ◽

MARCO MARATEA ◽

...

Keyword(s):

Knowledge Base ◽

Robot Control ◽

Ad Hoc ◽

Answer Set Programming ◽

Automated Planning ◽

Control Architecture ◽

Articulated Objects ◽

Setup Accuracy ◽

Dual Arm ◽

Answer Set

Abstract The manipulation of articulated objects is of primary importance in Robotics and can be considered as one of the most complex manipulation tasks. Traditionally, this problem has been tackled by developing ad hoc approaches, which lack flexibility and portability. In this paper, we present a framework based on answer set programming (ASP) for the automated manipulation of articulated objects in a robot control architecture. In particular, ASP is employed for representing the configuration of the articulated object for checking the consistency of such representation in the knowledge base and for generating the sequence of manipulation actions. The framework is exemplified and validated on the Baxter dual-arm manipulator in the first, simple scenario. Then, we extend such scenario to improve the overall setup accuracy and to introduce a few constraints in robot actions execution to enforce their feasibility. The extended scenario entails a high number of possible actions that can be fruitfully combined together. Therefore, we exploit macro actions from automated planning in order to provide more effective plans. We validate the overall framework in the extended scenario, thereby confirming the applicability of ASP also in more realistic Robotics settings and showing the usefulness of macro actions for the robot-based manipulation of articulated objects.

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Finding optimal plans for multiple teams of robots through a mediator: A logic-based approach

Theory and Practice of Logic Programming ◽

10.1017/s1471068413000525 ◽

2013 ◽

Vol 13 (4-5) ◽

pp. 831-846 ◽

Cited By ~ 12

Author(s):

ESRA ERDEM ◽

VOLKAN PATOGLU ◽

ZEYNEP G. SARIBATUR ◽

PETER SCHÜLLER ◽

TANSEL URAS

Keyword(s):

Computational Complexity ◽

Energy Efficient ◽

State Of The Art ◽

Answer Set Programming ◽

The State ◽

Action Languages ◽

Mathematical Definition ◽

Definition Of ◽

Answer Set

AbstractWe study the problem of finding optimal plans for multiple teams of robots through a mediator, where each team is given a task to complete in its workspace on its own and where teams are allowed to transfer robots between each other, subject to the following constraints: 1) teams (and the mediator) do not know about each other's workspace or tasks (e.g., for privacy purposes); 2) every team can lend or borrow robots, but not both (e.g., transportation/calibration of robots between/for different workspaces is usually costly). We present a mathematical definition of this problem and analyze its computational complexity. We introduce a novel, logic-based method to solve this problem, utilizing action languages and answer set programming for representation, and the state-of-the-art ASP solvers for reasoning. We show the applicability and usefulness of our approach by experiments on various scenarios of responsive and energy-efficient cognitive factories.

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A Constructive semantic characterization of aggregates in answer set programming

Theory and Practice of Logic Programming ◽

10.1017/s1471068406002936 ◽

2007 ◽

Vol 7 (3) ◽

pp. 355-375 ◽

Cited By ~ 40

Author(s):

TRAN CAO SON ◽

ENRICO PONTELLI

Keyword(s):

Computational Complexity ◽

Logic Programming ◽

Answer Set Programming ◽

Technical Note ◽

Consequence Operator ◽

The Cost ◽

Answer Sets ◽

Answer Set

AbstractThis technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion ofaggregate solution. Under certain conditions, this operator behaves identically to the three-valued immediate consequence operator ΦaggrPfor aggregate programs, independently proposed in Pelov (2004) and Pelovet al.(2004). This operator allows us to closely tie the computational complexity of the answer set checking and answer sets existence problems to the cost of checking a solution of the aggregates in the program. Finally, we relate the semantics described by the operator to other proposals for logic programming with aggregates.

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On Uniform Equivalence of Epistemic Logic Programs

Theory and Practice of Logic Programming ◽

10.1017/s1471068419000218 ◽

2019 ◽

Vol 19 (5-6) ◽

pp. 826-840

Author(s):

WOLFGANG FABER ◽

MICHAEL MORAK ◽

STEFAN WOLTRAN

Keyword(s):

Computational Complexity ◽

Epistemic Logic ◽

State Of The Art ◽

Answer Set Programming ◽

Polynomial Hierarchy ◽

Logic Programs ◽

The Third ◽

New Research ◽

Answer Set

AbstractEpistemic Logic Programs (ELPs) extend Answer Set Programming (ASP) with epistemic negation and have received renewed interest in recent years. This led to the development of new research and efficient solving systems for ELPs. In practice, ELPs are often written in a modular way, where each module interacts with other modules by accepting sets of facts as input, and passing on sets of facts as output. An interesting question then presents itself: under which conditions can such a module be replaced by another one without changing the outcome, for any set of input facts? This problem is known as uniform equivalence, and has been studied extensively for ASP. For ELPs, however, such an investigation is, as of yet, missing. In this paper, we therefore propose a characterization of uniform equivalence that can be directly applied to the language of state-of-the-art ELP solvers. We also investigate the computational complexity of deciding uniform equivalence for two ELPs, and show that it is on the third level of the polynomial hierarchy.

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Answer Set Programming for Judgment Aggregation

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2019/231 ◽

2019 ◽

Author(s):

Ronald de Haan ◽

Marija Slavkovik

Keyword(s):

Computational Complexity ◽

Answer Set Programming ◽

Judgment Aggregation ◽

Worst Case ◽

Wide Range ◽

Benchmark Instances ◽

Hard Problems ◽

Automated Tool ◽

The Way ◽

Answer Set

Judgment aggregation (JA) studies how to aggregate truth valuations on logically related issues. Computing the outcome of aggregation procedures is notoriously computationally hard, which is the likely reason that no implementation of them exists as of yet. However, even hard problems sometimes need to be solved. The worst-case computational complexity of answer set programming (ASP) matches that of most problems in judgment aggregation. We take advantage of this and propose a natural and modular encoding of various judgment aggregation procedures and related problems in JA into ASP. With these encodings, we achieve two results: (1) paving the way towards constructing a wide range of new benchmark instances (from JA) for answer set solving algorithms; and (2) providing an automated tool for researchers in the area of judgment aggregation.

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