arXiv subjects

Amelia Bădică

Publications and source records attributed to Amelia Bădică.

4 recordsLinked to original sources

arXiv2026

On the Triangle Inequality for the Jaccard Distance in Arbitrary Lattices

This paper presents new theoretical results on generalizing the Jaccard distance for lattices and real valuations. We demonstrate that when the valuation is strictly positive, monotone, and modular, the Jaccard distance satisfies the triangle inequality on arbitrary lattices, effectively generalizing earlier results that depended heavily on distributivity. Moving to relatively complemented distributive lattices (which safely drop the requirement for the global bounds found in Boolean algebras), we prove the triangle inequality holds as long as the valuation is positive, monotone, supermodular, and $\log$-submodular. Additionally, we adapt the symmetric-difference Jaccard formulation for submodular valuations to sectionally complemented distributive lattices. Shifting to necessary conditions, we prove that supermodularity is a strict requirement for the standard generalized Jaccard distance to operate as a valid metric. Finally, we map the practical value of relaxing these structural constraints to computational fields like quantum information theory, formal concept analysis, and machine learning, closing with a brief look at open mathematical problems.

cs.AI↗

arXiv2026

Foundations of MT-PDCL: Measure-Theoretic Probabilistic Definite Clause Logic

Standard probabilistic logic programming frameworks typically rely on grounding logic programs into discrete propositional representations. This operational requirement restricts exact inference to finite domains and discrete probability distributions. In this paper, we introduce Measure-Theoretic Probabilistic Definite Clause Logic (MT-PDCL), a generalized foundational framework that eliminates this finite-domain restriction. By explicitly defining stochastic variables over bounded index domains and equipping the interpretation space with standard Borel $σ$-algebras, MT-PDCL allows logical variables to operate natively over continuous measurable spaces. Building on Continuous Distribution Semantics, MT-PDCL models probabilistic rules as mutually independent causal events. However, rather than aggregating these derivations via finite boolean circuits, declarative entailment is formally defined through exact Lebesgue integration over the continuous measure space. We introduce a continuous immediate consequence operator that unifies the integration of continuous prior distributions with the evaluation of exact continuous observations. We demonstrate that this approach replaces the combinatorial bottleneck of discrete grounding with exact, algebraic, and structurally differentiable inference. While this transition trades discrete combinatorics for the geometric curse of dimensionality, it achieves the expressive power of continuous probabilistic models while preserving the pure declarative syntax of definite clause logic.

cs.AI↗

arXiv2025

Contemporary Agent Technology: LLM-Driven Advancements vs Classic Multi-Agent Systems

This contribution provides our comprehensive reflection on the contemporary agent technology, with a particular focus on the advancements driven by Large Language Models (LLM) vs classic Multi-Agent Systems (MAS). It delves into the models, approaches, and characteristics that define these new systems. The paper emphasizes the critical analysis of how the recent developments relate to the foundational MAS, as articulated in the core academic literature. Finally, it identifies key challenges and promising future directions in this rapidly evolving domain.

cs.MA↗

arXiv2023

Exploring usability of Reddit in data science and knowledge processing

This contribution argues that Reddit, as a massive, categorized, open-access dataset, is a useful data source, for "almost any topic". Hence, it can be used in data science, e.g. for knowledge exploration. This statement is backed-up with presented analysis, based on 180 manually annotated papers, related to Reddit itself, and data acquired from popular databases of scientific papers. Finally, an open source tool is introduced, which provides an easy access to Reddit resources, and an exploratory data analysis of how Reddit covers selected topics. These functions can be used as a prelude analysis to a broader exploration of Reddit's applicability.

cs.IR↗