scholarly journals Complexity Results and Algorithms for Extension Enforcement in Abstract Argumentation

2017 ◽  
Vol 60 ◽  
pp. 1-40 ◽  
Author(s):  
Johannes P. Wallner ◽  
Andreas Niskanen ◽  
Matti Järvisalo
Keyword(s):  
Computational Complexity ◽  
Formal Model ◽  
Legal Reasoning ◽  
Knowledge Representation And Reasoning ◽  
Polynomial Hierarchy ◽  
Prototype System ◽  
Multi Agent Systems ◽  
Abstract Argumentation ◽  
Complexity Results ◽  
Complete Problems

Argumentation is an active area of modern artificial intelligence (AI) research, with connections to a range of fields, from computational complexity theory and knowledge representation and reasoning to philosophy and social sciences, as well as application-oriented work in domains such as legal reasoning, multi-agent systems, and decision support. Argumentation frameworks (AFs) of abstract argumentation have become the graph-based formal model of choice for many approaches to argumentation in AI, with semantics defining sets of jointly acceptable arguments, i.e., extensions. Understanding the dynamics of AFs has been recently recognized as an important topic in the study of argumentation in AI. In this work, we focus on the so-called extension enforcement problem in abstract argumentation as a recently proposed form of argumentation dynamics. We provide a nearly complete computational complexity map of argument-fixed extension enforcement under various major AF semantics, with results ranging from polynomial-time algorithms to completeness for the second level of the polynomial hierarchy. Complementing the complexity results, we propose algorithms for NP-hard extension enforcement based on constraint optimization under the maximum satisfiability (MaxSAT) paradigm. Going beyond NP, we propose novel MaxSAT-based counterexample-guided abstraction refinement procedures for the second-level complete problems and present empirical results on a prototype system constituting the first approach to extension enforcement in its generality.

scholarly journals An Efficient Java-Based Solver for Abstract Argumentation Frameworks: jArgSemSAT

2017 ◽  
Vol 26 (02) ◽  
pp. 1750002 ◽  
Author(s):  
Federico Cerutti ◽  
Mauro Vallati ◽  
Massimiliano Giacomin
Keyword(s):  
Computational Complexity ◽  
Web Service ◽  
Computational Models ◽  
State Of The Art ◽  
Legal Reasoning ◽  
Intelligence Analysis ◽  
Abstract Argumentation ◽  
Current State ◽  
In Virtue Of ◽  
Argumentation Systems

Dung’s argumentation frameworks are adopted in a variety of applications, from argument-mining, to intelligence analysis and legal reasoning. Despite this broad spectrum of already existing applications, the mostly adopted solver—in virtue of its simplicity—is far from being comparable to the current state-of-the-art solvers. On the other hand, most of the current state-of-the-art solvers are far too complicated to be deployed in real-world settings. In this paper we provide and extensive description of jArgSemSAT, a Java re-implementation of ArgSemSAT. ArgSemSAT represents the best single solver for argumentation semantics with the highest level of computational complexity. We show that jArgSemSAT can be easily integrated in existing argumentation systems (1) as an off-the-shelf, standalone, library; (2) as a Tweety compatible library; and (3) as a fast and robust web service freely available on the Web. Our large experimental analysis shows that despite being written in Java, jArgSemSAT would have scored in most of the cases among the three bests solvers for the two semantics with highest computational complexity “Stable and Preferred” in the last competition on computational models of argumentation.

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

Logical Characterizations of Bounded Query Classes I: Logspace Oracle Machines

1993 ◽  
Vol 18 (1) ◽  
pp. 65-92
Author(s):  
Iain A. Stewart
Keyword(s):  
Truth Table ◽  
Complexity Class ◽  
Polynomial Hierarchy ◽  
Complexity Classes ◽  
Turing Machines ◽  
Complete Problems

We consider three sub-logics of the logic (±HP)*[FOs] and show that these sub-logics capture the complexity classes obtained by considering logspace deterministic oracle Turing machines with oracles in NP where the number of oracle calls is unrestricted and constant, respectively; that is, the classes LNP and LNP[O(1)]. We conclude that if certain logics are of the same expressibility then the Polynomial Hierarchy collapses. We also exhibit some new complete problems for the complexity class LNP via projection translations (the first to be discovered: projection translations are extremely weak logical reductions between problems) and characterize the complexity class LNP[O(1)] as the closure of NP under a new, extremely strict truth-table reduction (which we introduce in this paper).

