Year:

  1.  3
    On the Impact of Interpretability Methods in Active Image Augmentation Method.Flávio Arthur Oliveira Santos, Cleber Zanchettin, Leonardo Nogueira Matos & Paulo Novais - 2022 - Logic Journal of the IGPL 30 (4):611-621.
    Robustness is a significant constraint in machine learning models. The performance of the algorithms must not deteriorate when training and testing with slightly different data. Deep neural network models achieve awe-inspiring results in a wide range of applications of computer vision. Still, in the presence of noise or region occlusion, some models exhibit inaccurate performance even with data handled in training. Besides, some experiments suggest deep learning models sometimes use incorrect parts of the input information to perform inference. Active image (...)
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  2. Solving a Two-Stage Supply Chain Network Design Problem with Fixed Costs by a Hybrid Genetic Algorithm.Ovidiu Cosma, Petrică C. Pop & Cosmin Sabo - 2022 - Logic Journal of the IGPL 30 (4):622-634.
    In this paper we investigate a particular two-stage supply chain network design problem with fixed costs. In order to solve this complex optimization problem, we propose an efficient hybrid algorithm, which was obtained by incorporating a linear programming optimization problem within the framework of a genetic algorithm. In addition, we integrated within our proposed algorithm a powerful local search procedure able to perform a fine tuning of the global search. We evaluate our proposed solution approach on a set of large (...)
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  3. Parsimonious Modelling for Estimating Hospital Cooling Demand to Improve Energy Efficiency.Eduardo Dulce-Chamorro & Francisco Javier Martinez-de-Pison - 2022 - Logic Journal of the IGPL 30 (4):635-648.
    Of all the different types of public buildings, hospitals are the biggest energy consumers. Cooling systems for air conditioning and healthcare uses are particularly energy intensive. Forecasting hospital thermal-cooling demand is a remarkable and innovative method capable of improving the overall energy efficiency of an entire cooling system. Predictive models allow users to forecast the activity of water-cooled generators and adapt power generation to the real demand expected for the day ahead, while avoiding inefficient subcooling. In addition, the maintenance costs (...)
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  4.  4
    Editorial: Special Issue HAIS19-IGPL.Hilde Pérez García, Lidia Sánchez González, Manuel Castejón Limas, Héctor Quintián & Emilio Corchado - 2022 - Logic Journal of the IGPL 30 (4):563-565.
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  5. Adaptive Orthogonal Characteristics of Bio-Inspired Neural Networks.Naohiro Ishii, Toshinori Deguchi, Masashi Kawaguchi, Hiroshi Sasaki & Tokuro Matsuo - 2022 - Logic Journal of the IGPL 30 (4):578-598.
    In recent years, neural networks have attracted much attention in the machine learning and the deep learning technologies. Bio-inspired functions and intelligence are also expected to process efficiently and improve existing technologies. In the visual pathway, the prominent features consist of nonlinear characteristics of squaring and rectification functions observed in the retinal and visual cortex networks, respectively. Further, adaptation is an important feature to activate the biological systems, efficiently. Recently, to overcome short-comings of the deep learning techniques, orthogonality for the (...)
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  6. A One-Class Classifier Based on a Hybrid Topology to Detect Faults in Power Cells.Esteban Jove, José-Luis Casteleiro-Roca, Héctor Quintián, Francisco Zayas-Gato, Gianni Vercelli & José Luis Calvo-Rolle - 2022 - Logic Journal of the IGPL 30 (4):679-694.
    The use of batteries became essential in our daily life in electronic devices, electric vehicles and energy storage systems in general terms. As they play a key role in many devices, their design and implementation must follow a thorough test process to check their features at different operating points. In this circumstance, the appearance of any kind of deviation from the expected operation must be detected. This research deals with real data registered during the testing phase of a lithium iron (...)
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  7.  2
    Employees Balance and Stability as Key Points in Organizational Performance.José Neves, Nuno Maia, Goreti Marreiros, Mariana Neves, Ana Fernandes, Jorge Ribeiro, Isabel Araújo, Nuno Araújo, Liliana Ávidos, Filipa Ferraz, António Capita, Nicolás Lori, Victor Alves & Henrique Vicente - 2022 - Logic Journal of the IGPL 30 (4):664-678.
