Ofer Arieli

KR Conference 2025 Conference Paper

Compactness and Preservation in Logical Argumentation Frameworks

• Ofer Arieli
• Christian Strasser

Logic-based argumentation is a formal method for constructing, evaluating and comparing arguments. In this paper we address two (related) key issues concerning the representation of logical argumentation frameworks: how to describe them in a compact way, and how to move from one framework to another while preserving their basic logical characteristics. The results are applied to various forms of attack rules and different kinds of argumentative semantics, and are demonstrated for transitions between several 3-valued logics and classical logic. As a byproduct, our results are also used for converting logic-based argumentation frameworks to assumption-based argumentation frameworks.

AAAI Conference 2024 Conference Paper

Defeasible Normative Reasoning: A Proof-Theoretic Integration of Logical Argumentation

• Ofer Arieli
• Kees van Berkel
• Christian Straßer

We present a novel computational approach to resolving conflicts among norms by nonmonotonic normative reasoning (in constrained I/O logics). Our approach extends standard sequent-based proof systems and makes them more adequate to nonmonotonic reasoning by adding to the sequents annotations that keep track of what is known about the defeasible status of the derived sequents. This makes transparent the reasons according to which norms should be applicable or inapplicable, and accordingly the sequents that make use of such norms are accepted or retracted. We also show that this proof theoretic method has tight links to the semantics of formal argumentation frameworks. The outcome of this paper is thus a threefold characterization result that relates, in the context of nonmonotonic normative reasoning, three traditional ingredients of AI-based reasoning methods: maximally consistent sets of premises (in constrained I/O logics), derived sequents (which are accepted in corresponding annotated sequent calculi), and logical arguments (that belong to the grounded extensions of the induced logical argumentation frameworks).

KR Conference 2024 Conference Paper

Deontic Reasoning Based on Inconsistency Measures

• Ofer Arieli
• Kees van Berkel
• Badran Raddaoui
• Christian Strasser

Conflicts are inherent to normative systems. In this paper, we explore a novel approach to normative reasoning by quantifying the amount of conflicts within normative systems. We refine the idea from classical logic, according to which a formula is a consequence of a knowledge base in case its negation renders the knowledge base inconsistent. In our approach, whether a formula is a logical consequence depends, for instance, on its negation's marginal contribution to the inconsistency of the given knowledge base. Accordingly, various inconsistency measures and corresponding (nonmonotonic and paraconsistent) normative entailment relations are analyzed relative to a number of logical properties. To illustrate our approach, we adopt Input/Output logic, a renowned formalism in deontic logic, specifically designed for defeasible normative reasoning. As an application, the resulting entailment relations provide recommendations to agents for minimizing norm conflicts, and may be incorporated in a number of implementations (like the Tweety libraries and the LogiKey framework) by involving inconsistency measurements in normative reasoning.

AIJ Journal 2024 Journal Article

Non-deterministic approximation fixpoint theory and its application in disjunctive logic programming

• Jesse Heyninck
• Ofer Arieli
• Bart Bogaerts

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to dealing with non-deterministic constructs that allow to handle indefinite information, represented e. g. by disjunctive formulas. This is done by generalizing the main constructions and corresponding results of AFT to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.

IJCAI Conference 2024 Conference Paper

Semantics for Non-Flat Assumption-Based Argumentation, Revisited

• Jesse Heyninck
• Ofer Arieli

Assumption-based argumentation (ABA) is an argumentative formalism that allows for reasoning on the basis of defeasible assumptions and strict rules. Standard semantics for this formalism sometimes give rise to problematic behaviour in the presence of rules with assumptions in their heads. In this paper, we introduce a six-valued labelling semantics that overcomes these shortcomings while preserving all the usual properties of the standard Dung-style three-valued semantics for ABA frameworks, including existence of the complete semantics, uniqueness of the grounded semantics and preservation of the computational complexity of all main reasoning processes.

AIJ Journal 2023 Journal Article

A postulate-driven study of logical argumentation

• Ofer Arieli
• Annemarie Borg
• Christian Straßer

Logical argumentation is a well-known approach to modeling non-monotonic reasoning with conflicting information. In this paper we provide a comprehensive postulate-based study of properties of logical argumentation frameworks and a full characterization of their semantics and inference relations. In this way we identify well-behaved formal argumentative models of drawing logically justified inferences from a given set of possibly conflicting defeasible, as well as strict assumptions. Given some desiderata in terms of rationality postulates, we consider the conditions that an argumentation framework should fulfill for the desiderata to hold. One purpose of this approach is to assist designers to “plug-in” pre-defined formalisms according to actual needs. To this end, we present a classification of argumentation frameworks relative to the types of attacks they implement. In turn, for each class we determine which desiderata are satisfied. Our study is highly abstract, supposing only a minimal set of requirements on the considered underlying deductive systems, and in this way covering a broad range of formalisms, including classical, intuitionistic and modal logics.

