Publications – Domingo López Rodríguez

Categories

All (30)

Aggregation (1)

Algorithm (17)

Approximate reasoning (3)

Approximation (1)

Association rules (3)

Bipolarity (1)

Bonds (4)

C++ (1)

CARVE (2)

Canonical basis (5)

CbO (4)

Clustering (1)

Cybersecurity (1)

Data mining (2)

Decomposition (2)

Embeddings (1)

Empirical analysis (1)

FCA (19)

Fuzzy FCA (11)

Fuzzy systems (1)

GCN (1)

Graph theory (2)

Heuristics (1)

Implications (7)

Knowledge discovery (1)

Lattice theory (10)

Logic (2)

Machine learning (3)

Malware (1)

Minimal generators (3)

Mixed attributes (4)

NLP (1)

Neural networks (1)

Neuroscience (1)

Optimization (3)

Parallel computing (1)

Performance (2)

Performance benchmark (1)

Publication idea (30)

Python (1)

R (1)

RDF (1)

Semantic web (1)

Similarity (1)

Similarity metrics (1)

Simplification (1)

Software (1)

Symbolic AI (1)

Theoretical CS (6)

Theoretical computer science (1)

Topic modeling (1)

XAI (2)

Ideas

A logic-based framework for mining and simplifying partial implications (association rules)

Association rules

Data mining

Logic

Simplification

FCA

Publication idea

Association rule mining creates many redundant rules. This paper proposes a formal ‘Simplification Logic’ (SLAR) to manipulate and reduce sets of association rules (with confidence < 1) to a smaller, non-redundant basis without losing information.

Domingo López Rodríguez, María Eugenia Cornejo Piñero

A native CbO algorithm for computing the mixed concept lattice

FCA

Mixed attributes

Algorithm

Optimization

CbO

Publication idea

This idea proposes a new ‘native’ CbO-style algorithm (Mixed-InClose) for computing mixed concept lattices. It operates directly on contexts with positive and negative attributes, using logical pruning to be more efficient than attribute-doubling or projection-based methods.

Domingo López Rodríguez, Francisco Pérez Gámez, Simon Andrews

A pyramidal approach for parallel computation of the Luxenburger basis

FCA

Algorithm

Parallel computing

Association rules

Publication idea

This paper introduces a novel pyramidal, divide-and-conquer algorithm for computing the Luxenburger basis of association rules. We develop a ‘recombination operator’ to synthesize partial bases in parallel, aiming to make the computation feasible for contexts with many attributes.

Domingo López Rodríguez

A rigorous foundation for the pseudo-intent in fuzzy formal concept analysis: The notion of essential generator

Fuzzy FCA

Theoretical CS

Canonical basis

Implications

Lattice theory

Publication idea

This research proposes a new, robust definition for pseudo-intents in fuzzy FCA. We define them by their functional role as ‘essential generators’, which we prove leads to a sound, complete, and non-redundant implication basis, solving issues from previous definitions.

Domingo López Rodríguez

A unified view of inter-contextual similarity: Bonds, intermediate quantifiers, and metrics on concept lattices

FCA

Lattice theory

Bonds

Similarity metrics

Theoretical computer science

Publication idea

This paper develops a unified theory of FCA bonds, moving beyond the simple universal/existential dichotomy. We introduce ‘intermediate quantifiers’ for more flexible bond construction and formalize the notion of a bond as a similarity metric that quantifies the structural coherence between two concept lattices.

Domingo López Rodríguez, Ondrej Krídlo, Samuel Molina Ruiz, Dominika Kotlárová

Advanced property inference in RDF graphs using approximate and generalized bonds

RDF

Semantic web

FCA

Bonds

Approximate reasoning

Algorithm

Publication idea

This paper extends our prior work on RDF property inference by applying two new theories: approximate bonds and intermediate-quantifier bonds. This allows our FCA-based method to handle noisy data more robustly and gives users fine-grained control over the inference process. We demonstrate this provides a more flexible and powerful tool for knowledge graph completion.