DocBase

2013 ◽  
pp. 365-393
Author(s):  
Arijit Sengupta ◽  
Ramesh Venkataraman
Keyword(s):  
Query Processing ◽  
Query Language ◽  
Formal Model ◽  
Query Languages ◽  
Prototype System ◽  
Storage And Retrieval ◽  
Visual Query Formulation ◽  
Visual Query ◽  
Nested Relations ◽  
Entity Relationship

This chapter introduces a complete storage and retrieval architecture for a database environment for XML documents. DocBase, a prototype system based on this architecture, uses a flexible storage and indexing technique to allow highly expressive queries without the necessity of mapping documents to other database formats. DocBase is an integration of several techniques that include (i) a formal model called Heterogeneous Nested Relations (HNR), (ii) a conceptual model XER (Extensible Entity Relationship), (ii) formal query languages (Document Algebra and Calculus), (iii) a practical query language (Document SQL or DSQL), (iv) a visual query formulation method with QBT (Query By Templates), and (v) the DocBase query processing architecture. This paper focuses on the overall architecture of DocBase including implementation details, describes the details of the query-processing framework, and presents results from various performance tests. The paper summarizes experimental and usability analyses to demonstrate its feasibility as a general architecture for native as well as embedded document manipulation methods.

Quantifying over events in probability logic: an introduction

2016 ◽  
Vol 27 (8) ◽  
pp. 1581-1600
Author(s):  
STANISLAV O. SPERANSKI
Keyword(s):  
Computational Complexity ◽  
Boolean Algebras ◽  
Probability Logic ◽  
Discrete Probability ◽  
Complexity Results ◽  
Probability Spaces

In this article we describe a bunch of probability logics with quantifiers over events, and develop primary techniques for proving computational complexity results (in terms of m-degrees) about these logics, mainly over discrete probability spaces. Also the article contains a comparison with some other probability logics and a discussion of interesting analogies with research in the metamathematics of Boolean algebras, demonstrating a number of attractive features and intuitive advantages of the present proposal.

scholarly journals Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 322
Author(s):  
Vitaly Kocharovsky ◽  
Vladimir Kocharovsky ◽  
Sergey Tarasov
Keyword(s):  
Quantum Computing ◽  
Quantum Information ◽  
Computational Complexity ◽  
Critical Phenomena ◽  
Complex Variables ◽  
Integral Representations ◽  
Many Body ◽  
Fractal Structures ◽  
Information Processes ◽  
Complete Problems

We reveal the analytic relations between a matrix permanent and major nature’s complexities manifested in critical phenomena, fractal structures and chaos, quantum information processes in many-body physics, number-theoretic complexity in mathematics, and ♯P-complete problems in the theory of computational complexity. They follow from a reduction of the Ising model of critical phenomena to the permanent and four integral representations of the permanent based on (i) the fractal Weierstrass-like functions, (ii) polynomials of complex variables, (iii) Laplace integral, and (iv) MacMahon master theorem.

A METHODOLOGY FOR MODELING MULTI-AGENT SYSTEMS USING NESTED PETRI NETS

2012 ◽  
Vol 22 (07) ◽  
pp. 891-925 ◽  
Author(s):  
LILY CHANG ◽  
XUDONG HE ◽  
SOL M. SHATZ
Keyword(s):  
Formal Model ◽  
Dynamic Structure ◽  
Software Systems ◽  
Multi Agent Systems ◽  
New Paradigm ◽  
Distributed Software ◽  
Agent Systems ◽  
Multi Agent ◽  
Communication And Coordination ◽  
Multi Agents

In the past two decades, multi-agent systems have emerged as a new paradigm for conceptualizing large and complex distributed software systems. Even though there are many conceptual frameworks for using multi-agent systems, there is no well established and widely accepted method for the representation of multi-agent systems. We adapt a well-known formal model, predicate transition nets, to include the notions of dynamic structure, agent communication and coordination to address the representation problems. This paper presents a comprehensive methodology for modeling multi-agents based on the extensions. We demonstrate our modeling approach with an example. Several case studies on different application domains from our previous works are also discussed.

Computational Complexity Analysis of Selective Breeding Algorithm

2014 ◽  
Vol 591 ◽  
pp. 172-175
Author(s):  
M. Chandrasekaran ◽  
P. Sriramya ◽  
B. Parvathavarthini ◽  
M. Saravanamanikandan
Keyword(s):  
Computational Complexity ◽  
Selective Breeding ◽  
Heuristic Algorithms ◽  
Complexity Analysis ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Approximate Solutions ◽  
Problem Size ◽  
Combinatorial Optimization Problems ◽  
Complete Problems

In modern years, there has been growing importance in the design, analysis and to resolve extremely complex problems. Because of the complexity of problem variants and the difficult nature of the problems they deal with, it is arguably impracticable in the majority time to build appropriate guarantees about the number of fitness evaluations needed for an algorithm to and an optimal solution. In such situations, heuristic algorithms can solve approximate solutions; however suitable time and space complication take part an important role. In present, all recognized algorithms for NP-complete problems are requiring time that's exponential within the problem size. The acknowledged NP-hardness results imply that for several combinatorial optimization problems there are no efficient algorithms that realize a best resolution, or maybe a close to best resolution, on each instance. The study Computational Complexity Analysis of Selective Breeding algorithm involves both an algorithmic issue and a theoretical challenge and the excellence of a heuristic.

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