KR Conference 2023 Conference Paper

Simple Contrapositive Assumption-Based Argumentation with Partially-Ordered Preferences

• Ofer Arieli
• Jesse Heyninck

We show that assumption-based argumentation frameworks, based on contrapositive logics and partially-ordered preference functions, provide a solid platform for argumentation-based reasoning. Two useful properties of the preference functions are identified (selectivity and max-lower-boundedness), and extended forms of attacks relations are supported (exists-attacks and forall-attacks), which assure several desirable properties and a variety of reasoning modes.

NMR Workshop 2022 Conference Paper

Abductive Reasoning with Sequent-Based Argumentation

• Ofer Arieli
• AnneMarie Borg
• Matthis Hesse
• Christian Straßer

We show that logic-based argumentation, and in particular sequent-based frameworks, is a robust argumentative setting for abductive reasoning and explainable artificial intelligence.

IJCAI Conference 2022 Conference Paper

Annotated Sequent Calculi for Paraconsistent Reasoning and Their Relations to Logical Argumentation

• Ofer Arieli
• Kees van Berkel
• Christian Straßer

We introduce annotated sequent calculi, which are extensions of standard sequent calculi, where sequents are combined with annotations that represent their derivation statuses. Unlike in ordinary calculi, sequents that are derived in annotated calculi may still be retracted in the presence of conflicting sequents, thus inferences are made under stricter conditions. Conflicts in the resulting systems are handled like in adaptive logics and argumentation theory. The outcome is a robust family of proof systems for non-monotonic reasoning with inconsistent information, where revision considerations are fully integrated into the object level of the proofs. These systems are shown to be strongly connected to logical argumentation.

KR Conference 2021 Conference Paper

Approximation Fixpoint Theory for Non-Deterministic Operators and Its Application in Disjunctive Logic Programming

• Jesse Heyninck
• Ofer Arieli

Approximation fixpoint theory (AFT) constitutes an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to non-deterministic constructs such as disjunctive information. This is done by generalizing the main constructions and corresponding results to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.

KR Conference 2021 Conference Paper

Characterizations and Classifications of Argumentative Entailments

• Ofer Arieli
• Annemarie Borg
• Christian Straßer

In this paper we provide a detailed analysis of the inference process induced by logical argumentation frameworks. The frameworks may be defined with respect to any propositional language and logic, different arguments that represent deductions in the logic, various support-based attack relations between arguments, and all the complete Dung-style semantics for the frameworks. We show that, ultimately, for characterizing the inference process with respect to a given framework, extension-based semantics may be divided into two types: single-extension and multiple-extension, which induce respective kinds of entailment relations. These entailments are further classified by the way they tolerate new information (nonmonotonicity-related properties) and maintain conflicts among arguments (inconsistency-related properties).

FLAP Journal 2021 Journal Article

Logic-Based Approaches to Formal Argumentation.

• Ofer Arieli
• Annemarie Borg
• Jesse Heyninck
• Christian Straßer

We study the logical foundations of Dung-style argumentation frameworks. Logicbased methods in the context of argumentation theory are described from two perspectives: (a) a survey of logic-based instantiations of argumentation frameworks, their properties and relations, and (b) a review of logical methods for the study of argumentation dynamics. In this chapter we restrict ourselves to Tarskian logics, based on (propositional) languages and corresponding (constructive) semantics or syntactic rule-based systems.

ECAI Conference 2020 Conference Paper

Prioritized Simple Contrapositive Assumption-Based Frameworks

• Ofer Arieli
• Jesse Heyninck

Simple contrapositive assumption-based frameworks are a general setting for structured argumentation, providing a robust approach to reasoning with arguments and counter-arguments. In this paper we extend these frameworks with priorities and introduce some new results concerning the semantics of the resulting formalisms.

TCS Journal 2019 Journal Article

Logical argumentation by dynamic proof systems

• Ofer Arieli
• Christian Straßer

In this paper we provide a proof theoretical investigation of logical argumentation, where arguments are represented by sequents, conflicts between arguments are represented by sequent elimination rules, and deductions are made by dynamic proof systems extending standard sequent calculi. The idea is to imitate argumentative movements in which certain claims are introduced or withdrawn in the presence of counter-claims. This is done by a dynamic evaluation of sequences of sequents, in which the latter are considered ‘derived’ or ‘not derived’ according to the content of the sequence. We show that decisive conclusions of such a process correspond to well-accepted consequences of the underlying argumentation framework. The outcome is therefore a general and modular proof-theoretical approach for paraconsistent and non-monotonic reasoning with argumentation systems.

