Metaphysical graphical structuralism is the view that at some fundamental level the world is a mathematical graph of nodes and edges. Randall Dipert has advanced a graphical structuralist theory of fundamental particulars and Alexander Bird has advanced a graphical structuralist theory of fundamental properties. David Oderberg has posed a powerful challenge to graphical structuralism: that it entails the absurd inexistence of the world or the absurd cessation of all change. In this paper I defend graphical structuralism. A sharper formulation, (...) some theorems about such structures, and careful attention to the interaction of metaphysical and mathematical features, shows that the absurdities depend on assumptions that are not essential to the view and brings to light a surprising fact about the necessary structure of fundamental properties. (shrink)

Graph games are interactive scenarios with a wide range of applications. This position paper discusses old and new graph games in tandem with matching logics and identifies general questions behind this match. Throughout, we pursue two strands: logic as a way of analyzing existing graph games, and logic as an inspiration for designing new graph games. Our aim is modest: we propose a perspective that complements existing game-theoretic and computational ones, we raise questions, make observations, and (...) suggest research directions—technical results are left to future work. But frankly, our main aim with this survey paper is to show that graph games are concrete, fun, easy to grasp, and yet challenging to study. (shrink)

We show that there exist 2 ℵ 0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any first-order definable class of relational structures. Using a variant of this construction, we resolve a long-standing question of Fine, by exhibiting a bimodal logic that is valid in its canonical frames, but is not sound and complete for any first-order definable class of Kripke frames (a monomodal example can then be obtained using simulation results of (...) Thomason). The constructions use the result of Erd $\H{o}$ s that there are finite graphs with arbitrarily large chromatic number and girth. (shrink)

Let us call a property that is essentially dispositional a potency.1 David Armstrong thinks that potencies do not exist. All sparse properties are essentially categorical, where sparse properties are the explanatory properties of the type science seeks to discover. An alternative view, but not the only one, is that all sparse properties are potencies or supervene upon them. In this paper I shall consider the differences between these views, in particular the objections Armstrong raises against potencies.

The belief that Aristotle opposes potency (dunamis) to actuality (energeia or entelecheia) has gone untested. This essay defines and distinguishes forms of the Opposition Hypothesis—the Actualization, Privation, and Modal—examining the texts and arguments adduced to support them. Using Aristotle’s own account of opposition, the texts appear instead to show that potency and actuality are compatible, while arguments for their opposition produce intractable problems. Notably, Aristotle’s refutation of the Megarian Identity Hypothesis applies with equal or greater force to the (...) Opposition Hypothesis. For Aristotle, then, potency and actuality are compatible. (shrink)

As a distinctive voice in the current philosophy of technology, postphenomenology elucidates various ways of how technologies “shape” both the world and humans in it. Distancing itself from more speculative approaches, postphenomenology advocates the so-called empirical turn in philosophy of technology: It focuses on diverse effects of particular technologies instead of speculating on the essence of technology and its general impact. Critics of postphenomenology argue that by turning to particularities and emphasizing that technologies are always open to different uses and (...) interpretations, postphenomenology becomes unable to realize how profoundly technology determines our being in the world. Seeking to evaluate the postphenomenological ability to radically reflect on the human being conditioned by technology, I discuss the two most pertinent criticisms of postphenomenology: an “existential” one by Robert C. Scharff and an “ontological” one by Jochem Zwier, Vincent Blok, and Pieter Lemmens. Assessing the ontological alternative, I point to incapacity of Heidegger’s concept of Enframing to do justice to material technologies. Simultaneously, I acknowledge the necessity of speculating on technology as transcending concrete technologies. Such speculating would be instrumental in reviving Ihde’s idea of non-neutrality of technology in its full philosophical potency. (shrink)

We introduce a framework for a graph-theoretic analysis of the semantic paradoxes. Similar frameworks have been recently developed for infinitary propositional languages by Cook and Rabern, Rabern, and Macauley. Our focus, however, will be on the language of first-order arithmetic augmented with a primitive truth predicate. Using Leitgeb’s notion of semantic dependence, we assign reference graphs (rfgs) to the sentences of this language and define a notion of paradoxicality in terms of acceptable decorations of rfgs with truth values. It (...) is shown that this notion of paradoxicality coincides with that of Kripke. In order to track down the structural components of an rfg that are responsible for paradoxicality, we show that any decoration can be obtained in a three-stage process: first, the rfg is unfolded into a tree, second, the tree is decorated with truth values (yielding a dependence tree in the sense of Yablo), and third, the decorated tree is re-collapsed onto the rfg. We show that paradoxicality enters the picture only at stage three. Due to this we can isolate two basic patterns necessary for paradoxicality. Moreover, we conjecture a solution to the characterization problem for dangerous rfgs that amounts to the claim that basically the Liar- and the Yablo graph are the only paradoxical rfgs. Furthermore, we develop signed rfgs that allow us to distinguish between ‘positive’ and ‘negative’ reference and obtain more fine-grained versions of our results for unsigned rfgs. (shrink)

This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of vertices; every missing edge corresponds to an independence relation. These features lead to a simple parameterization of the corresponding set of distributions in the Gaussian case.

