Hannes Strass

AAAI Conference 2026 Conference Paper

Non-Monotonic S4F Standpoint Logic

• Piotr Gorczyca
• Hannes Strass

Standpoint logics offer unified modal logic-based formalisms for representing multiple heterogeneous viewpoints. At the same time, many non-monotonic reasoning frameworks can be naturally captured using modal logics — in particular using the modal logic S4F. In this work, we propose a novel formalism called S4F Standpoint Logic, which generalises both S4F and standpoint propositional logic and is therefore capable of expressing multi-viewpoint, non-monotonic semantic commitments. We define its syntax and semantics and analyze its computational complexity, obtaining the result that S4F Standpoint Logic is not computationally harder than its constituent logics, whether in monotonic or non-monotonic form. We also outline mechanisms for credulous and sceptical acceptance and illustrate the framework with an example.

IJCAI Conference 2025 Conference Paper

Approximation Fixpoint Theory as a Unifying Framework for Fuzzy Logic Programming Semantics

• Pascal Kettmann
• Jesse Heyninck
• Hannes Strass

Fuzzy logic programming is an established approach for reasoning under uncertainty. Several semantics from classical, two-valued logic programming have been generalized to the case of fuzzy logic programs. In this paper, we show that two of the most prominent classical semantics, namely the stable model and the well-founded semantics, can be reconstructed within the general framework of approximation fixpoint theory (AFT). This not only widens the scope of AFT from two- to many-valued logics, but allows a wide range of existing AFT results to be applied to fuzzy logic programming. As first examples of such applications, we clarify the formal relationship between existing semantics, generalize the notion of stratification from classical to fuzzy logic programs, and devise “more precise” variants of the semantics.

NMR Workshop 2024 Conference Paper

Adding Standpoint Modalities to Non-Monotonic S4F: Preliminary Results

• Piotr Gorczyca
• Hannes Strass

Standpoint logics allow to represent multiple heterogeneous viewpoints in a unifying framework based on modal logic. We propose to combine standpoint modalities with the single modality of the non-monotonic modal logic S4F, thus defining standpoint S4F. The resulting language allows to express semantic commitments based on default reasoning. We define syntax and semantics of the logic, study the computational complexity of reasoning problems in the fragment of simple theories, and showcase standpoint S4F by exemplifying two concrete instantiations of the general language – standpoint default logic and standpoint argumentation frameworks.

KR Conference 2023 Conference Paper

Pushing the Boundaries of Tractable Multiperspective Reasoning: A Deduction Calculus for Standpoint EL+

• Lucía Gómez Álvarez
• Sebastian Rudolph
• Hannes Strass

Standpoint EL is a multi-modal extension of the popular description logic EL that allows for the integrated representation of domain knowledge relative to diverse standpoints or perspectives. Advantageously, its satisfiability problem has recently been shown to be in PTime, making it a promising framework for large-scale knowledge integration. In this paper, we show that we can further push the expressivity of this formalism, arriving at an extended logic, called Standpoint EL+, which allows for axiom negation, role chain axioms, self-loops, and other features, while maintaining tractability. This is achieved by designing a satisfiability-checking deduction calculus, which at the same time addresses the need for practical algorithms. We demonstrate the feasibility of our calculus by presenting a prototypical Datalog implementation of its deduction rules.

IJCAI Conference 2023 Conference Paper

Tractable Diversity: Scalable Multiperspective Ontology Management via Standpoint EL

• Lucía Gómez Álvarez
• Sebastian Rudolph
• Hannes Strass

The tractability of the lightweight description logic EL has allowed for the construction of large and widely used ontologies that support semantic interoperability. However, comprehensive domains with a broad user base are often at odds with strong axiomatisations otherwise useful for inferencing, since these are usually context dependent and subject to diverging perspectives. In this paper we introduce Standpoint EL, a multi-modal extension of EL that allows for the integrated representation of domain knowledge relative to diverse, possibly conflicting standpoints (or contexts), which can be hierarchically organised and put in relation to each other. We establish that Standpoint EL still exhibits EL's favourable PTime standard reasoning, whereas introducing additional features like empty standpoints, rigid roles, and nominals makes standard reasoning tasks intractable.