FLAP Journal 2019 Journal Article

Preface.

• Ofer Arieli
• Anna Zamansky

AAMAS Conference 2019 Conference Paper

Simple Contrapositive Assumption-Based Frameworks

• Jesse Heyninck
• Ofer Arieli

We study the Dung semantics for extended forms of assumptionbased argumentation frameworks (ABFs), based on any contrapositive propositional logic, and whose defeasible rules are expressed by arbitrary formulas in that logic. New results on the well-founded semantics for such ABFs are reported, the redundancy of the closure condition is shown, and the use of disjunctive attacks is investigated. Useful properties of the generalized frameworks are also considered.

AAMAS Conference 2018 Conference Paper

Hypersequential Argumentation Frameworks: An Instantiation in the Modal Logic S5

• Annemarie Borg
• Ofer Arieli

In this paper we introduce hypersequent-based frameworks for the modeling of defeasible reasoning by means of logic-based argumentation. These frameworks are an extension of sequent-based argumentation frameworks, in which arguments are represented not only by sequents, but by more general expressions, called hypersequents. This generalization allows to incorporate, as the deductivebase of our formalism, some well-studied logics like the modal logic S5, the relevant logic RM, and Gödel–Dummett logic LC, to which no cut-free sequent calculi are known. In this paper we take S5 as the core logic and show that the hypersequent-based argumentation frameworks that are obtained in this case yield a robust defeasible variant of S5 with several desirable properties.

AAMAS Conference 2018 Conference Paper

Prioritized Sequent-Based Argumentation

• Ofer Arieli
• Annemarie Borg
• Christian Stra�er

In this paper we integrate priorities in sequent-based argumentation. The former is a useful and extensively investigated tool in the context of non-monotonic reasoning, and the latter is a modular and general way of handling logical argumentation. Their combination offers a platform for representing and reasoning with maximally consistent subsets of prioritized knowledge bases. Moreover, many frameworks of the resulting formalisms satisfy common rationality postulates and other desirable properties, like conflict preservation.

KR Conference 2016 Short Paper

Argumentative Approaches to Reasoning with Maximal Consistency

• Ofer Arieli
• Christian Strasser

Sequent-Based Argumentation Reasoning with the maximally consistent subsets (MCS) of the premises is a well-known approach for handling contradictory information. We introduce two argumentation-based methods for doing so: a declarative approach that is related to Dung-style semantics for abstract argumentation, and a computational approach that is based on extensions of Gentzentype proofs systems. This brings about a new perspective on reasoning with MCS which shows a strong link between the latter and argumentation systems, and which can be extended to related formalisms. A by-product of this is the introduction of a dynamic proof system for classical logic and rebuttal attacks, which is sound and complete with respect to Dung’s stable semantics for the associated argumentation framework. According to Dung (1995), abstract argumentation frameworks may be viewed as directed graphs as follows: Definition 1 An (abstract) argumentation framework is a pair AF = Args, Attack , where Args is a denumerable set of elements, called arguments, and Attack is a relation on Args ×Args, whose instances are called attacks. D A B C E Figure 1: An argumentation framework with five arguments and six attacks.

JELIA Conference 2012 Conference Paper

Conflict-Tolerant Semantics for Argumentation Frameworks

• Ofer Arieli

Abstract We introduce new kinds of semantics for abstract argumentation frameworks, in which, while all the accepted arguments are justified (in the sense that each one of them must be defended), they may still attack each other. The rationality behind such semantics is that in reality there are situations in which contradictory arguments coexist in the same theory, yet the collective set of accepted arguments is not trivialized, in the sense that other arguments may still be rejected. To provide conflict-tolerant semantics for argumentation frameworks we extend the two standard approaches for defining coherent (conflict-free) semantics for argumentation frameworks: the extension-based approach and the labeling-based approach. We show that the one-to-one relationship between extensions and labelings of conflict-free semantics is carried on to a similar correspondence between the extended approaches for providing conflict-tolerant semantics. Thus, in our setting as well, these are essentially two points of views for the same thing.

IJCAI Conference 2011 Conference Paper

What Is an Ideal Logic for Reasoning with Inconsistency?

• Ofer Arieli
• Arnon Avron
• Anna Zamansky

Many AI applications are based on some underlying logic that tolerates inconsistent information in a non-trivial way. However, it is not always clear what should be the exact nature of such a logic, and how to choose one for a specific application. In this paper, we formulate a list of desirable properties of `ideal' logics for reasoning with inconsistency, identify a variety of logics that have these properties, and provide a systematic way of constructing, for every n > 2, a family of such n-valued logics.