    System analyses deal with interrelationships between different variables that keep the system in balance. In many analysis of complex thinking, a system is viewed as a complex unit in which the ‘whole’ is not reduced to the ‘sum’ of its parts; the system becomes an ambiguous item because it consists of several entities that interact with unforeseen results or, in other words, it is situated at a transdisciplinary level, it is impossible for an area to have a complete reading of (...)
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  8.  6
    Air Pollution Monitoring Using WSN Nodes with Machine Learning Techniques: A Case Study.Paul D. Rosero-Montalvo, Vivian F. López-Batista, Ricardo Arciniega-Rocha & Diego H. Peluffo-Ordóñez - 2022 - Logic Journal of the IGPL 30 (4):599-610.
    Air pollution is a current concern of people and government entities. Therefore, in urban scenarios, its monitoring and subsequent analysis is a remarkable and challenging issue due mainly to the variability of polluting-related factors. For this reason, the present work shows the development of a wireless sensor network that, through machine learning techniques, can be classified into three different types of environments: high pollution levels, medium pollution and no noticeable contamination into the Ibarra City. To achieve this goal, signal smoothing (...)
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  9.  2
    Design of a New Distributed NoSQL Database with Distributed Hash Tables.Agustín San Román Guzmán, Diego Valdeolmillos, Alberto Rivas, Angélica González Arrieta & Pablo Chamoso - 2022 - Logic Journal of the IGPL 30 (4):566-577.
    Databases play a fundamental role in today’s world, being used by most companies, especially those that offer services through the Internet. Today there is a wide variety of database models, each adapted for use according to the specific requirements of each application. Traditionally, the relational models with centralized architectures have been used mostly due to their simplicity and general-purpose query language, which made relational systems suitable for almost any application. However, with the growth of the Internet in recent decades, both (...)
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  10.  3
    Deep Convolutional Neural Networks on Automatic Classification for Skin Tumour Images.Svetlana Simić, Svetislav D. Simić, Zorana Banković, Milana Ivkov-Simić, José R. Villar & Dragan Simić - 2022 - Logic Journal of the IGPL 30 (4):649-663.
    The skin, uniquely positioned at the interface between the human body and the external world, plays a multifaceted immunologic role in human life. In medical practice, early accurate detection of all types of skin tumours is essential to guide appropriate management and improve patients’ survival. The most important issue is to differentiate between malignant skin tumours and benign lesions. The aim of this research is the classification of skin tumours by analysing medical skin tumour dermoscopy images. This paper is focused (...)
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  11.  5
    Computability and the Symmetric Difference Operator.Uri Andrews, Peter M. Gerdes, Steffen Lempp, Joseph S. Miller & Noah D. Schweber - 2022 - Logic Journal of the IGPL 30 (3):499-518.
    Combinatorial operations on sets are almost never well defined on Turing degrees, a fact so obvious that counterexamples are worth exhibiting. The case we focus on is the symmetric-difference operator; there are pairs of degrees for which the symmetric-difference operation is well defined. Some examples can be extracted from the literature, e.g. from the existence of nonzero degrees with strong minimal covers. We focus on the case of incomparable r.e. degrees for which the symmetric-difference operation is well defined.
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  12.  11
    Proof Systems for 3-Valued Logics Based on Gödel’s Implication.Arnon Avron - 2022 - Logic Journal of the IGPL 30 (3):437-453.
    The logic $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ was introduced in Robles and Mendéz as a paraconsistent logic which is based on Gödel’s 3-valued matrix, except that Kleene–Łukasiewicz’s negation is added to the language and is used as the main negation connective. We show that $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ is exactly the intersection of $G3^{\{1\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ and $G3^{\{1,0.5\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$, the two truth-preserving 3-valued logics which are based on the same truth tables. We then construct a Hilbert-type system which has for $\to $ as its sole rule of inference, and is (...)
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  13.  3
    Unification with Parameters in the Implication Fragment of Classical Propositional Logic.Philippe Balbiani & Mojtaba Mojtahedi - 2022 - Logic Journal of the IGPL 30 (3):454-464.
    In this paper, we show that the implication fragment of classical propositional logic is finitary for unification with parameters.
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  14.  2
    Restricted Rules of Inference and Paraconsistency.Sankha S. Basu & Mihir K. Chakraborty - 2022 - Logic Journal of the IGPL 30 (3):534-560.