AIJ Journal 2022 Journal Article

An abstract, logical approach to characterizing strong equivalence in non-monotonic knowledge representation formalisms

• Ringo Baumann
• Hannes Strass

Two knowledge bases are strongly equivalent if and only if they are mutually interchangeable in arbitrary contexts. This notion is of high interest for any logical formalism, since it allows to locally replace parts of a given theory without changing its meaning. In contrast to classical logic, where strong equivalence coincides with standard equivalence (having the same models), it is possible to find ordinary but not strongly equivalent objects for any nonmonotonic formalism available in the literature. Consequently, much effort has been devoted to characterizing strong equivalence for knowledge representation formalisms such as logic programs under the stable model semantics, Reiter's default logic, or Dung's argumentation frameworks. For example, strong equivalence for logic programs under stable models can be characterized by so-called HT-models. More precisely, two logic programs are strongly equivalent if and only if they are standard equivalent in the logic of here and there. This means that the logic of here and there can be seen as a characterizing formalism for logic programs under stable model semantics. The aim of this article is to study whether the existence of such characterization logics can be guaranteed for any logic. One main result is that every knowledge representation formalism that allows for a notion of strong equivalence on its finite knowledge bases also possesses a canonical characterizing formalism. In particular, we argue that those characterizing formalisms can be seen as classical, monotonic logics. Moreover, we will not only show the existence of characterizing formalism, but even that the model theory of any characterizing logic is uniquely determined (up to isomorphism).

AAAI Conference 2018 Conference Paper

Weighted Abstract Dialectical Frameworks

• Gerhard Brewka
• Hannes Strass
• Johannes Wallner
• Stefan Woltran

Abstract Dialectical Frameworks (ADFs) generalize Dung’s argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance degrees for the arguments. This makes ADFs applicable in domains where both the initial status of arguments and their relationship are only insufficiently specified by Boolean functions. We define all standard ADF semantics for the weighted case, including grounded, preferred and stable semantics. We illustrate our approach using acceptance degrees from the unit interval and show how other valuation structures can be integrated. In each case it is sufficient to specify how the generalized acceptance conditions are represented by formulas, and to specify the information ordering underlying the characteristic ADF operator. We also present complexity results for problems related to weighted ADFs.

FLAP Journal 2017 Journal Article

Abstract Dialectical Frameworks. An Overview.

• Gerhard Brewka
• Stefan Ellmauthaler
• Hannes Strass
• Johannes P. Wallner
• Stefan Woltran

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.

AAAI Conference 2016 Conference Paper

Boolean Functions with Ordered Domains in Answer Set Programming

• Mario Alviano
• Wolfgang Faber
• Hannes Strass

Boolean functions in Answer Set Programming have proven a useful modelling tool. They are usually specified by means of aggregates or external atoms. A crucial step in computing answer sets for logic programs containing Boolean functions is verifying whether partial interpretations satisfy a Boolean function for all possible values of its undefined atoms. In this paper, we develop a new methodology for showing when such checks can be done in deterministic polynomial time. This provides a unifying view on all currently known polynomialtime decidability results, and furthermore identifies promising new classes that go well beyond the state of the art. Our main technique consists of using an ordering on the atoms to significantly reduce the necessary number of model checks. For many standard aggregates, we show how this ordering can be automatically obtained.

KR Conference 2016 Short Paper

Classical Logics for Characterizing Strong Equivalence in Non-Classical Logics

• Ringo Baumann
• Hannes Strass

AIJ Journal 2016 Journal Article

On rejected arguments and implicit conflicts: The hidden power of argumentation semantics

• Ringo Baumann
• Wolfgang Dvořák
• Thomas Linsbichler
• Christof Spanring
• Hannes Strass
• Stefan Woltran

argumentation frameworks (afs) are one of the most studied formalisms in AI and are formally simple tools to model arguments and their conflicts. The evaluation of an af yields extensions (with respect to a semantics) representing alternative acceptable sets of arguments. For many of the available semantics two effects can be observed: there exist arguments in the given af that do not appear in any extension (rejected arguments); there exist pairs of arguments that do not occur jointly in any extension, albeit there is no explicit conflict between them in the given af (implicit conflicts). In this paper, we investigate the question whether these situations are only a side-effect of particular afs, or whether rejected arguments and implicit conflicts contribute to the expressiveness of the actual semantics. We do so by introducing two subclasses of afs, namely compact and analytic frameworks. The former class contains afs that do not contain rejected arguments with respect to a semantics at hand; afs from the latter class are free of implicit conflicts for a given semantics. Frameworks that are contained in both classes would be natural candidates towards normal forms for afs since they minimize the number of arguments on the one hand, and on the other hand maximize the information on conflicts, a fact that might help argumentation systems to evaluate afs more efficiently. Our main results show that under stable, preferred, semi-stable, and stage semantics neither of the classes is able to capture the full expressive power of these semantics; we thus also refute a recent conjecture by Baumann et al. on implicit conflicts. Moreover, we give a detailed complexity analysis for the problem of deciding whether an af is compact, resp. analytic. Finally, we also study the signature of these subclasses for the mentioned semantics and shed light on the question under which circumstances an arbitrary framework can be transformed into an equivalent compact, resp. analytic, af.

