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Jörg Pührer

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8 papers

2 author rows

AIJ Journal 2020 Journal Article

Realizability of three-valued semantics for abstract dialectical frameworks

Jörg Pührer

We investigate fundamental properties of three-valued semantics for abstract dialectical frameworks (ADFs). In particular, we deal with realizability, i. e. , the question whether there exists an ADF that has a given set of interpretations as its semantics. We provide necessary and sufficient conditions that hold for a set of three-valued interpretations whenever there is an ADF realizing it under admissible, complete, grounded, or preferred semantics. Moreover, we show how to construct such an ADF in case of realizability. Our results lay the ground for studying the expressiveness of ADFs under three-valued semantics. Since ADFs generalize many existing approaches, our results have immediate impact on many argumentation formalisms including abstract argumentation frameworks. As first applications, we study implications of our results on the existence of certain join operators on ADFs. Furthermore, we exploit our (exact) characterizations to obtain realizability results also for a more relaxed setting, where realizing ADFs may contain hidden statements.

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JELIA Conference 2019 Conference Paper

Multi-valued GRAPPA

Gerhard Brewka
Jörg Pührer
Stefan Woltran

Abstract Abstract dialectical frameworks (ADFs) are generalizations of Dung’s argumentation frameworks which allow arbitrary relationships among arguments to be expressed. In particular, arguments can not only attack each other, they also may provide support for other arguments and interact in various complex ways. The ADF approach has recently been extended in two different ways. On the one hand, GRAPPA is a framework that applies the key notions underlying ADFs – in particular their operator-based semantics – directly to arbitrary labelled graphs. This allows users to represent argumentation scenarios in their favourite graphical representations without giving up the firm ground of well-defined semantics. On the other hand, ADFs have been further generalized to the multi-valued case to enable fine-grained acceptance values. In this paper we unify these approaches and develop a multi-valued version of GRAPPA combining the advantages of both extensions.

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AIJ Journal 2018 Journal Article

Reactive multi-context systems: Heterogeneous reasoning in dynamic environments

Gerhard Brewka
Stefan Ellmauthaler
Ricardo Gonçalves
Matthias Knorr
João Leite
Jörg Pührer

Managed multi-context systems (mMCSs) allow for the integration of heterogeneous knowledge sources in a modular and very general way. They were, however, mainly designed for static scenarios and are therefore not well-suited for dynamic environments in which continuous reasoning over such heterogeneous knowledge with constantly arriving streams of data is necessary. In this paper, we introduce reactive multi-context systems (rMCSs), a framework for reactive reasoning in the presence of heterogeneous knowledge sources and data streams. We show that rMCSs are indeed well-suited for this purpose by illustrating how several typical problems arising in the context of stream reasoning can be handled using them, by showing how inconsistencies possibly occurring in the integration of multiple knowledge sources can be handled, and by arguing that the potential non-determinism of rMCSs can be avoided if needed using an alternative, more skeptical well-founded semantics instead with beneficial computational properties. We also investigate the computational complexity of various reasoning problems related to rMCSs. Finally, we discuss related work, and show that rMCSs do not only generalize mMCSs to dynamic settings, but also capture/extend relevant approaches w. r. t. dynamics in knowledge representation and stream reasoning.

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ECAI Conference 2016 Conference Paper

A Uniform Account of Realizability in Abstract Argumentation

Thomas Linsbichler
Jörg Pührer
Hannes Strass

We introduce a general framework for analyzing realizability in abstract dialectical frameworks (ADFs) and various of its subclasses. In particular, the framework applies to Dung argumentation frameworks, SETAFs by Nielsen and Parsons, and bipolar ADFs. We present a uniform characterization method for the admissible, complete, preferred and model/stable semantics. We employ this method to devise an algorithm that decides realizability for the mentioned formalisms and semantics; moreover the algorithm allows for constructing a desired knowledge base whenever one exists. The algorithm is built in a modular way and thus easily extensible to new formalisms and semantics. We have implemented our approach in answer set programming, and used the implementation to obtain several novel results on the relative expressiveness of the abovemen-tioned formalisms.