    In this paper, we study two companions of a logic, viz., the left variable inclusion companion and the restricted rules companion, their nature and interrelations, especially in connection with paraconsistency. A sufficient condition for the two companions to coincide has also been proved. Two new logical systems—intuitionistic paraconsistent weak Kleene logic and paraconsistent pre-rough logic —are presented here as examples of logics of left variable inclusion. IPWK is the left variable inclusion companion of intuitionistic propositional logic and is also the (...)
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  15.  7
    Recovering Decimation-Based Cryptographic Sequences by Means of Linear CAs.Sara D. Cardell, Diego F. Aranha & Amparo Fúster-Sabater - 2022 - Logic Journal of the IGPL 30 (3):561-561.
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  16. New Tableau Characterizations for Non-Clausal MaxSAT Problem.Guido Fiorino - 2022 - Logic Journal of the IGPL 30 (3):422-436.
    In this paper, we provide non-clausal tableau calculi for the maximum satisfiability problem and its variants. We discuss both basic calculi to characterize the problem and their modifications to reduce the proof size.
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  17.  4
    ∞-Groupoid Generated by an Arbitrary Topological Λ-Model.Daniel O. Martínez-Rivillas & Ruy J. G. B. de Queiroz - 2022 - Logic Journal of the IGPL 30 (3):465-488.
    The lambda calculus is a universal programming language. It can represent the computable functions, and such offers a formal counterpart to the point of view of functions as rules. Terms represent functions and this allows for the application of a term/function to any other term/function, including itself. The calculus can be seen as a formal theory with certain pre-established axioms and inference rules, which can be interpreted by models. Dana Scott proposed the first non-trivial model of the extensional lambda calculus, (...)
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  18.  2
    Gödel Justification Logics and Realization.Nicholas Pischke - 2022 - Logic Journal of the IGPL 30 (3):343-408.
    We study the topic of realization from classical justification logics in the context of the recently introduced Gödel justification logics. We show that the standard Gödel modal logics of Caicedo and Rodriguez are not realized by the Gödel justification logics and moreover, we study possible extensions of the Gödel justification logics, which are strong enough to realize the standard Gödel modal logics. On the other hand, we study the fragments of the standard Gödel modal logics, which are realized by the (...)
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  19.  4
    Undecidability of the Logic of Partial Quasiary Predicates.Mikhail Rybakov & Dmitry Shkatov - 2022 - Logic Journal of the IGPL 30 (3):519-533.
    We obtain an effective embedding of the classical predicate logic into the logic of partial quasiary predicates. The embedding has the property that an image of a non-theorem of the classical logic is refutable in a model of the logic of partial quasiary predicates that has the same cardinality as the classical countermodel of the non-theorem. Therefore, we also obtain an embedding of the classical predicate logic of finite models into the logic of partial quasiary predicates over finite structures. As (...)
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  20.  11
    Tarski’s Undefinability Theorem and the Diagonal Lemma.Saeed Salehi - 2022 - Logic Journal of the IGPL 30 (3):489-498.
    We prove the equivalence of the semantic version of Tarski’s theorem on the undefinability of truth with the semantic version of the diagonal lemma and also show the equivalence of a syntactic version of Tarski’s undefinability theorem with a weak syntactic diagonal lemma. We outline two seemingly diagonal-free proofs for these theorems from the literature and show that the syntactic version of Tarski’s theorem can deliver Gödel–Rosser’s incompleteness theorem.
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  21.  1
    Dualities for Bounded Prelinear Hilbert Algebras.Hernán J. San Martín & Valeria A. Sígal - 2022 - Logic Journal of the IGPL 30 (3):409-421.
    This paper deals about dualities for bounded prelinear Hilbert algebras. In particular, we give an Esakia-style duality between the algebraic category of bounded prelinear Hilbert algebras and a category of H-spaces whose morphisms are certain continuous p-morphisms.
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  22.  2
    Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder.Christian Amor, José M. Pérez, Philipp Schlatter, Ricardo Vinuesa & Soledad Le Clainche - 2022 - Logic Journal of the IGPL 30 (2):263-276.
    This article introduces some soft computing methods generally used for data analysis and flow pattern detection in fluid dynamics. These techniques decompose the original flow field as an expansion of modes, which can be either orthogonal in time, or in space or in time and space, or they can simply be selected using some sophisticated statistical techniques. The performance of these methods is tested in the turbulent wake of a wall-mounted square cylinder. This highly complex flow is suitable to show (...)
