Orfeas Menis Mastromichalakis, Jason Liartis, Kristina Rose, Antoine Isaac, Giorgos Stamou. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.

Riddle-solving requires advanced reasoning skills, pushing Large Language Models (LLMs) to engage in abstract thinking and creative problem-solving, often revealing limitations in their cognitive abilities. In this paper, we examine the riddle-solving capabilities of LLMs using a multiple-choice format, exploring how different prompting techniques impact performance on riddles that demand diverse reasoning skills. To enhance results, we introduce RISCORE (RIddle Solving with COntext REcontruciton) a novel fully automated prompting method that generates and utilizes contextually reconstructed sentence-based puzzles in conjunction with the original examples to create few-shot exemplars. Our experiments demonstrate that RISCORE significantly improves the performance of language models in both vertical and lateral thinking tasks, surpassing traditional exemplar selection strategies across a variety of few-shot settings.

The advent of Large Language Models (LLMs) has revolutionized product recommenders, yet their susceptibility to adversarial manipulation poses critical challenges, particularly in realworld commercial applications.Our approach is the first one to tap into human psychological principles, seamlessly modifying product descriptions, making such manipulations hard to detect.In this work, we investigate cognitive biases as black-box adversarial strategies, drawing parallels between their effects on LLMs and human purchasing behavior.Through extensive evaluation across models of varying scale, we find that certain biases, such as social proof, consistently boost product recommendation rate and ranking, while others, like scarcity and exclusivity, surprisingly reduce visibility.Our results demonstrate that cognitive biases are deeply embedded in state-of-the-art LLMs, leading to highly unpredictable behavior in product recommendations and posing significant challenges for effective mitigation. 1

Machine Translation (MT) systems frequently encounter gender-ambiguous occupational terms, where they must assign gender without explicit contextual cues.While individual translations in such cases may not be inherently biased, systematic patterns-such as consistently translating certain professions with specific genders-can emerge, reflecting and perpetuating societal stereotypes.This ambiguity challenges traditional instance-level singleanswer evaluation approaches, as no single gold standard translation exists.To address this, we introduce GRAPE, a probability-based metric designed to evaluate gender bias by analyzing aggregated model responses.Alongside this, we present GAMBIT, a benchmarking dataset in English with gender-ambiguous occupational terms.Using GRAPE, we evaluate several MT systems and examine whether their gendered translations in Greek and French align with or diverge from societal stereotypes, real-world occupational gender distributions, and normative standards 1 .

Contract review is a complex and time-intensive task that typically demands specialized legal expertise, rendering it largely inaccessible to non-experts. Moreover, legal interpretation is rarely straightforward—ambiguity is pervasive, and judgments often hinge on subjective assessments. Compounding these challenges, contracts are usually confidential, restricting their use with proprietary models and necessitating reliance on open-source alternatives. To address these challenges, we introduce PAKTON: a fully open-source, end-to-end, multi-agent framework with plug-and-play capabilities. PAKTON is designed to handle the complexities of contract analysis through collaborative agent workflows and a novel retrieval-augmented generation (RAG) component, enabling automated legal document review that is more accessible, adaptable, and privacy-preserving. Experiments demonstrate that PAKTON outperforms both general-purpose and pretrained models in predictive accuracy, retrieval performance, explainability, completeness, and grounded justifications as evaluated through a human study and validated with automated metrics.

Multimodal models are critical for music understanding tasks, as they capture the complex interplay between audio and lyrics. However, as these models become more prevalent, the need for explainability grows—understanding how these systems make decisions is vital for ensuring fairness, reducing bias, and fostering trust. In this paper, we introduce MusicLIME, a model-agnostic feature importance explanation method designed for multimodal music models. Unlike traditional unimodal methods, which analyze each modality separately without considering the interaction between them, often leading to incomplete or misleading explanations, MusicLIME reveals how audio and lyrical features interact and contribute to predictions, providing a holistic view of the model’s decision-making. Additionally, we enhance local explanations by aggregating them into global explanations, giving users a broader perspective of model behavior. Through this work, we contribute to improving the interpretability of multimodal music models, empowering users to make informed choices, and fostering more equitable, fair, and transparent music understanding systems.