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JELIA Conference 2016 Conference Paper

Inconsistency Management in Reactive Multi-context Systems

Gerhard Brewka
Stefan Ellmauthaler
Ricardo Gonçalves 0001
Matthias Knorr 0001
João Leite 0001
Jörg Pührer

Abstract We address the problem of global inconsistency in reactive multi-context systems (rMCSs), a framework for reactive reasoning in the presence of heterogeneous knowledge sources that can deal with continuous input streams. Their semantics is given in terms of equilibria streams. The occurrence of inconsistencies, where rMCSs fail to have an equilibria stream, can render the entire system useless. We discuss various methods for handling this problem, following different strategies such as repairing the rMCS, or even relaxing the notion of equilibria stream so that it can go through inconsistent states.

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ECAI Conference 2014 Conference Paper

Multi-Context Systems for Reactive Reasoning in Dynamic Environments

Gerhard Brewka
Stefan Ellmauthaler
Jörg Pührer

We show in this paper how managed multi-context systems (mMCS) can be turned into a reactive formalism suitable for continuous reasoning in dynamic environments. We extend mMCS with (abstract) sensors and define the notion of a run of the extended systems. We then show how typical problems arising in online reasoning can be addressed: handling potentially inconsistent sensor input, modeling intelligent forms of forgetting, and controlling the reasoning effort spent by contexts. We also investigate the complexity of some important related decision problems.

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KR Conference 2012 Conference Paper

On the Small-Scope Hypothesis for Testing Answer-Set Programs

Johannes Oetsch
Michael Prischink
Jörg Pührer
Martin Schwengerer
Hans Tompits

Though testing is the prevalent means to find errors in traditional software development, this subject has been addressed for ASP only recently (Janhunen et al. 2010; 2011; Febbraro et al. 2011). In particular, the small-scope hypothesis in traditional testing states that a high proportion of errors can be found by testing a program for all test inputs that are taken from some relatively small scope (Jackson and Damon 1996), i. e., by restricting the number of objects a test input is composed of. This suggests that it can be quite effective to test a program exhaustively for some restricted small scope instead of deliberately selecting test inputs from a larger one. A small-scope hypothesis in ASP would be a matter of interest for two reasons. First, it would allow to devise effective testing methods for uniform problem encodings (the prevailing representation mode ASP is used). For illustration, assume we encoded by means of ASP, using the rules below, the graph problem of testing whether a graph is disconnected, where problem instances are represented by facts over an input signature with predicates edge/2 and node/1: In software testing, the small-scope hypothesis states that a high proportion of errors can be found by testing a program for all test inputs within some small scope. In this paper, we evaluate the small-scope hypothesis for answer-set programming (ASP). To this end, we follow work in traditional testing and base our evaluation on mutation analysis. In fact, we show that a rather limited scope is sufficient for testing ASP encodings from a representative set of benchmark problems. Our experimental evaluation facilitates effective methods for testing in ASP. Also, it gives some justification to analyse programs at the propositional level after grounding them over a small domain.

ECAI Conference 2010 Conference Paper

On Testing Answer-Set Programs

Tomi Janhunen
Ilkka Niemelä
Johannes Oetsch
Jörg Pührer
Hans Tompits

Answer-set programming (ASP) is a well-acknowledged paradigm for declarative problem solving, yet comparably little effort has been spent on the investigation of methods to support the development of answer-set programs. In particular, systematic testing of programs, constituting an integral part of conventional software development, has not been discussed for ASP thus far. In this paper, we fill this gap and develop notions enabling the structural testing of answer-set programs, i. e. , we address testing based on test cases that are chosen with respect to the internal structure of a given answer-set program. More specifically, we introduce different notions of coverage that measure to what extent a collection of test inputs covers certain important structural components of the program. In particular, we introduce metrics corresponding to path and branch coverage from conventional testing. We also discuss complexity aspects of the considered notions and give strategies how test inputs that yield increasing (up to total) coverage can be automatically generated.

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