Domingo López Rodríguez, Marek Reformat, Ondrej Krídlo, Manuel Ojeda Aciego

Approximation of fuzzy concept lattices by similarity

Fuzzy FCA

Algorithm

Approximation

Lattice theory

Similarity

Publication idea

This research tackles the ‘concept explosion’ problem in L-FCA by proposing a formal method for lattice approximation. We investigate using different similarity measures to select a representative subset of concepts. The goal is an algorithm that computes this smaller, approximated lattice directly.

Domingo López Rodríguez, Radim Bělohlávek, Ángel Mora Bonilla, Manuel Ojeda Hernández

Beyond certainty: Defining and analyzing relevance measures for formal implications

FCA

Implications

Association rules

Knowledge discovery

Data mining

Publication idea

This paper addresses the “informativity” problem of large canonical bases in FCA. We propose a framework of relevance measures (like lift, improvement, and stability) adapted from association rule mining to filter and rank formal implications, making them more interpretable and useful for domain experts.

Domingo López Rodríguez, Kira Adaricheva

Characterization of consistent aggregation functions for fuzzy concept lattices

Fuzzy FCA

Lattice theory

Aggregation

Theoretical CS

Publication idea

This research explores ‘consistent’ aggregation functions for generating fuzzy concepts. We provide a complete theoretical characterization of these functions, proving they must take a specific form involving a residuum. This opens a path for new generative algorithms for lattice construction.

Domingo López Rodríguez, Carlos Bejines, Manuel Ojeda-Hernández

Computing minimal generators in mixed contexts: A direct approach

FCA

Mixed attributes

Minimal generators

Algorithm

Publication idea

This paper proposes a direct algorithm for computing the minimal generators of a mixed context, avoiding prior decomposition. It uses the simplification logic for mixed attributes to define and identify these generators natively, offering a more streamlined and efficient path.

Domingo López Rodríguez, Francisco Pérez Gámez

Computing the canonical basis in L-FCA: An adaptation of CbO algorithms

Fuzzy FCA

Algorithm

Canonical basis

Implications

CbO

Publication idea

This paper addresses the lack of efficient algorithms for computing the L-fuzzy canonical basis. We introduce a formal definition for L-fuzzy pseudo-intents and develop ‘Fuzzy LinCbO’, the first CbO-based algorithm to solve this problem, bridging a critical gap in logical knowledge extraction for graded data.

Domingo López Rodríguez, Manuel Ojeda Hernández, Jan Konečný, Simon Andrews

Computing the complete lattice of bonds via a close-by-one strategy

FCA

Bonds

Algorithm

Lattice theory

CbO

Publication idea

This paper fills a major algorithmic gap in FCA by proposing ‘Bond-CbO’, the first algorithm to compute the complete lattice of bonds. We adapt the Close-by-One strategy by defining the necessary theoretical building blocks, such as ‘maximal bonds’ and a bond infimum operator. This provides the first practical method for exploring the entire space of inter-contextual relationships.

Domingo López Rodríguez, Samuel Molina Ruiz

Detecting malware families via minimal generators of behavioral concepts

Cybersecurity

FCA

Algorithm

Minimal generators

Malware

Publication idea

This paper proposes a novel FCA-based malware detection framework. We use the minimal generators of behavioral concepts as robust, interpretable signatures to classify malware. This method provides high accuracy and clear, human-readable explanations for security analysts.

Domingo López Rodríguez, Manuel Ojeda-Hernández, Ángel Mora

Direct implication bases in L-FCA: A generalization of the exchange condition to residuated lattices

Fuzzy FCA

Lattice theory

Theoretical CS

Implications

Publication idea

This research aims to solve a key open problem in L-FCA: generalizing the ‘exchange condition’ to arbitrary residuated lattices. By providing this theoretical characterization for direct implication bases, this work paves the way for new algorithms that can compute L-fuzzy closures in linear time.