Studies to neutrosophic graphs happens to be not only innovative and interesting, but gives a new dimension to graph theory. The classic coloring of edge problem happens to give various results. Neutrosophic tree will certainly find lots of applications in data mining when certain levels of indeterminacy is involved in the problem. Several open problems are suggested.

Graphs are employed to define a variety of distance-based binary merging operators. We provide logical characterization results for each class of merging operators introduced and discuss the extension of this approach to the merging of sequences and multisets.

Modeling mechanisms is central to the biological sciences – for purposes of explanation, prediction, extrapolation, and manipulation. A closer look at the philosophical literature reveals that mechanisms are predominantly modeled in a purely qualitative way. That is, mechanistic models are conceived of as representing how certain entities and activities are spatially and temporally organized so that they bring about the behavior of the mechanism in question. Although this adequately characterizes how mechanisms are represented in biology textbooks, contemporary biological research practice (...) shows the need for quantitative, probabilistic models of mechanisms, too. In this paper we argue that the formal framework of causal graph theory is well-suited to provide us with models of biological mechanisms that incorporate quantitative and probabilistic information. On the ba-sis of an example from contemporary biological practice, namely feedback regulation of fatty acid biosynthesis in Brassica napus, we show that causal graph theoretical models can account for feedback as well as for the multi-level character of mechanisms. However, we do not claim that causal graph theoretical representations of mechanisms are advantageous in all respects and should replace common qualitative models. Rather, we endorse the more balanced view that causal graph theoretical models of mechanisms are useful for some purposes, while being insufficient for others. (shrink)

A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of (...) the generality of the approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with nondeterministic semantics, and subsume all logics endowed with an algebraic semantics. (shrink)

We describe Peirce’s 1903 system of modal gamma graphs, its transformation rules of inference, and the interpretation of the broken-cut modal operator. We show that Peirce proposed the normality rule in his gamma system. We then show how various normal modal logics arise from Peirce’s assumptions concerning the broken-cut notation. By developing an algebraic semantics we establish the completeness of fifteen modal logics of gamma graphs. We show that, besides logical necessity and possibility, Peirce proposed an epistemic interpretation of the (...) broken-cut modality, and that he was led to analyze constructions of knowledge in the style of epistemic logic. (shrink)

It is a widespread assumption in philosophy of science that data is what is explained by theory—that data itself is not explanatory. I draw on instances of representational and explanatory practice from mammalian chronobiology to suggest that this assumption is unsustainable. In many instances, biologists employ representations of data in explanatory ways that are not reducible to constraints on or evidence for representations of mechanisms. Data graphs are used to exemplify relationships between quantities in the mechanism, and often these representations (...) are necessary for explaining particular aspects of the phenomena under study. I argue that this kind of representation is distinct from representing laws or generalizations, and its primary purpose is to convey particular types or patterns of quantitative relationships. The benefit of the analysis is two-fold. First, it provides a more accurate account of explanatory practice in broadly mechanistic analysis in biology. Second, it suggests that there is not an explanatory “fundamental” type of representation in biology. Rather, the practice of explanation consists in the construction of different types of representations and their employment for distinct explanatory purposes. (shrink)

Legal Judgment Prediction (LJP) is a typical application of Artificial Intelligence in the intelligent judiciary. Current research primarily focuses on automatically predicting law articles, charges, and terms of penalty based on the fact description of cases. However, existing methods for LJP have limitations, such as neglecting document structure and ignoring case similarities. We propose a novel framework called Graph Contrastive Learning with Augmentation (GCLA) for legal judgment prediction to address these issues. GCLA constructs trainable document-level graphs for fact description, (...) capturing local and global context through sentence-level subgraphs. Graph augmentation enhances robustness. We introduce a comparison case relation perspective, using graph contrastive learning to model case-text label relationships effectively. Experimental results on real-world datasets demonstrate the competitive performance of GCLA. (shrink)

In this paper, we analyze and discuss Schopenhauer’s n-term diagrams for eristic dialectics from a graph-theoretical perspective. Unlike logic, eristic dialectics does not examine the validity of an isolated argument, but the progression and persuasiveness of an argument in the context of a dialogue or even controversy. To represent these dialogue situations, Schopenhauer created large maps with concepts and Euler-type diagrams, which from today’s perspective are a specific form of graphs. We first present the original method with Euler-type diagrams, (...) then give the most important graph-theoretical definitions, then discuss Schopenhauer’s diagrams graph-theoretically and finally give an example of how the graphs or diagrams can be used to analyze dialogues. (shrink)

