Broadening the Applicability of Conditional Syntax Splitting for Reasoning from Conditional Belief Bases
Authors: Lars-Phillip Spiegel, Jonas Haldimann, Jesse Heyninck, Gabriele Kern-Isberner, Christoph Beierle
Organizations: FernUniversität in Hagen, Hagen, Germany · University of Cape Town and CAIR, Cape Town, South Africa · TU Wien, Vienna, Austria · Open Universiteit, Heerlen, 6419 AT, the Netherlands · TU Dortmund University, Dortmund, Germany
In nonmonotonic reasoning from conditional belief bases, an inference operator satisfying syntax splitting postulates allows for taking only the relevant parts of a belief base into account, provided that the belief base splits into subbases based on disjoint signatures. Because such disjointness is rare in practice, safe conditional syntax splitting has been proposed as a generalization of syntax splitting, allowing the conditionals in the subbases to share some atoms. Recently this overlap of conditionals has been shown to be limited to trivial, self-fulfilling conditionals. In this article, we propose a generalization of safe conditional syntax splittings that broadens the applicability of splitting postulates. In contrast to safe conditional syntax splitting, our generalized notion supports syntax splittings of a belief base Δ where the subbases of Δ may share atoms and nontrivial conditionals. We illustrate how this new notion overcomes limitations of previous splitting concepts, and we identify genuine splittings, separating them from simple splittings that do not provide benefits for inductive inference from Δ. We introduce adjusted inference postulates based on our generalization of conditional syntax splitting, and we evaluate several popular inductive inference operators with respect to these postulates. Furthermore, we show that, while every inductive inference operator satisfying generalized conditional syntax splitting also satisfies conditional syntax splitting, the reverse does not hold.
Figures & tables
Figure 1: The order <Δblex over worlds from Example 20 . The corresponding values of ∣ξΔb0(ω)∣,∣ξΔb1(ω)∣ are indicated on the left.
Figure 2: The preferred structure on worlds <Δbw in Example 27 . An edge ω→ω′ indicates that ω<Δbwω′ ; edges that can be obtained from transitivity are omitted.
Figure 3: Transformation rules {R1,…,R6} for simplifying (the constraint-inducing sets of) CR(Δ) . A pair ⟨V,F⟩i represents the sets of constraint variables in the minimum expressions associated to the verification and the falsification, respectively, of the i -th conditional δi∈Δ in the constraint Ci∈CR(Δ) modeling the acceptance condition of δi .
We present TruthSplit, an interactive system for multi-perspective argument analysis. Existing argumentation tools typically analyze properties of the argument itself, such as structure, quality, stance, or persuasiveness, while leaving perspective-specific background knowledge implicit. TruthSplit addresses this gap by supporting an exploratory analysis of how the same claim can lead to different conclusions when interpreted through worldview-specific values, assumptions, and conceptual definitions. We refer to this perspective-dependent analysis as conditional validity. Given an input argumentative text, TruthSplit extracts claims and premises, applies a three-layer natural language inference (NLI) approach to assess both logical and worldview-specific normative consistency, and conditions large language model (LLM) reasoning on structured worldview profiles that encode core values and decision principles. The system then generates perspective-specific interpretations, identifies value conflicts and assumption gaps, and visualizes divergence through interactive analytical interfaces.
Benjamin Stieger, Maximilian Terberger, Thomas Huber +1
This work proposes novel splitting techniques for argumentation formalisms that incorporate supports between defeasible elements. We base our studies on bipolar set-based argumentation frameworks (BSAFs) which generalize argumentation frameworks with collective attacks (SETAFs), as well as bipolar argumentation frameworks (BAFs), by incorporating both collective attacks and supports. Notably, BSAFs establish a crucial link to structured argumentation as they naturally capture general (potentially non-flat) assumption-based argumentation. The increase in expressiveness calls for diverse forms of splitting. We consider splits over collective attacks (thereby generalizing the recently proposed splitting techniques for SETAFs), splits over collective supports, as well as splits over both collective attacks and supports. We establish suitable splitting schemata and prove their correctness for the most common argumentation semantics.
Matti Berthold, Lydia Blümel, Giovanni Buraglio +1
FernUniversität in Hagen, Germany · TU Wien, Austria · TU Dortmund, Germany
Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first step in a reasoning chain based on belief functions is inference: how to learn a belief measure from the available data. In this survey we focus, in particular, on making inference from statistical data, and review the most significant contributions in the area.
Fabio Cuzzolin
Institute for AI, Data Analysis and Systems (AIDAS) · School of Engineering, Computing & Mathematics, Oxford Brookes University