KR Conference 2010 Conference Paper

Maximally Paraconsistent Three-Valued Logics

• Ofer Arieli
• Arnon Avron
• Anna Zamansky

Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper, we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We first show that most of the logics that are based on properly non-deterministic three-valued matrices are not maximally paraconsistent. Then we show that in contrast, in the deterministic case all the natural three-valued paraconsistent logics are maximal. This includes well-known three-valued paraconsistent logics like P1, LP, J3, PAC and SRM3, as well as any extension of them obtained by enriching their languages with extra three-valued connectives. In this paper, we investigate strong maximality of paraconsistent logics based on three-valued deterministic and non-deterministic matrices. The former are one of the oldest and most common ways of defining a paraconsistent logic. The latter are a recent natural generalization of the former, introduced in (Avron and Lev 2005), in which nondeterministic interpretations of connectives are allowed. Under a very minimal and natural assumption about the interpretation of negation in these matrices, we show that in the deterministic case, all natural three-valued paraconsistent logics are maximal in the strong sense. Our result applies to such well-known paraconsistent logics as Sette’s logic P1, Priest’s LP, the semi-relevant logic SRM3, the logics PAC and J3, and any extension of one of these logics obtained by enriching its language with extra three-valued connectives. 1 In the non-deterministic case things are quite different, though. We show that paraconsistent logics induced by properly non-deterministic three-valued matrices are usually not maximal, except for a few special cases (which are fully characterized). However, even these exceptional cases are redundant, as we show that any maximally paraconsistent logic defined by an n-valued non-deterministic matrix can be fully characterized also by a deterministic one.

KR Conference 2010 Conference Paper

On the Application of the Disjunctive Syllogism in Paraconsistent Logics Based on Four States of Belief

• Ofer Arieli

We identify three classes of four-state paraconsistent logics according to their different approaches towards the disjunctive syllogism, and investigate three representatives of these approaches: Quasi-classical logic, which always accepts this principle, Belnap’s logic, that rejects the disjunctive syllogism altogether, and a logic of inconsistency minimization that restricts its application to consistent fragments only. These logics are defined in a syntactic and a semantic style, which are linked by a simple transformation. It is shown that the three formalisms accommodate knowledge minimization, and that the most liberal formalism towards the disjunctive syllogism is also the strongest among the three, while the most cautious logic is the weakest one.

JELIA Conference 2010 Conference Paper

Similarity-Based Inconsistency-Tolerant Logics

• Ofer Arieli
• Anna Zamansky

Abstract Many logics for AI applications that are defined by denotational semantics are trivialized in the presence of inconsistency. It is therefore often desirable, and practically useful, to refine such logics in a way that inconsistency does not cause the derivation of any formula, and, at the same time, inferences with respect to consistent premises are not affected. In this paper, we introduce a general method of doing so by incorporating preference relations defined in terms of similarities. We exemplify our method for three of the most common denotational semantics (standard many-valued matrices, their non-deterministic generalization, and possible worlds semantics), and demonstrate their usefulness for reasoning with inconsistency.

KR Conference 2008 Conference Paper

Accuracy and Efficiency of Fixpoint Methods for Approximate Query Answering in Locally Complete Databases

• &Aacute
• lvaro Cortés-Calabuig
• Marc Denecker
• Ofer Arieli
• Maurice Bruynooghe

Standard databases convey Reiter's closed-world assumption that an atom not in the database is false. This assumption is relaxed in locally closed databases that are sound but only partially complete about their domain. One of the consequences of the weakening of the closed-world assumption is that query answering in locally closed databases is undecidable. In this paper, we develop efficient approximate methods for query answering, based on fixpoint computations, and investigate conditions that assure the optimality of these methods. Our approach of approximative reasoning may be incorporated in different contexts where incompleteness plays a major role and efficient reasoning is imperative.

AAAI Conference 2007 Conference Paper

Approximate Query Answering in Locally Closed Databases

• Alvaro Cortes-Calabuig
• Ofer Arieli

The Closed-World Assumption (CWA) on databases expresses that an atom not in the database is false. A more appropriate assumption for databases that are sound but partially incomplete, is the Local Closed- World Assumption (LCWA), which is a local form of the CWA, expressing that the database is complete in a certain area, called the ‘window of expertise’. Databases consisting of a standard database instance augmented with a collection of LCWA’s are called locally closed databases. In this paper, we investigate the complexity of certain and possible query answering in such databases. As it turns out that these problems are intractable, we develop efficient approximate methods to underestimate certain answers and overestimate possible answers. We prove that under certain conditions, our methods produce complete answers.

