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Kees van Berkel

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4 papers

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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).

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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.

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JAIR Journal 2024 Journal Article

Proof Theory and Decision Procedures for Deontic STIT Logics

Tim S. Lyon
Kees van Berkel

This paper provides a set of cut-free complete sequent-style calculi for deontic STIT (‘See To It That’) logics used to formally reason about choice-making, obligations, and norms in a multi-agent setting. We leverage these calculi to write a proof-search algorithm deciding deontic, multi-agent STIT logics with (un)limited choice and introduce a loop-checking mechanism to ensure the termination of the algorithm. Despite the acknowledged potential for deontic reasoning in the context of autonomous, multi-agent scenarios, this work is the first to provide a syntactic decision procedure for this class of logics. Our proofsearch procedure is designed to provide verifiable witnesses/certificates of the (in)validity of formulae, which permits an analysis of the (non)theoremhood of formulae and act as explanations thereof. We show how the proof system and decision algorithm can be used to automate normative reasoning tasks such as duty checking (viz. determining an agent’s obligations relative to a given knowledge base), compliance checking (viz. determining if a choice, considered by an agent as potential conduct, complies with the given knowledge base), and joint fulfillment checking (viz. determining whether under a specified factual context an agent can jointly fulfill all their duties).

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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.

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