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  23.  3
    Uncertainty Estimation in the Forecasting of the 222Rn Radiation Level Time Series at the Canfranc Underground Laboratory.Miguel Cárdenas-Montes - 2022 - Logic Journal of the IGPL 30 (2):227-238.
    Nowadays decision making is strongly supported by the high-confident point estimations produced by deep learning algorithms. In many activities, they are sufficient for the decision-making process. However, in some other cases, confidence intervals are required too for an appropriate decision-making process. In this work, a first attempt to generate point estimations with confidence intervals for the $^{222}$Rn radiation level time series at Canfranc Underground Laboratory is presented. To predict the low-radiation periods allows correctly scheduling the unshielded periods for maintenance operations (...)
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  24.  3
    Improving Wearable-Based Fall Detection with Unsupervised Learning.Mirko Fáñez, José R. Villar, Enrique de la Cal, Víctor M. González & Javier Sedano - 2022 - Logic Journal of the IGPL 30 (2):314-325.
    Fall detection is a challenging task that has received the attention of the research community in the recent years. This study focuses on FD using data gathered from wearable devices with tri-axial accelerometers, developing a solution centered in elderly people living autonomously. This research includes three different ways to improve a FD method: an analysis of the event detection stage, comparing several alternatives, an evaluation of features to extract for each detected event and an appraisal of up to 6 different (...)
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  25.  3
    One-Class-Based Intelligent Classifier for Detecting Anomalous Situations During the Anesthetic Process.Alberto Leira, Esteban Jove, Jose M. Gonzalez-Cava, José-Luis Casteleiro-Roca, Héctor Quintián, Francisco Zayas-Gato, Santiago Torres Álvarez, Svetlana Simić, Juan-Albino Méndez-Pérez & José Luis Calvo-Rolle - 2022 - Logic Journal of the IGPL 30 (2):326-341.
    Closed-loop administration of propofol for the control of hypnosis in anesthesia has evidenced an outperformance when comparing it with manual administration in terms of drug consumption and post-operative recovery of patients. Unlike other systems, the success of this strategy lies on the availability of a feedback variable capable of quantifying the current hypnotic state of the patient. However, the appearance of anomalies during the anesthetic process may result in inaccurate actions of the automatic controller. These anomalies may come from the (...)
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  26.  2
    Distal Learning of the Incremental Capacity Curve of a LiFePO4 Battery.Luciano Sánchez, José Otero, Manuela González, David Anseán, Alana A. Zülke & Inés Couso - 2022 - Logic Journal of the IGPL 30 (2):301-313.
    An intelligent model of the incremental capacity curve of an automotive lithium-ferrophosphate battery is presented. The relative heights of the two major peaks of the IC curve can be acquired from high-current discharges, thus enabling the state of health estimation of the battery while the vehicle is being operated and in certain cases, aging mechanisms can be suggested. Our model has been validated using a large dataset representing different degradation scenarios, obtained from a recently available open-source database.
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  27.  3
    The Effect of Iterative Learning Control on the Force Control of a Hydraulic Cushion.Ignacio Trojaola, Iker Elorza, Eloy Irigoyen, Aron Pujana-Arrese & Carlos Calleja - 2022 - Logic Journal of the IGPL 30 (2):214-226.
    An iterative learning control algorithm is presented for the force control circuit of a hydraulic cushion. A control scheme consisting of a PI controller, feed-forward and feedback-linearization is first derived. The uncertainties and nonlinearities of the proportional valve, the main system actuator, prevent the accurate tracking of the pressure reference signal. Therefore, an extra ILC FF signal is added to counteract the valve model uncertainties. The unknown valve dynamics are attenuated by adding a fourth-order low-pass filter to the iterative learning (...)
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  28.  2
    Generation of Synthetic Data with Conditional Generative Adversarial Networks.Belén Vega-Márquez, Cristina Rubio-Escudero & Isabel Nepomuceno-Chamorro - 2022 - Logic Journal of the IGPL 30 (2):252-262.