Domingo López Rodríguez, Manuel Ojeda-Hernández, Kira Adaricheva

Extending contextual decomposition to L-FCA: The fuzzy CARVE algorithm

Fuzzy FCA

Algorithm

Decomposition

CARVE

Publication idea

This idea extends the CARVE decomposition algorithm to L-fuzzy contexts (Fuzzy CARVE). We introduce ‘alpha-universality’ as a graded version of universal elements and prove how the L-fuzzy lattice can be reconstructed after decomposition. This aims to provide a ‘divide-and-conquer’ strategy for L-FCA.

Domingo López Rodríguez, Tim Pattison

Extending contextual decomposition: Efficient concept lattice construction via articulation points

FCA

Algorithm

Graph theory

Lattice theory

Publication idea

This research idea proposes a new algorithm (APD) for efficient concept lattice construction. It uses a graph-theoretic decomposition based on articulation points, making it effective for dense contexts where traditional methods like CARVE fail.

Domingo López Rodríguez

From decomposition to deduction: Computing the canonical basis with AUGMENTED CARVE

FCA

Algorithm

Canonical basis

Implications

Decomposition

CARVE

Publication idea

This paper extends the AUGMENTED CARVE algorithm to compute the minimal (canonical) basis of implications directly. We propose new synthesis rules and a method for ‘pseudo-intent propagation’ to filter redundancies during the divide-and-conquer process, aiming to be faster than monolithic algorithms.

Domingo López Rodríguez, Manuel Ojeda-Hernández, Tim Pattison

From lattices to logic: Adapting the InClose algorithm for efficient canonical basis computation

FCA

Algorithm

Canonical basis

Implications

Optimization

Publication idea

This paper extends the efficient InClose algorithm from lattice generation to computing the canonical basis of implications. We present InClose-Imp, a new method that integrates pseudo-intent checking into InClose’s incremental framework, providing a competitive alternative to traditional algorithms.

Domingo López Rodríguez, Simon Andrews

From simplification to minimality: Computing the canonical basis of mixed implications

FCA

Mixed attributes

Canonical basis

Implications

Algorithm

Publication idea

This paper moves beyond simplifying mixed implications to finding the true canonical basis. We define the ‘mixed pseudo-intents’ needed to establish minimality. The goal is a direct algorithm to compute this minimal basis, completing the theory for logical systems with bipolar information.

Domingo López Rodríguez, Francisco Pérez Gámez, Manuel Ojeda Aciego

Graded preconcept lattices: An extension of FCA using functional degrees of inclusion and similarity

Fuzzy FCA

Lattice theory

Theoretical CS

Approximate reasoning

Publication idea

This paper introduces a more nuanced FCA framework by defining a ‘degree of conceptuality’ for any pair of fuzzy sets (a preconcept). This creates a graded lattice where standard concepts are the top-cut, and lower cuts represent ‘approximate’ lattices. The idea is also extended to implications, defining ‘phi-valid’ rules.

Domingo López Rodríguez, Manuel Ojeda Aciego, Nicolás Madrid

L-mixed formal concept analysis: Integrating graded truth and bipolarity

Fuzzy FCA

Mixed attributes

Lattice theory

Theoretical CS

Bipolarity

Publication idea

This research introduces ‘L-Mixed FCA’, a new framework that unifies graded truth (L-FCA) and bipolar information (mixed FCA). It models data using pairs of values (certainty of presence, possibility of presence) to handle complex, real-world uncertainty in a single, expressive model.

Domingo López Rodríguez, Jan Konečný

Logical validation of neural networks: An explainable AI framework based on formal concept analysis

XAI

FCA

Neural networks

Machine learning

Logic

Publication idea

This paper proposes an XAI framework using Formal Concept Analysis (FCA) to validate neural networks. We generate a ‘local’ context around a prediction, compute its implication basis, and score its ‘local logical consistency’ against the global data. We also suggest using this score as a new loss function.