TARK Conference 2007 Conference Paper

Commonsense reasoning by distance semantics

• Ofer Arieli

We introduce a uniform distance semantics for different paradigms that require nonmonotonic and paraconsistent reasoning, among which are mediators of independent data-sources, integrators of prioritized knowledge-bases, operators for iterated belief revision, and analytic tools of decision support systems. We show that the consequence relations that are induced by our framework share some desirable properties and demonstrate this by relevant applications.

JELIA Conference 2006 Conference Paper

Distance-Based Repairs of Databases

• Ofer Arieli
• Marc Denecker
• Maurice Bruynooghe

Abstract We introduce a general framework for repairing inconsistent databases by distance-based considerations. The uniform way of representing repairs and their semantics clarifies the essence behind various approaches to consistency restoration in database systems, helps to compare the underlying formalisms, and relates them to existing methods of defining belief revision operators, merging data sets, and integrating information systems.

LPAR Conference 2006 Conference Paper

Representation of Partial Knowledge and Query Answering in Locally Complete Databases

• Alvaro Cortés-Calabuig
• Marc Denecker
• Ofer Arieli
• Maurice Bruynooghe

Abstract The Local Closed-World Assumption (LCWA) is a generalization of Reiter’s Closed-World Assumption (CWA) for relational databases that may be incomplete. Two basic questions that are related to this assumption are: (1) how to represent the fact that only part of the information is known to be complete, and (2) how to properly reason with this information, that is: how to determine whether an answer to a database query is complete even though the database information is incomplete. In this paper we concentrate on the second issue based on a treatment of the first issue developed in earlier work of the authors. For this we consider a fixpoint semantics for declarative theories that represent locally complete databases. This semantics is based on 3-valued interpretations that allow to distinguish between the certain and possible consequences of the database’s theory.

ECAI Conference 2004 Conference Paper

Paraconsistent Preferential Reasoning by Signed Quantified Boolean Formulae

• Ofer Arieli

LPAR Conference 2001 Conference Paper

Coherent Composition of Distributed Knowledge-Bases Through Abduction

• Ofer Arieli
• Bert Van Nuffelen
• Marc Denecker
• Maurice Bruynooghe

Abstract We introduce an abductive method for coherent composition of distributed data. Our approach is based on an abductive inference procedure that is applied on a meta-theory that relates different, possibly inconsistent, input databases. Repairs of the integrated data are computed, resultingin a consistent output database that satisfies the meta-theory. Our framework is based on the A -system, which is an abductive system that implements SLDNFA-resolution. The outcome is a robust application that, to the best of our knowledge, is more expressive (thus more general) than any other existing application for coherent data integration.

JELIA Conference 2000 Conference Paper

An Algorithmic Approach to Recover Inconsistent Knowledge-Bases

• Ofer Arieli

Abstract We consider an algorithmic approach for revising inconsistent data and restoring its consistency. This approach detects the “spoiled” part of the data (i. e. , the set of assertions that cause inconsistency), deletes it from the knowledge-base, and then draws classical conclusions from the “recovered” information. The essence of this approach is its coherence with the original (possibly inconsistent) data: On one hand it is possible to draw classical conclusions from any data that is not related to the contradictory information, while on the other hand, the only inferences allowed by this approach are those that do not contradict any former conclusion. This method may therefore be used by systems that restore consistent information and are obliged to their resource of information. Common examples of this case are diagnostic procedures that analyse faulty components of malfunction devices, and database management systems that amalgamate distributed knowledgebases.

AIJ Journal 1998 Journal Article

The value of the four values

• Ofer Arieli
• Arnon Avron

In his well-known paper “How computer should think” Belnap (1977) argues that four-valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the four-valued structure has among Ginsberg's bilattices is similar to the role that the two-valued algebra has among Boolean algebras. Specifically, we provide several theorems that show that the most useful bilattice-valued logics can actually be characterized as four-valued inference relations. In addition, we compare the use of three-valued logics with the use of four-valued logics, and show that at least for the task of handling inconsistent or uncertain information, the comparison is in favor of the latter.

CSL Conference 1997 Conference Paper

Four-Valued Diagnoses for Stratified Knowledge-Bases

• Ofer Arieli
• Arnon Avron

Abstract We present a four-valued approach for recovering consistent data from inconsistent set of assertions. For a common family of knowledge-bases we also provide an efficient algorithm for doing so automaticly. This method is particularly useful for making model-based diagnoses.