AIJ Journal 2015 Journal Article

Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory

• Hannes Strass
• Johannes Peter Wallner

dialectical frameworks (ADFs) have recently been proposed as a versatile generalization of Dung's abstract argumentation frameworks (AFs). In this paper, we present a comprehensive analysis of the computational complexity of ADFs. Our results show that while ADFs are one level up in the polynomial hierarchy compared to AFs, there is a useful subclass of ADFs which is as complex as AFs while arguably offering more modeling capacities. As a technical vehicle, we employ the approximation fixpoint theory of Denecker, Marek and Truszczyński, thus showing that it is also a useful tool for complexity analysis of operator-based semantics.

JAIR Journal 2015 Journal Article

Expressiveness of Two-Valued Semantics for Abstract Dialectical Frameworks

• Hannes Strass

We analyse the expressiveness of Brewka and Woltran's abstract dialectical frameworks for two-valued semantics. By expressiveness we mean the ability to encode a desired set of two-valued interpretations over a given propositional vocabulary A using only atoms from A. We also compare ADFs' expressiveness with that of (the two-valued semantics of) abstract argumentation frameworks, normal logic programs and propositional logic. While the computational complexity of the two-valued model existence problem for all these languages is (almost) the same, we show that the languages form a neat hierarchy with respect to their expressiveness. We then demonstrate that this hierarchy collapses once we allow to introduce a linear number of new vocabulary elements. We finally also analyse and compare the representational succinctness of ADFs (for two-valued model semantics), that is, their capability to represent two-valued interpretation sets in a space-efficient manner.

IJCAI Conference 2015 Conference Paper

On the Computational Complexity of Naive-Based Semantics for Abstract Dialectical Frameworks

• Sarah Alice Gaggl
• Sebastian Rudolph
• Hannes Strass

Abstract dialectical frameworks (ADFs) are a powerful generalization of Dung’s abstract argumentation frameworks. ADFs allow to model argumentation scenarios such that ADF semantics then provide interpretations of the scenarios. Among the considerable number of ADF semantics, the naivebased ones are built upon the fundamental concept of conflict-freeness. Intuitively, a three-valued interpretation of an ADF’s statements is conflict-free iff all true statements can possibly be accepted, and all false statements cannot possibly be accepted. In this paper, we perform an exhaustive analysis of the computational complexity of naive-based semantics. The results are quite interesting, for some of them involve little-known classes of the so-called Boolean hierarchy (another hierarchy in between classes of the polynomial hierarchy). Furthermore in credulous and sceptical entailment, the complexity can be different depending on whether we check for truth or falsity of a specific statement.

AAAI Conference 2015 Conference Paper

The Relative Expressiveness of Abstract Argumentation and Logic Programming

• Hannes Strass

We analyze the relative expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued interpretations over a given propositional vocabulary A using only atoms from A. While the computational complexity of the two-valued model existence problem for all these languages is (almost) the same, we show that the languages form a neat hierarchy with respect to their expressiveness. We then demonstrate that this hierarchy collapses once we allow to introduce a linear number of new vocabulary elements.

KR Conference 2014 Conference Paper

Analyzing the Computational Complexity of Abstract Dialectical Frameworks via Approximation Fixpoint Theory

