Decomposing Inconsistencies: Marginal Contributions and Pooling Techniques

Authors: Christian Straßer, Badran Raddaoui, Said Jabbour

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Reproducibility Variable Result LLM Response
Research Type Theoretical We propose a systematic framework for deriving local inconsistency measures from global ones by employing notions of marginal contributions inspired by cooperative game theory, including Shapley and Banzhaf values. Conversely, we explore methods for constructing global inconsistency measures by aggregating local contributions using various pooling techniques. A key research question arises: which combinations of marginal contribution notions (ma C) and pooling mechanisms (P) are compatible? Compatibility is defined such that, given a global measure I, applying (P) to the marginal contributions derived from I yields the same result as directly applying I, and vice versa. We analyze this compatibility condition and identify specific pairs of methods, (ma C) and (P), that satisfy it across various inconsistency frameworks. Our findings provide a deeper understanding of the interplay between global and local inconsistency measures, providing a foundation for designing principled and interpretable inconsistency evaluation methods in logic-based systems. The main result of our study is that for each of the three g2l-approaches to obtain local measures via marginal contributions from global measures, a l2g-pooling method can be identified, under which we obtain retracting pairs of measures, and vice versa.
Researcher Affiliation Academia Christian Straßer1 , Badran Raddaoui2 , Said Jabbour3 1Institute for Philosophy II, Ruhr Universit at Bochum, Germany 2SAMOVAR, T el ecom Sud Paris, Institut Polytechnique de Paris, France 3CRIL, Universit e d Artois & CNRS, France EMAIL, EMAIL, EMAIL
Pseudocode No The paper does not contain any explicit pseudocode or algorithm blocks. It primarily consists of mathematical definitions, theorems, lemmas, and proofs.
Open Source Code No The paper discusses theoretical concepts and frameworks. It does not contain any statements about providing open-source code for the described methodology, nor does it provide links to code repositories.
Open Datasets No This paper is theoretical and focuses on mathematical definitions and properties of inconsistency measures within propositional logic. It does not refer to or use any specific datasets for empirical evaluation.
Dataset Splits No As the paper is theoretical and does not conduct experiments on datasets, there is no mention of dataset splits (training, validation, test).
Hardware Specification No The paper is theoretical and presents a formal framework; therefore, it does not describe any specific hardware used for experiments.
Software Dependencies No The paper is theoretical and focuses on logical frameworks and proofs. It does not mention any specific software dependencies or version numbers needed for replication.
Experiment Setup No As a theoretical paper, it does not describe experimental setups, hyperparameters, or training configurations.