Despite the dominance of convolutional and transformer-based architectures in image-to-image retrieval, these models are prone to biases arising from low-level visual features, such as color. Recognizing the lack of semantic understanding as a key limitation, we propose a novel scene graph-based retrieval framework that emphasizes semantic content over superficial image characteristics. Prior approaches to scene graph retrieval predominantly rely on supervised Graph Neural Networks (GNNs), which require ground truth graph pairs driven from image captions. However, the inconsistency of caption-based supervision stemming from variable text encodings undermine retrieval reliability. To address these, we present SCENIR, a Graph Autoencoder-based unsupervised retrieval framework, which eliminates the dependence on labeled training data. Our model demonstrates superior performance across metrics and runtime efficiency, outperforming existing vision-based, multimodal, and supervised GNN approaches. We further advocate for Graph Edit Distance (GED) as a deterministic and robust ground truth measure for scene graph similarity, replacing the inconsistent caption-based alternatives for the first time in image-to-image retrieval evaluation. Finally, we validate the generalizability of our method by applying it to unannotated datasets via automated scene graph generation, while substantially contributing in advancing state-of-the-art in counterfactual image retrieval. The source code is available at https://github.com/nickhaidos/scenir-icml2025.

Learning to cooperate in distributed partially observable environments with no communication abilities poses significant challenges for multi-agent deep reinforcement learning (MARL). This paper addresses key concerns in this domain, focusing on inferring state representations from individual agent observations and leveraging these representations to enhance agents' exploration and collaborative task execution policies. To this end, we propose a novel state modelling framework for cooperative MARL, where agents infer meaningful belief representations of the non-observable state, with respect to optimizing their own policies, while filtering redundant and less informative joint state information. Building upon this framework, we propose the MARL SMPE$^2$ algorithm. In SMPE$^2$, agents enhance their own policy's discriminative abilities under partial observability, explicitly by incorporating their beliefs into the policy network, and implicitly by adopting an adversarial type of exploration policies which encourages agents to discover novel, high-value states while improving the discriminative abilities of others. Experimentally, we show that SMPE$^2$ outperforms a plethora of state-of-the-art MARL algorithms in complex fully cooperative tasks from the MPE, LBF, and RWARE benchmarks.

Recent black-box counterfactual generation frameworks fail to take into account the semantic content of the proposed edits, while relying heavily on training to guide the generation process. We propose a novel, plug-and-play black-box counterfactual generation framework, which suggests step-by-step edits based on theoretical guarantees of optimal edits to produce human-level counterfactual explanations with zero training. Our framework utilizes a pre-trained image editing diffusion model, and operates without access to the internals of the classifier, leading to an explainable counterfactual generation process. Throughout our experimentation, we showcase the explanatory gap between human reasoning and neural model behavior by utilizing both Convolutional Neural Network (CNN), Vision Transformer (ViT) and Large Vision Language Model (LVLM) classifiers, substantiated through a comprehensive human evaluation.

As machine learning (ML) models and datasets increase in complexity, the demand for methods that enhance explainability and interpretability becomes paramount. Prototypes, by encapsulating essential characteristics within data, offer insights that enable tactical decision-making and enhance transparency. Traditional prototype methods often rely on sub-symbolic raw data and opaque latent spaces, reducing explainability and increasing the risk of misinterpretations. This paper presents a novel framework that utilizes semantic descriptions to define prototypes and provide clear explanations, effectively addressing the shortcomings of conventional methods. Our approach leverages concept-based descriptions to cluster data on the semantic level, ensuring that prototypes not only represent underlying properties intuitively but are also straightforward to interpret. Our method simplifies the interpretative process and effectively bridges the gap between complex data structures and human cognitive processes, thereby enhancing transparency and fostering trust. Our approach outperforms existing widely-used prototype methods in facilitating human understanding and informativeness, as validated through a user survey.

The era of transfer learning has revolutionized the fields of Computer Vision and Natural Language Processing, bringing powerful pretrained models with exceptional performance across a variety of tasks. Specifically, Natural Language Processing tasks have been dominated by transformer-based language models. In Natural Language Inference and Natural Language Generation tasks, the BERT model and its variants, as well as the GPT model and its successors, demonstrated exemplary performance. However, the majority of these models are pretrained and assessed primarily for the English language or on a multilingual corpus. In this paper, we introduce GreekBART, the first Seq2Seq model based on BART-base architecture and pretrained on a large-scale Greek corpus. We evaluate and compare GreekBART against BART-random, Greek-BERT, and XLM-R on a variety of discriminative tasks. In addition, we examine its performance on two NLG tasks from GreekSUM, a newly introduced summarization dataset for the Greek language. The model, the code, and the new summarization dataset will be publicly available.