• Hannes Strass
• Johannes Peter Wallner

relationship between different arguments (called statements in ADFs) is specified by acceptance conditions. These are Boolean functions indicating the conditions under which a statement s can be accepted when given the acceptance status of all statements with a direct link to s (its parents). ADFs have been successfully employed to address the shortcomings of AFs: Brewka and Gordon (2010) translated Carneades to ADFs and for the first time allowed cyclic dependencies amongst arguments; for rule-based defeasible theories we (Strass 2013b) showed how to deal with the problems observed by Caminada and Amgoud (2007). There is a great number of semantics for AFs already, and many of them have been generalized to ADFs. Thus it might not be clear to potential ADF users which semantics are adequate for a particular application domain. In this regard, knowing the computational complexity of semantics can be a valuable guide. However, existing complexity results for ADFs are scattered over different papers, miss several semantics and some of them present upper bounds only. In this paper, we provide a comprehensive complexity analysis for ADFs. In line with the literature, we represent acceptance conditions by propositional formulas as they provide a compact and elegant way to represent Boolean functions. Technically, we base our complexity analysis on the approximation fixpoint theory (AFT) by Denecker, Marek and Truszczyński (2000; 2003; 2004). This powerful framework provides an algebraic account of how monotone and nonmonotone two-valued operators can be approximated by monotone three- or four-valued operators. (As an example of an operator to be approximated, think of the two-valued van Emden-Kowalski consequence operator from logic programming.) AFT embodies the intuitions of decades of KR research; we believe that this is very valuable also for relatively recent languages (such as ADFs), because we get the enormously influential formalizations of intuitions of Reiter and others for free. (As a liberal variation on Newton, we could say that approximation fixpoint theory allows us to take the elevator up to the shoulders of giants instead of walking up the stairs.) In fact, approximation fixpoint theory can be and partially has already been used to define some of the semantics of ADFs (Brewka et al. 2013; Strass 2013a). There, we generalized various AF and logic programming semantics to ADFs using AFT, which has provided us with two families of semantics, that we call – for rea- Abstract dialectical frameworks (ADFs) have recently been proposed as a versatile generalization of Dung’s abstract argumentation frameworks (AFs). In this paper, we present a comprehensive analysis of the computational complexity of ADFs. Our results show that while ADFs are one level up in the polynomial hierarchy compared to AFs, there is a useful subclass of ADFs which is as complex as AFs while arguably offering more modeling capacities. As a technical vehicle, we employ the approximation fixpoint theory of Denecker, Marek and Truszczyński, thus showing that it is also a useful tool for complexity analysis of operator-based semantics.

ECAI Conference 2014 Conference Paper

Compact Argumentation Frameworks

• Ringo Baumann
• Wolfgang Dvorák
• Thomas Linsbichler
• Hannes Strass
• Stefan Woltran

Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different semantics? (2) Under which circumstances can AFs be transformed into equivalent compact ones? (3) Finally, we show that compact AFs are indeed a non-trivial subclass, since the verification problem remains coNP-hard for certain semantics.

ECAI Conference 2014 Conference Paper

From Default and Autoepistemic Logics to Disjunctive Answer Set Programs via the Logic of GK

• Jianmin Ji
• Hannes Strass

We show how the pure logic of GK can be embedded into disjunctive logic programming. The translation we present is polynomial, but not modular, and introduces new variables. The result can then be used to compute the extension/expansion semantics of default and autoepistemic logics using disjunctive ASP solvers.

IJCAI Conference 2013 Conference Paper

Abstract Dialectical Frameworks Revisited

• Gerhard Brewka
• Stefan Ellmauthaler
• Hannes Strass
• Johannes Peter Wallner
• Stefan Woltran

We present various new concepts and results related to abstract dialectical frameworks (ADFs), a powerful generalization of Dung’s argumentation frameworks (AFs). In particular, we show how the existing definitions of stable and preferred semantics which are restricted to the subcase of so-called bipolar ADFs can be improved and generalized to arbitrary frameworks. Furthermore, we introduce preference handling methods for ADFs, allowing for both reasoning with and about preferences. Finally, we present an implementation based on an encoding in answer set programming.

AIJ Journal 2013 Journal Article

Approximating operators and semantics for abstract dialectical frameworks

• Hannes Strass

We provide a systematic in-depth study of the semantics of abstract dialectical frameworks (ADFs), a recent generalisation of Dungʼs abstract argumentation frameworks. This is done by associating with an ADF its characteristic one-step consequence operator and defining various semantics for ADFs as different fixpoints of this operator. We first show that several existing semantical notions are faithfully captured by our definition, then proceed to define new ADF semantics and show that they are proper generalisations of existing argumentation semantics from the literature. Most remarkably, this operator-based approach allows us to compare ADFs to related nonmonotonic formalisms like Dung argumentation frameworks and propositional logic programs. We use polynomial, faithful and modular translations to relate the formalisms, and our results show that both abstract argumentation frameworks and abstract dialectical frameworks are at most as expressive as propositional normal logic programs.

KR Conference 2010 Conference Paper

State Defaults and Ramifications in the Unifying Action Calculus

• Ringo Baumann
• Gerhard Brewka
• Hannes Strass
• Michael Thielscher
• Vadim Zaslawski

We present a framework for reasoning about actions that not only solves the frame and ramification problems, but also the state default problem—the problem to determine what normally holds at a given time point. Yet, the framework is general enough not to be tied to a specific time structure. This is achieved as follows: We use effect axioms that draw ideas both from Reiter’s successor state axioms and the nonmonotonic causal theories by Giunchiglia et al. These axioms are formulated in a recently proposed unifying action calculus to guarantee independence of a specific underlying notion of time. Reiter’s default logic is then wrapped around the resulting calculus and plays a key role in solving the ramification as well as the state default problem.