scholarly journals Answer Set Programming for Judgment Aggregation

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.

scholarly journals Complex optimization in answer set programming

2011 ◽  
Vol 11 (4-5) ◽  
pp. 821-839 ◽  
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.

scholarly journals Forgetting in Answer Set Programming – A Survey

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.

scholarly journals Applications of Answer Set Programming

AI Magazine ◽  
2016 ◽  
Vol 37 (3) ◽  
pp. 53-68 ◽  
Author(s):  
Esra Erdem ◽  
Michael Gelfond ◽  
Nicola Leone
Keyword(s):  
Computational Biology ◽  
Knowledge Representation ◽  
Continuous Improvement ◽  
Answer Set Programming ◽  
Industrial Applications ◽  
Knowledge Representation And Reasoning ◽  
Wide Range ◽  
Answer Set

ASP has been applied fruitfully to a wide range of areas in AI and in other fields, both in academia and in industry, thanks to the expressive representation languages of ASP and the continuous improvement of ASP solvers. We present some of these ASP applications, in particular, in knowledge representation and reasoning, robotics, bioinformatics and computational biology as well as some industrial applications. We discuss the challenges addressed by ASP in these applications and emphasize the strengths of ASP as a useful AI paradigm.

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

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.

scholarly journals UNBELIEVABLE O(L^1.5) WORST CASE COMPUTATIONAL COMPLEXITY ACHIEVED BY spdspds ALGORITHM FOR LINEAR PROGRAMMING PROBLEM

2021 ◽  
Author(s):  
KESHAVA PRASAD HALEMANE
Keyword(s):  
Linear Programming ◽  
Computational Complexity ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Decision Strategy ◽  
Worst Case ◽  
Wide Range ◽  
Primal Dual ◽  
Pivot Selection ◽  
Optimum Solution

The Symmetric Primal-Dual Symplex Pivot Decision Strategy (spdspds) is a novel iterative algorithm to solve linear programming problems. Here, a symplex pivoting operation is considered simply as an exchange between a basic (dependent) variable and a non-basic (independent) variable, in the Tucker's Compact Symmetric Tableau (CST) which is a unique symmetric representation common to both the primal as well as the dual of a linear programming problem in its standard canonical form. From this viewpoint, the classical simplex pivoting operation of Dantzig may be considered as a restricted special case. The infeasibility index associated with a symplex tableau is defined as the sum of the number of primal variables and the number of dual variables, which are infeasible. A measure of goodness as a global effectiveness measure of a pivot selection is defined/determined as/by the decrease in the infeasibility index associated with such a pivot selection. At each iteration the selection of the symplex pivot element is governed by the anticipated decrease in the infeasibility index - seeking the best possible decrease in the infeasibility index - from among a wide range of candidate choices with non-zero values - limited only by considerations of potential numerical instability. The algorithm terminates when further reduction in the infeasibility index is not possible; then the tableau is checked for the terminal tableau type to facilitate the problem classification - a termination with an infeasibility index of zero indicates optimum solution. The worst case computational complexity of spdspds is shown to be O(L^1.5).

Testing Multi-Threaded Applications Using Answer Set Programming

2018 ◽  
Vol 28 (08) ◽  
pp. 1151-1175 ◽  
Author(s):  
Xiaozhen Xue ◽  
Sima Siami-Namini ◽  
Akbar Siami Namin
Keyword(s):  
Answer Set Programming ◽  
Test Case ◽  
Multithreaded Programs ◽  
Java Programs ◽  
Hard Problems ◽  
Race Conditions ◽  
Data Races ◽  
Execution Order ◽  
Np Hard Problems ◽  
Answer Set

We introduce a technique to formally represent and specify race conditions in multithreaded applications. Answer set programming (ASP) is a logic-based knowledge representation paradigm to formally express belief acquired through reasoning in an application domain. The transparent and expressiveness representation of problems along with powerful non-monotonic reasoning power enable ASP to abstractly represent and solve some certain classes of NP hard problems in polynomial times. We use ASP to formally express race conditions and thus represent potential data races often occurred in multithreaded applications with shared memory models. We then use ASP to generate all possible test inputs and thread interleaving, i.e. scheduling, whose executions would result in deterministically exposing thread interleaving failures. We evaluated the proposed technique with some moderate sized Java programs, and our experimental results confirm that the proposed technique can practically expose common data races in multithreaded programs with low false positive rates. We conjecture that, in addition to generating threads scheduling whose execution order leads to the exposition of data races, ASP has several other applications in constraint-based software testing research and can be utilized to express and solve similar test case generation problems where constraints play a key role in determining the complexity of searches.

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

2013 ◽  
Vol 13 (4-5) ◽  
pp. 831-846 ◽  
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.

scholarly journals The power of non-ground rules in Answer Set Programming

2016 ◽  
Vol 16 (5-6) ◽  
pp. 552-569 ◽  
Author(s):  
MANUEL BICHLER ◽  
MICHAEL MORAK ◽  
STEFAN WOLTRAN
Keyword(s):  
Complexity Analysis ◽  
State Of The Art ◽  
Answer Set Programming ◽  
Expressive Power ◽  
Polynomial Hierarchy ◽  
Practical Realization ◽  
Simple Rules ◽  
Speed Up ◽  
Hard Problems ◽  
Answer Set

AbstractAnswer set programming (ASP) is a well-established logic programming language that offers an intuitive, declarative syntax for problem solving. In its traditional application, a fixed ASP program for a given problem is designed and the actual instance of the problem is fed into the program as a set of facts. This approach typically results in programs with comparably short and simple rules. However, as is known from complexity analysis, such an approach limits the expressive power of ASP; in fact, an entire NP-check can be encoded into a single large rule body of bounded arity that performs both a guess and a check within the same rule. Here, we propose a novel paradigm for encoding hard problems in ASP by making explicit use of large rules which depend on the actual instance of the problem. We illustrate how this new encoding paradigm can be used, providing examples of problems from the first, second, and even third level of the polynomial hierarchy. As state-of-the-art solvers are tuned towards short rules, rule decomposition is a key technique in the practical realization of our approach. We also provide some preliminary benchmarks which indicate that giving up the convenient way of specifying a fixed program can lead to a significant speed-up.

Spatial Reasoning about String Loops and Holes in Temporal ASP

2020 ◽  
Author(s):  
Pedro Cabalar ◽  
Paulo E. Santos
Keyword(s):  
Spatial Reasoning ◽  
Answer Set Programming ◽  
New Formalism ◽  
Systematic Testing ◽  
Substantial Modification ◽  
Representation Language ◽  
Automated Tool ◽  
Natural Way ◽  
Answer Set

This paper introduces a new formalism for the automated solution of spatial scenarios involving strings and holed objects. In particular, we revisit a previous formalisation that allows string loops to be treated as holes, but make a substantial modification by removing a previous limitation that prevented a string to cross its own loops. The formalisation introduced in the present paper relies on string segments as basic entities and achieves a greater degree of elaboration tolerance by using inertia to describe those parts of the physical scenario that are unaffected by a given action. As a representation language, we have used Temporal Answer Set Programming since it provides a simple and natural way to deal with time and inertia while, at the same time, it is accompanied by the automated tool 'telingo' that allows a systematic testing of the effects of any sequence of actions. As an illustrative example, we have studied the African Ring puzzle, a problem involving loops crossed by a unique string, and provided the first formalisation of its solution, to the best of our knowledge.

A Constructive semantic characterization of aggregates in answer set programming

2007 ◽  
Vol 7 (3) ◽  
pp. 355-375 ◽  
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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