Exploring the capabilities of Large Language Models (LLMs) in puzzle solving unveils critical insights into their potential and challenges in AI, marking a significant step towards understanding their applicability in complex reasoning tasks.This survey leverages a unique taxonomy-dividing puzzles into rule-based and rule-less categories-to critically assess LLMs through various methodologies, including prompting techniques, neuro-symbolic approaches, and fine-tuning.Through a critical review of relevant datasets and benchmarks, we assess LLMs' performance, identifying significant challenges in complex puzzle scenarios.Our findings highlight the disparity between LLM capabilities and human-like reasoning, particularly in those requiring advanced logical inference.The survey underscores the necessity for novel strategies and richer datasets to advance LLMs' puzzle-solving proficiency and contribute to AI's logical reasoning and creative problem-solving advancements.

Counterfactual explanations (CEs) based on concepts are explanations that consider alternative scenarios to understand which high-level semantic features contributed to particular model predictions. In this work, we propose CEs based on the semantic graphs accompanying input data to achieve more descriptive, accurate, and human-aligned explanations. Building upon state-of-the-art (SotA) conceptual attempts, we adopt a model-agnostic edit-based approach and introduce leveraging GNNs for efficient Graph Edit Distance (GED) computation. With a focus on the visual domain, we represent images as scene graphs and obtain their GNN embeddings to bypass solving the NP-hard graph similarity problem for all input pairs, an integral part of CE computation process. We apply our method to benchmark and real-world datasets with varying difficulty and availability of semantic annotations. Testing on diverse classifiers, we find that our CEs outperform previous SotA explanation models based on semantics, including both white and black-box as well as conceptual and pixel-level approaches. Their superiority is proven quantitatively and qualitatively, as validated by human subjects, highlighting the significance of leveraging semantic edges in the presence of intricate relationships. Our model-agnostic graph-based approach is widely applicable and easily extensible, producing actionable explanations across different contexts. The code is available at https://github.com/aggeliki-dimitriou/SGCE.

Visual Word Sense Disambiguation (VWSD) is a novel challenging task with the goal of retrieving an image among a set of candidates, which better represents the meaning of an ambiguous word within a given context.In this paper, we make a substantial step towards unveiling this interesting task by applying a varying set of approaches.Since VWSD is primarily a text-image retrieval task, we explore the latest transformer-based methods for multimodal retrieval.Additionally, we utilize Large Language Models (LLMs) as knowledge bases to enhance the given phrases and resolve ambiguity related to the target word.We also study VWSD as a unimodal problem by converting to text-to-text and image-to-image retrieval, as well as question-answering (QA), to fully explore the capabilities of relevant models.To tap into the implicit knowledge of LLMs, we experiment with Chain-of-Thought (CoT) prompting to guide explainable answer generation.On top of all, we train a learn to rank (LTR) model in order to combine our different modules, achieving competitive ranking results.Extensive experiments on VWSD demonstrate valuable insights to effectively drive future directions.

Counterfactual explanations have been argued to be one of the most intuitive forms of explanation. They are typically defined as a minimal set of edits on a given data sample that, when applied, changes the output of a model on that sample. However, a minimal set of edits is not always clear and understandable to an end-user, as it could constitute an adversarial example (which is indistinguishable from the original data sample to an end-user). Instead, there are recent ideas that the notion of minimality in the context of counterfactuals should refer to the semantics of the data sample, and not to the feature space. In this work, we build on these ideas, and propose a framework that provides counterfactual explanations in terms of knowledge graphs. We provide an algorithm for computing such explanations (given some assumptions about the underlying knowledge), and quantitatively evaluate the framework with a user study.

Recent breakthroughs in NLP research, such as the advent of Transformer models have indisputably contributed to major advancements in several tasks. However, few works research robustness and explainability issues of their evaluation strategies. In this work, we examine the behavior of high-performing pre-trained language models, focusing on the task of semantic similarity for visual vocabularies. First, we address the need for explainable evaluation metrics, necessary for understanding the conceptual quality of retrieved instances. Our proposed metrics provide valuable insights in local and global level, showcasing the inabilities of widely used approaches. Secondly, adversarial interventions on salient query semantics expose vulnerabilities of opaque metrics and highlight patterns in learned linguistic representations.