    The generation of synthetic data is becoming a fundamental task in the daily life of any organization due to the new protection data laws that are emerging. Because of the rise in the use of Artificial Intelligence, one of the most recent proposals to address this problem is the use of Generative Adversarial Networks. These types of networks have demonstrated a great capacity to create synthetic data with very good performance. The goal of synthetic data generation is to create data (...)
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  29.  3
    Test Case Prioritization—ANT Algorithm With Faults Severity.Andreea Vescan, Camelia-M. Pintea & Petrică C. Pop - 2022 - Logic Journal of the IGPL 30 (2):277-288.
    Regression testing is applied whenever a code changes, ensuring that the modifications fixed the fault and no other faults are introduced. Due to a large number of test cases to be run, test case prioritization is one of the strategies that allows to run the test cases with the highest fault rate first. The aim of the paper is to present an optimized test case prioritization method inspired by ant colony optimization, test case prioritization–ANT. The criteria used by the optimization (...)
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  30.  5
    The Impact of Different System Call Representations on Intrusion Detection.Sarah Wunderlich, Markus Ring, Dieter Landes & Andreas Hotho - 2022 - Logic Journal of the IGPL 30 (2):239-251.
    Over the years, artificial neural networks have been applied successfully in many areas including IT security. Yet, neural networks can only process continuous input data. This is particularly challenging for security-related, non-continuous data like system calls of an operating system. This work focuses on five different options to preprocess sequences of system calls so that they can be processed by neural networks. These input options are based on one-hot encodings and learning word2vec, GloVe or fastText representations of system calls. As (...)
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  31.  4
    Practical Approach in Verification of Security Systems Using Satisfiability Modulo Theories.Agnieszka M. Zbrzezny, Sabina Szymoniak & Miroslaw Kurkowski - 2022 - Logic Journal of the IGPL 30 (2):289-300.
    The paper presents a novel method for the verification of security protocols’ time properties. The new method uses a translation to satisfiability modulo theories problem. In our approach, we model protocol users’ behaviours using networks of synchronized timed automata. Suitably specified correctness properties are defined as a reachability property of some chosen states in an automata network. Then, the network of timed automata and the property are translated to an SMT problem and checked using an SMT-solver and a BMC algorithm. (...)
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  32.  3
    Lyndon’s Interpolation Property for the Logic of Strict Implication.Narbe Aboolian & Majid Alizadeh - 2022 - Logic Journal of the IGPL 30 (1):34-70.
    The main result proves Lyndon’s and Craig’s interpolation properties for the logic of strict implication ${\textsf{F}}$, with a purely syntactical method. A cut-free G3-style sequent calculus $ {\textsf{GF}} $ and its single-succedent variant $ \textsf{GF}_{\textsf{s}} $ are introduced. $ {\textsf{GF}} $ can be extended to a G3-variant of the sequent calculus GBPC3 for Visser’s basic logic. Also a simple syntactic proof of known embedding result of $ {\textsf{F}} $ into $ {\textsf{K}} $ is provided. An extension of $ {\textsf{F}} $, (...)
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  33.  3
    Saturated Models of First-Order Many-Valued Logics.Guillermo Badia & Carles Noguera - 2022 - Logic Journal of the IGPL 30 (1):1-20.
    This paper is devoted to the problem of existence of saturated models for first-order many-valued logics. We consider a general notion of type as pairs of sets of formulas in one free variable that express properties that an element of a model should, respectively, satisfy and falsify. By means of an elementary chains construction, we prove that each model can be elementarily extended to a $\kappa $-saturated model, i.e. a model where as many types as possible are realized. In order (...)
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  34.  2
    Frame-Validity Games and Lower Bounds on the Complexity of Modal Axioms.Philippe Balbiani, David Fernández-Duque, Andreas Herzig & Petar Iliev - 2022 - Logic Journal of the IGPL 30 (1):155-185.
    We introduce frame-equivalence games tailored for reasoning about the size, modal depth, number of occurrences of symbols and number of different propositional variables of modal formulae defining a given frame property. Using these games, we prove lower bounds on the above measures for a number of well-known modal axioms; what is more, for some of the axioms, we show that they are optimal among the formulae defining the respective class of frames.
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  35.  14
    On Bivalent Semantics and Natural Deduction for Some Infectious Logics.Alex Belikov - 2022 - Logic Journal of the IGPL 30 (1):186-210.
