scholarly journals Existential Abstraction on Argumentation Frameworks via Clustering

2021 ◽  
Author(s):  
Zeynep G. Saribatur ◽  
Johannes P. Wallner
Keyword(s):  
Artificial Intelligence ◽  
Model Checking ◽  
Answer Set Programming ◽  
Knowledge Bases ◽  
The State ◽  
State Explosion ◽  
Complexity Results ◽  
Reasoning Tasks ◽  
Answer Set

Argumentation in Artificial Intelligence (AI) builds on formal approaches to reasoning argumentatively. Common to many such approaches is to use argumentation frameworks (AFs) as reasoning engines, with AFs being composed of arguments and attacks between arguments, which are instantiated from knowledge bases in a principle-based manner. While representing what can be argued for in an AF provides a conceptually clean way, this process can face challenges arising from generating a large number of arguments, which can act as a barrier to explainability. Inspired by successful approaches to model checking where the state explosion is mitigated by applying existential abstraction, we study an adaption of existential abstraction in form of clustering arguments in an AF to address an associated "argument explosion". In this paper, we provide a foundational investigation of this form of existential abstraction by defining semantics of the resulting clustered AFs, which balance two inherent aspects of existential abstractions: abstracting from concrete AFs and not permitting too much spuriousness (i.e., conclusions that hold on the abstraction but not on the original AF). Moreover, we show properties of clustered AFs, including complexity results, discuss use of clusterings for explaining results of reasoning tasks, and employ the recently introduced methodology of abstraction in answer set programming (ASP) for obtaining and reasoning over clustered AFs.

scholarly journals A Formal Approach for Cautious Reasoning in Answer Set Programming (Extended Abstract)

2020 ◽  
Author(s):  
Giovanni Amendola ◽  
Carmine Dodaro ◽  
Marco Maratea
Keyword(s):  
Answer Set Programming ◽  
Satisfiability Modulo Theories ◽  
Propositional Satisfiability ◽  
Formal Approach ◽  
Boolean Formulas ◽  
Reasoning Tasks ◽  
Answer Set

The issue of describing in a formal way solving algorithms in various fields such as Propositional Satisfiability (SAT), Quantified SAT, Satisfiability Modulo Theories, Answer Set Programming (ASP), and Constraint ASP, has been relatively recently solved employing abstract solvers. In this paper we deal with cautious reasoning tasks in ASP, and design, implement and test novel abstract solutions, borrowed from backbone computation in SAT. By employing abstract solvers, we also formally show that the algorithms for solving cautious reasoning tasks in ASP are strongly related to those for computing backbones of Boolean formulas. Some of the new solutions have been implemented in the ASP solver WASP, and tested.

Complexity results for probabilistic answer set programming

2020 ◽  
Vol 118 ◽  
pp. 133-154 ◽  
Author(s):  
Denis Deratani Mauá ◽  
Fabio Gagliardi Cozman
Keyword(s):  
Answer Set Programming ◽  
Complexity Results ◽  
Answer Set

scholarly journals Action-Centered Information Retrieval

2019 ◽  
Vol 20 (2) ◽  
pp. 249-272
Author(s):  
MARCELLO BALDUCCINI ◽  
EMILY C. LEBLANC
Keyword(s):  
Information Retrieval ◽  
Side Effects ◽  
Answer Set Programming ◽  
The State ◽  
Semantic Level ◽  
Action Language ◽  
The World ◽  
Answer Set

AbstractInformation retrieval (IR) aims at retrieving documents that are most relevant to a query provided by a user. Traditional techniques rely mostly on syntactic methods. In some cases, however, links at a deeper semantic level must be considered. In this paper, we explore a type of IR task in which documents describe sequences of events, and queries are about the state of the world after such events. In this context, successfully matching documents and query requires considering the events’ possibly implicit uncertain effects and side effects. We begin by analyzing the problem, then propose an action language-based formalization, and finally automate the corresponding IR task using answer set programming.

scholarly journals Reasoning with Forest Logic Programs and f-hybrid knowledge bases

2011 ◽  
Vol 13 (3) ◽  
pp. 395-463
Author(s):  
CRISTINA FEIER ◽  
STIJN HEYMANS
Keyword(s):  
Answer Set Programming ◽  
Knowledge Bases ◽  
Logic Programs ◽  
Decidability Result ◽  
Tree Shape ◽  
Alternative Approach ◽  
Hybrid Framework ◽  
Hybrid Knowledge ◽  
Satisfiability Checking ◽  
Answer Set

