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Aggregation functions are generally defined and used to combine several numerical values into a single one, so that the final result of the aggregation takes into account all the individual values in a given manner. Such functions are…
Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
This paper presents a formal approach to explaining change of inference in Quantitative Bipolar Argumentation Frameworks (QBAFs). When drawing conclusions from a QBAF and updating the QBAF to then again draw conclusions (and so on), our…
Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive…
Causal models are playing an increasingly important role in machine learning, particularly in the realm of explainable AI. We introduce a conceptualisation for generating argumentation frameworks (AFs) from causal models for the purpose of…
Subadditive set functions play a pivotal role in computational economics (especially in combinatorial auctions), combinatorial optimization or artificial intelligence applications such as interpretable machine learning. However, specifying…
This paper provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted…
In recent years, numerous mathematical models of opinion formation have been developed, incorporating diverse interaction mechanisms such as imitation and majority rule. However, limited attention has been given to models grounded in…
Generating a concise summary from a large collection of arguments on a given topic is an intriguing yet understudied problem. We propose to represent such summaries as a small set of talking points, termed "key points", each scored…
Inspired from a joint work by A. Beckmann, S. Buss and S. Friedman, we propose a class of set-theoretic functions, predicatively computable functions. Each function in this class is polynomial time computable when we restrict to finite…
A common problem in various applications is the additive decomposition of the output of a function with respect to its input variables. Functions with binary arguments can be axiomatically decomposed by the famous Shapley value. For the…
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine--grained…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
Argumentation is one of society's foundational pillars, and, sparked by advances in NLP and the vast availability of text data, automated mining of arguments receives increasing attention. A decisive property of arguments is their strength…
A "numerical set-expression" is a term specifying a cascade of arithmetic and logical operations to be performed on sets of non-negative integers. If these operations are confined to the usual Boolean operations together with the result of…
In this work, which is done in the context of a (moded) logic programming language, we devise a data-flow analysis dedicated to computing what we call argument profiles. Such a profile essentially describes, for each argument of a…
In formal argumentation, a distinction can be made between extension-based semantics, where sets of arguments are either (jointly) accepted or not, and ranking-based semantics, where grades of acceptability are assigned to arguments.…
Inspired by e-participation systems, in this paper we propose a new model to represent human debates and methods to obtain collective conclusions from them. This model overcomes drawbacks of existing approaches by allowing users to…