    In this work, we propose a variant of so-called informational semantics, a technique elaborated by Voishvillo, for two infectious logics, Deutsch’s ${\mathbf{S}_{\mathbf{fde}}}$ and Szmuc’s $\mathbf{dS}_{\mathbf{fde}}$. We show how the machinery of informational semantics can be effectively used to analyse truth and falsity conditions of disjunction and conjunction. Using this technique, it is possible to claim that disjunction and conjunction can be rightfully regarded as such, a claim which was disputed in the recent literature. Both ${\mathbf{S}_{\mathbf{fde}}}$ and $\mathbf{dS}_{\mathbf{fde}}$ are formalized in (...)
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  36.  5
    The Logic of Orthomodular Posets of Finite Height.Ivan Chajda & Helmut Länger - 2022 - Logic Journal of the IGPL 30 (1):143-154.
    Orthomodular posets form an algebraic formalization of the logic of quantum mechanics. A central question is how to introduce implication in such a logic. We give a positive answer whenever the orthomodular poset in question is of finite height. The crucial advantage of our solution is that the corresponding algebra, called implication orthomodular poset, i.e. a poset equipped with a binary operator of implication, corresponds to the original orthomodular poset and that its implication operator is everywhere defined. We present here (...)
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  37.  7
    An Infinitary Axiomatization of Dynamic Topological Logic.Somayeh Chopoghloo & Morteza Moniri - 2022 - Logic Journal of the IGPL 30 (1):124-142.
    Dynamic topological logic is a multi-modal logic that was introduced for reasoning about dynamic topological systems, i.e. structures of the form $\langle{\mathfrak{X}, f}\rangle $, where $\mathfrak{X}$ is a topological space and $f$ is a continuous function on it. The problem of finding a complete and natural axiomatization for this logic in the original tri-modal language has been open for more than one decade. In this paper, we give a natural axiomatization of $\textsf{DTL}$ and prove its strong completeness with respect to (...)
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  38.  9
    Logics of (In)Sane and (Un)Reliable Beliefs.Jie Fan - 2022 - Logic Journal of the IGPL 30 (1):78-100.
    Inspired by an interesting quotation from the literature, we propose four modalities, called ‘sane belief’, ‘insane belief’, ‘reliable belief’ and ‘unreliable belief’, and introduce logics with each operator as the modal primitive. We show that the four modalities constitute a square of opposition, which indicates some interesting relationships among them. We compare the relative expressivity of these logics and other related logics, including a logic of false beliefs from the literature. The four main logics are all less expressive than the (...)
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  39.  2
    A Remark on Functional Completeness of Binary Expansions of Kleene’s Strong 3-Valued Logic.Gemma Robles & José M. Méndez - 2022 - Logic Journal of the IGPL 30 (1):21-33.
    A classical result by Słupecki states that a logic L is functionally complete for the 3-element set of truth-values THREE if, in addition to functionally including Łukasiewicz’s 3-valued logic Ł3, what he names the ‘$T$-function’ is definable in L. By leaning upon this classical result, we prove a general theorem for defining binary expansions of Kleene’s strong logic that are functionally complete for THREE.
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  40.  38
    ‘Sometime a Paradox’, Now Proof: Yablo is Not First Order.Saeed Salehi - 2022 - Logic Journal of the IGPL 30 (1):71-77.
    Interesting as they are by themselves in philosophy and mathematics, paradoxes can be made even more fascinating when turned into proofs and theorems. For example, Russell’s paradox, which overthrew Frege’s logical edifice, is now a classical theorem in set theory, to the effect that no set contains all sets. Paradoxes can be used in proofs of some other theorems—thus Liar’s paradox has been used in the classical proof of Tarski’s theorem on the undefinability of truth in sufficiently rich languages. This (...)
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  41.  4
    Extensions in Graph Normal Form.Michał Walicki - 2022 - Logic Journal of the IGPL 30 (1):101-123.
    Graph normal form, introduced earlier for propositional logic, is shown to be a normal form also for first-order logic. It allows to view syntax of theories as digraphs, while their semantics as kernels of these digraphs. Graphs are particularly well suited for studying circularity, and we provide some general means for verifying that circular or apparently circular extensions are conservative. Traditional syntactic means of ensuring conservativity, like definitional extensions or positive occurrences guaranteeing exsitence of fixed points, emerge as special cases.
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