Savannahs cover 50% of the African continent and 20% of the global land surface. African savannahs are increasingly threatened by over-exploitation, deforestation, woody thickening and encroachment and, consequently, land degradation. In South Africa, savannah degradation is acute and accelerating, threatening the ecosystem services provided to some of the country's most vulnerable populations. Here, we devise a methodology for the accurate mapping and monitoring of the fraction of the woody component of savannah vegetation and apply it to the South African Northwest Province. Our approach involves the use of aerial photography for training and validation; the entire dry-season Landsat archive over the last three decades, and deep learning segmentation and classification techniques. Our results are able to identify areas of significant woody densification and encroachment, as well as areas with declining trends.

Evaluation of generative AI is a difficult problem, especially in artistic domains in which aesthetic qualities of generated samples are to an extent subjective, such as in music. The most widely accepted method for evaluating such models is to conduct a survey of users, which is a resource intensive process. In this work we propose a framework for cheaply evaluating generative models in the symbolic music domain by utilizing tools from music theory, such as the circle of fifths, with the goal of producing quantifiable metrics which reflect the “musicality” of a written score or MIDI file.

The massive digitization of artworks during the last decades created the need for categorization, analysis, and management of huge amounts of data related to abstract concepts, highlighting a challenging problem in the field of computer science. The rapid progress of artificial intelligence and neural networks has provided tools and technologies that seem worthy of the challenge. Recognition of various art features in artworks has gained attention in the deep learning society. In this paper, we are concerned with the problem of art style recognition using deep networks. We compare the performance of 8 different deep architectures (VGG16, VGG19, ResNet50, ResNet152, Inception- V3, DenseNet121, DenseNet201 and Inception-ResNet-V2), on two different art datasets, including 3 architectures that have never been used on this task before, leading to state-of-the-art performance. We study the effect of data preprocessing prior to applying a deep learning model. We introduce a stacking ensemble method combining the results of first-stage classifiers through a meta-classifier, with the innovation of a versatile approach based on multiple models that extract and recognize different characteristics of the input, creating a more consistent model compared to existing works and achieving state-of-the-art accuracy on the largest art dataset available (WikiArt - 68,55%). We also discuss the impact of the data and art styles themselves on the performance of our models forming a manifold perspective on the problem.

Query rewriting is an important technique for answering queries over data described using ontologies. In query rewriting the input, a conjunctive query (CQ) |$q$| and an ontology |$\mathcal {O}$|⁠, is transformed into a new datalog query that captures all answers of |$q$| over |$\mathcal {O}$| and any dataset |$D$|⁠. This process can be time-consuming as it is of high computational complexity. In many real-world applications, this can be particularly problematic as they involve frequent and relatively small modifications on quite large ontologies. Hence, a drawback of most of modern query rewriting systems is that every time the initial ontology is modified, e.g. when new axioms are added or existing ones removed, they compute a new rewriting from scratch. In this paper, we study the problem of computing a rewriting for a CQ over an ontology that has been modified. We do this by reusing the information obtained by the extraction of some previous rewriting with the goal of performing the least possible computations. We study the problem theoretically, present detailed algorithms for both ontology revision and ontology contraction and finally, present an extensive experimental evaluation using the well-known query rewriting systems Requiem and Rapid.

The paper presents an approach for optimizing the evaluation of SPARQL queries over OWL ontologies using SPARQL's OWL Direct Semantics entailment regime. The approach is based on the computation of lower and upper bounds, but we allow for much more expressive queries than related approaches. In order to optimize the evaluation of possible query answers in the upper but not in the lower bound, we present a query extension approach that uses schema knowledge from the queried ontology to extend the query with additional parts. We show that the resulting query is equivalent to the original one and we use the additional parts that are simple to evaluate for restricting the bounds of subqueries of the initial query. In an empirical evaluation we show that the proposed query extension approach can lead to a significant decrease in the query execution time of up to four orders of magnitude.