AbstractOpen Answer Set Programming (OASP) is an undecidable framework for integrating ontologies and rules. Although several decidable fragments of OASP have been identified, few reasoning procedures exist. In this paper, we provide a sound, complete, and terminating algorithm for satisfiability checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules have a tree shape and allow for inequality atoms and constants. The algorithm establishes a decidability result for FoLPs. Although believed to be decidable, so far only the decidability for two small subsets of FoLPs, local FoLPs and acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a hybrid framework where knowledge bases and FoLPs coexist, and we show that reasoning with such knowledge bases can be reduced to reasoning with FoLPs only. We note that f-hybrid knowledge bases do not require the usual (weakly) DL-safety of the rule component, thus providing a genuine alternative approach to current integration approaches of ontologies and rules.

scholarly journals The Seventh Answer Set Programming Competition: Design and Results

2019 ◽  
Vol 20 (2) ◽  
pp. 176-204 ◽  
Author(s):  
MARTIN GEBSER ◽  
MARCO MARATEA ◽  
FRANCESCO RICCA
Keyword(s):  
Knowledge Representation ◽  
Logic Programming ◽  
State Of The Art ◽  
Answer Set Programming ◽  
The State ◽  
International Conference ◽  
Knowledge Representation Language ◽  
Representation Language ◽  
The University ◽  
Answer Set

AbstractAnswer Set Programming (ASP) is a prominent knowledge representation language with roots in logic programming and non-monotonic reasoning. Biennial ASP competitions are organized in order to furnish challenging benchmark collections and assess the advancement of the state of the art in ASP solving. In this paper, we report on the design and results of the Seventh ASP Competition, jointly organized by the University of Calabria (Italy), the University of Genova (Italy), and the University of Potsdam (Germany), in affiliation with the 14th International Conference on Logic Programming and Non-Monotonic Reasoning (LPNMR 2017).

Checking Opacity of Vulnerable Critical Systems On-The-Fly

2015 ◽  
Vol 10 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Amina Bourouis ◽  
Kais Klai ◽  
Yamen El Touati ◽  
Nejib Ben Hadj-Alouane
Keyword(s):  
Model Checking ◽  
Efficient Algorithms ◽  
The State ◽  
Experimental Results ◽  
Critical Systems ◽  
State Explosion ◽  
Transition Systems ◽  
State Explosion Problem ◽  
Formal Definitions ◽  
Security Property

Opacity is a security property capturing a system's ability to keep a subset of its behavior hidden from passive, but knowledgeable, observers. In this paper we use the formal definitions of opacity in three of its forms (simple opacity, -step weak opacity and -step strong opacity), basing on finite Labeled Transition Systems as a model. Then we present efficient algorithms for verifying opacity in all these forms within the context of a hybrid, on-the-fly approach. This approach is based on the construction of a Symbolic Observation Graph (SOG) that allows not only the abstraction of the systems behavior but also the preservation of the structure necessary for conducting opacity checking. Our preliminary experimental results are promising and demonstrate effectiveness facing the state-explosion problem which represents the main drawback of existing model checking techniques.

scholarly journals Harnessing Incremental Answer Set Solving for Reasoning in Assumption-Based Argumentation

2021 ◽  
pp. 1-18
Author(s):  
TUOMO LEHTONEN ◽  
JOHANNES P. WALLNER ◽  
MATTI JӒRVISALO
Keyword(s):  
Logic Programming ◽  
Answer Set Programming ◽  
Polynomial Hierarchy ◽  
Np Hard ◽  
Abstraction Refinement ◽  
Recent Advances ◽  
Structured Argumentation ◽  
Reasoning Tasks ◽  
Answer Set

Abstract Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly studied logic programming fragment of ABA. In this work, we harness recent advances in incremental ASP solving for developing effective algorithms for reasoning tasks in the logic programming fragment of ABA that are presumably hard for the second level of the polynomial hierarchy, including skeptical reasoning under preferred semantics as well as preferential reasoning. In particular, we develop non-trivial counterexample-guided abstraction refinement procedures based on incremental ASP solving for these tasks. We also show empirically that the procedures are significantly more effective than previously proposed algorithms for the tasks.

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