Domingo López Rodríguez, Inmaculada de las Peñas Cabrera, Yadira Hernández Solano

Mining minimal generators with Close-by-One: A unified algorithm for binary and L-fuzzy contexts

FCA

Fuzzy FCA

Algorithm

Minimal generators

CbO

Publication idea

This paper proposes a unified algorithm for computing minimal generators by integrating the computation directly into the Close-by-One (CbO) framework. This single-pass approach works for both binary and L-fuzzy contexts, providing the first CbO-based method for fuzzy minimal generator computation.

Domingo López Rodríguez

On the efficiency of native vs. scaled algorithms for L-fuzzy concept lattice construction: An empirical analysis

Fuzzy FCA

Algorithm

Empirical analysis

Performance benchmark

Publication idea

This paper presents a large-scale empirical study comparing ‘native’ fuzzy algorithms against ‘scaled’ binary algorithms for L-fuzzy concept lattice construction. We identify the performance ‘tipping points’ based on context density and grade set size, providing clear guidelines for practitioners.

Domingo López Rodríguez, Ángel Mora, Manuel Ojeda Hernández

Optimizing CbO-based algorithms via heuristic attribute reordering in L-fuzzy contexts

Fuzzy FCA

Algorithm

Optimization

Performance

Heuristics

Publication idea

This paper investigates how reordering attributes in L-fuzzy contexts affects CbO algorithm performance. We propose and test heuristics, like ordering by non-zero entries or lower cone size, and show they can reduce runtime by up to 40%, providing a guide for selecting the best pre-processing strategy.

Domingo López Rodríguez, Jan Konečný

Robust inter-contextual linking: A theory of approximate bonds in FCA

FCA

Bonds

Approximate reasoning

Lattice theory

Publication idea

The standard definition of a bond in FCA is too strict for noisy data. This paper introduces ‘approximate bonds,’ which use similarity operators and tolerance thresholds to allow for a controlled degree of imperfection. This robust framework is better suited for practical applications.

Domingo López Rodríguez

Rule embeddings via lattice geometry: An algebraic approach to continuous representation of formal implications

FCA

Embeddings

Machine learning

Theoretical CS

Symbolic AI

Publication idea

This research introduces Rule2Vec_Alg, a novel, deterministic method to embed FCA’s logical implications into a continuous vector space. The algebraic approach preserves the Galois closure and lattice structure by design, bridging symbolic AI with geometric deep learning.

Domingo López Rodríguez

The F-transform on graphs: A novel interpretable layer for graph convolutional networks with application to brain connectome analysis

Fuzzy systems

GCN

XAI

Machine learning

Graph theory

Neuroscience

Publication idea

This paper extends the F-transform to weighted graphs, creating a new interpretable ‘F-Conv’ layer for GCNs. We apply it to brain connectome analysis, achieving high accuracy with full model transparency, unlike traditional black-box GCNs.

Domingo López Rodríguez (in collaboration with Prof. Irina Perfilieva’s Research Group)

Unsupervised topic modeling via implication clustering

FCA

Topic modeling

NLP

Clustering

Algorithm

Publication idea

This paper introduces a novel topic modeling framework using Formal Concept Analysis (FCA). By clustering the canonical basis of implications from a text, our method automatically discovers the optimal number of topics, offering a competitive, logic-based alternative to LDA.

Domingo López Rodríguez, L’ubomír Antoni, Ángel Mora Bonilla, Manuel Ojeda Hernández

fca-core: A high-performance C++ backend for multi-language formal concept analysis

FCA

Software

C++

R

Python

Performance

Publication idea

This paper presents fca-core, a new high-performance C++ library for FCA algorithms. It is designed with a C API to provide lightweight wrappers for languages like R (powering the new fcaR) and Python. Benchmarks show this backend provides speedups of one to two orders of magnitude, making large-scale FCA more accessible.

Domingo López Rodríguez, Dominik Dürrschnabel, Johannes Hirth, Tobias Hille, and the GIMAC group