Fuzzy extensions to description logics (DLs) have gained considerable attention the last decade. So far most works on fuzzy DLs have focused on either very expressive languages, like fuzzy OWL and OWL 2, or on highly inexpressive ones, like fuzzy OWL 2 QL and fuzzy OWL 2 EL. To the best of our knowledge, a fuzzy extension to the language OWL 2 RL has not been thoroughly studied so far. This language is very relevant since it combines both adequate expressive power as well as efficient reasoning algorithms which can be realized using rule-based (Datalog) technologies. In contrast to previous fuzzy extensions, a fuzzy extension of OWL 2 RL is not a straightforward task for the following reason. The main motivation of OWL 2 RL is that its axioms can be equivalently represented as Datalog rules. Hence, to achieve our goal we need to investigate which OWL 2 RL axioms when interpreted under the fuzzy setting can be transformed to equivalent fuzzy Datalog rules. We show that this is not, in general, possible for all axioms but we show that this ‘issue’ can to a large extent be alleviated. Moreover, we have performed an experimental evaluation with many well-known ontologies which showed that such axioms are not used so often in practice.

Query answering over OWL 2 DL ontologies is an important reasoning task for many modern applications. Unfortunately, due to its high computational complexity, OWL 2 DL systems are still not able to cope with datasets containing billions of data. Consequently, application developers often employ provably scalable systems which only support a fragment of OWL 2 DL and which are, hence, most likely incomplete for the given input. However, this notion of completeness is too coarse since it implies that there exists some query and some dataset for which these systems would miss answers. Nevertheless, there might still be a large number of user queries for which they can compute all the right answers even over OWL 2 DL ontologies. In the current paper, we investigate whether, given a query 𝒬 with only distinguished variables over an OWL 2 DL ontology 𝒯 and a system ans, it is possible to identify in an efficient way if ans is complete for 𝒬, 𝒯 and every dataset. We give sufficient conditions for (in)completeness and present a hybrid query answering algorithm which uses ans when it is complete, otherwise it falls back to a fully-fledged OWL 2 DL reasoner. However, even in the latter case, our algorithm still exploits ans as much as possible in order to reduce the search space of the OWL 2 DL reasoner. Finally, we have implemented our approach using a concrete system ans and OWL 2 DL reasoner obtaining encouraging results.

Fuzzy logic programming has been lately used as a general framework for representing and handling imprecise knowledge. In this paper, we define the syntax and the semantics of definite weighted fuzzy logic programs, which extend definite fuzzy logic programs by allowing the inclusion of different significance weights in the individual atoms that make up the antecedent of a fuzzy logic rule. The weights add expressiveness to a fuzzy logic program and allow the determination of the level up to which an atom in the antecedent of a rule may affect the truth value of its consequent. In describing the semantics of definite weighted fuzzy logic programs we introduce the notion of the generalized weighted fuzzy conjunction operator, which can be regarded as a weighted t-norm based aggregation. We determine the properties of generalized weighted fuzzy conjunction operators and provide several examples. A methodology for constructing generalized weighted fuzzy conjunction operators using generator functions of existing t-norms is also introduced. Finally, a method for setting up a parametric weighted fuzzy logic program and automatically adapting the weights of its rules using a numerical dataset is developed.

Description logics (DLs) are modern knowledge representation formalisms which are used today in many applications for reasoning with structured knowledge. Moreover, they are used in the semantic web (an extension of the current web) through the ontology language OWL. On the other hand fuzzy description logics (fuzzy-DLs) have been proposed as expressive logical formalisms capable of capturing and reasoning with vague and imprecise knowledge in the semantic web. In the current paper we investigate on the problem of reasoning with qualified cardinality restrictions (QCRs) in fuzzy DLs, extending previous results on simple number restrictions, thus we present a tableaux algorithm for the the fuzzy-DL fKD-ALCIQ.

Fuzzy ontologies are envisioned to be useful in the Semantic Web. Existing fuzzy ontology reasoners are not scalable enough to handle the scale of data that the Web provides. In this paper, we propose a framework of fuzzy query languages for fuzzy ontologies, and present query answering algorithms for these query languages over fuzzy DL-Lite ontologies. Moreover, this paper reports on implementation of our approach in the fuzzy DL-Lite query engine in the ONTOSEARCH2 system and preliminary, but encouraging, benchmarking results. To the best of our knowledge, this is the first ever scalable query engine for fuzzy ontologies.

The Semantic Web can be viewed as largely about "Knowledge meets the Web". Thus its vision includes ontologies and rules. A key requirement for the architecture of the Semantic Web is to be able to layer "rules on top of ontologies" and "ontologies on top of rules". This has as a counterpart the definition of a mapping between Description Logics and Logic Programming, which is known as Description Logic Programs. In this paper we extend the Description Logic Programs with fuzzy sets and fuzzy logic in order to be able to represent the imprecision and vagueness of real-life applications. We provide the common semantics of the mapping, and the conditions that must be met for this semantic equivalence, based on the model-theoretic semantics.

It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN.

The usefulness of the results of logic programming in real-life applications is sometimes limited due to the inability of this theory to model the uncertain and dynamic character of real environments. Fuzzy logic programming has been lately considered as an important framework for handling uncertainty in logic programming systems. Still, there is a need for modelling adaptation of logic programs and the progress in this area is rather slow. In the present paper, we first extend fuzzy logic programs in a direction that brings them closer to the connectionist approach: we introduce weighted fuzzy programs, which allow the association of significance weights with the atoms that make up the body of a logic rule. The weights add expressiveness to the programs and allow the determination of the degree with which an antecedent affects the value of the rule consequent. Then, we propose a neural network implementation of weighted fuzzy programs that is capable of computing the minimal Herbrand model of a weighted fuzzy program.

According to the emerging MPEG-7 standard, the semantic description of multimedia documents is expressed in terms of semantic entities such as objects, events, concepts, and relations among them. The semantic entities can be used as index terms, in order to support the semantic search process. In this paper, we propose a method that a) applies fuzzy relational operations (closure, composition) and fuzzy rules to expand a semantic encyclopedia and b) uses the encyclopedia to associate the semantic entities with the aid of a fuzzy thesaurus. This method is shown to reduce the need for human intervention in creating semantic descriptions of multimedia documents, as well as correct for incompleteness and inconsistency.

In this paper we formally define the problem of automatic detection of thematic categories in a semantically indexed document, and identify the main obstacles to overcome in this process. Furthermore, we explain how detection of thematic categories can be achieved, with the use of a fuzzy quasi-taxonomic relation. Our approach relies on a fuzzy hierarchical clustering algorithm; this algorithm uses a similarity measure that is based on the notion of context.

Knowledge-based fuzzy inference and neural learning are used in this paper in order to model the event recognition task in semantic video analysis. The advantage of their use is the symbolic nature of the representation of the knowledge concerning the events to be recognized. Moreover, this knowledge can be adapted with the aid of data taken from video sequences. The proposed system has been tested in soccer video sequences for detecting some complex predetermined (and represented in the form of rules) events.

As the annotation of multimedia documents uses multiple descriptors, it is possible to define multiple, semantically meaningful, similarity (or dissimilarity) relations among them. Therefore, for cases such as the mining of user interests for consumption of multimedia documents, based on usage history, where the clustering of documents is necessary, it is important to develop context aware clustering algorithms that are able to handle this type of information. We explain the relation between context, user interest and the multiple relations; furthermore, we present a clustering algorithm that is able to mine user interests from multi-relational data sets.

We use concepts from the lattice-based theory of morphological operators and fuzzy sets to develop generalized lattice image operators that can be expressed as nonlinear convolutions that are suprema or infima of fuzzy intersection or union norms. Our emphasis (different from previous works) is the construction of pairs of fuzzy dilation and erosion operators that form lattice adjunctions. This guarantees that their composition will be a valid algebraic opening or closing. The power, but also the difficulty, in applying these fuzzy operators to image analysis is the large variety of fuzzy norms and the absence of systematic ways in selecting them. Towards this goal, we have performed extensive experiments in applying these fuzzy operators to various nonlinear filtering and image analysis tasks, attempting first to understand the effect that the type of fuzzy norm and the shape/size of the structuring function has on the resulting new image operators. Further, we have developed some new fuzzy edge gradients and optimized their usage for edge detection on test problems via a parametric fuzzy norm.

This paper investigates and extends the use of fuzzy relation equations for the representation and study of fuzzy inference systems. Using the generalized sup-t (t is a triangular norm) composition of fuzzy relations and the study of sup-t fuzzy relation equations, interesting results are provided concerning the completeness and the theoretical soundness of the representation, as well as the ability to mathematically formulate and satisfy application-oriented design demands. Furthermore, giving a formal study of fuzzy partitions and some useful aspects of fuzzy associations and fuzzy systems, the paper can be used as a theoretical background for designing consistent fuzzy inference systems.