The evolution of the human mind through natural selection mandates that our conscious experiences are causally potent in order to leave a tangible impact upon the surrounding physical world. Any attempt to construct a functional theory of the conscious mind within the framework of classical physics, however, inevitably leads to causally impotent conscious experiences in direct contradiction to evolution theory. Here, we derive several rigorous theorems that identify the origin of the latter impasse in the mathematical properties of ordinary differential (...) equations employed in combination with the alleged functional production of the mind by the brain. Then, we demonstrate that a mind--brain theory consistent with causally potent conscious experiences is provided by modern quantum physics, in which the unobservable conscious mind is reductively identified with the quantum state of the brain and the observable brain is constructed by the physical measurement of quantum brain observables. The resulting quantum stochastic dynamics obtained from sequential quantum measurements of the brain is governed by stochastic differential equations, which permit genuine free will exercised through sequential conscious choices of future courses of action. Thus, quantum reductionism provides a solid theoretical foundation for the causal potency of consciousness, free will and cultural transmission. (shrink)

We examine possible causal structures of experiments with entangled quantum objects. Previously, these structures have been obscured by assuming a misleading probabilistic analysis of quantum non locality as 'Outcome Dependence or Parameter Dependence' and by directly associating these correlations with influences. Here we try to overcome these shortcomings: we proceed from a recent stronger Bell argument, which provides an appropriate probabilistic description, and apply the rigorous methods of causal graph theory. Against the standard view that there is only an (...) influence between the measurement outcomes, we show that there must be an influence from one setting to its distant outcome: EPR correlations can only come about if one of the outcomes is a common effect of both settings. Our discussion makes explicit under which assumptions similar conclusions from information theoretic considerations can be interpreted causally. (shrink)

May the same graph admit two different chromatic numbers in two different universes? How about infinitely many different values? and can this be achieved without changing the cardinals structure? In this paper, it is proved that in Gödel’s constructible universe, for every uncountable cardinal $$\mu $$ below the first fixed-point of the $$\aleph $$ -function, there exists a graph $$\mathcal G_\mu $$ satisfying the following.

Coreference resolution is a challenging natural language processing task, and it is difficult to identify the correct mentions of an entity that can be any noun or noun phrase. In this article, a semisupervised, two-stage pattern-based bootstrapping approach is proposed for the coreference resolution task. During Stage 1, the possible mentions are identified using word-based features, and during Stage 2, the correct mentions are identified by filtering the non-coreferents of an entity using statistical measures and graph-based features. Whereas the (...) existing approaches use morphosyntactic and number/gender agreement features, the proposed approach uses semantic graph-based context-level semantics and nested noun phrases in the correct mentions identification. Moreover, mentions without the number/gender information are identified, using the context-based features of the semantic graph. The evaluation performed for the coreference resolution shows significant improvements, when compared with the word association-based bootstrapping systems. (shrink)

Biomimicry studies natural systems and attempts to use the gained knowledge and understanding to solve human problems. Can biomimicry, if applied in urban planning, help to make our cities more sustainable or, precisely, more friendly for walkable and 15-minute city models? Various researchers identify the following features of natural systems as form fits function, catalysis of cooperation, local contextuality, continuity of development, diversity, integrity, redundancy, decentralization, multifunctionality, and less energy consumption (e.g. TOD if the energy needed for transportation is considered), (...) hierarchy, fractality, etc. The presented research has two objectives: analyze the possibility of describing and evaluating the degree of expression of the features of natural systems in urban spatial structures to use them for comparison, benchmarking, or creation of a biomimicry index; evaluate if cities with more strongly expressed biomimicry features could be considered more walkable and close to the 15-minute city concept. To give answers to the above-presented questions Riga, Vilnius, and Tallinn were investigated. They represent both certain similarities and differences in terms of history, urban planning, political context, size, etc. A simulative mathematical graph model was used as the main tool to describe and analyze complex urban structures based on spatial configurations. Various graph centralities were employed to describe and compare the expression of natural systems’ features in the selected cities. OSM data was used to overlap graph models with such information as the density of inhabitants, concentrations of various points of interest in order to evaluate walkability and 15-minute city friendliness. The research results could be seen as an important step for better understanding of informal principles of biomimicry that can help transform urban areas. (shrink)

The mathematical field of graph theory has recently been used to provide counterexamples to the Principle of the Identity of Indiscernibles. In response to this, it has been argued that appeal to relations between graphs allows the Principle to survive the counterexamples. In this paper, I aim to show why that proposal does not succeed.

The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The author not only provides (...) a thorough description of the theory, but also details its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory. (shrink)

A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of (...) two deductive systems is an m-graph whose nodes are language expressions and the m-edges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graph-theoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with non-deterministic semantics, logics with an algebraic semantics, logics with partial semantics and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided. (shrink)

It is shown that if ZF is consistent, then so is ZFC + GCH + "There is a graph with cardinality ℵ 2 and chromatic number ℵ 2 such that every subgraph of cardinality ≤ ℵ 1 has chromatic number ≤ ℵ 0 ". This partially answers a question of Erdos and Hajnal.

The focus of this article is the view about fundamental natural properties known as dispositional monism. This is a holistic view about nature, according to which all properties are essentially interrelated. The general question to be addressed concerns what kinds of features relational structures of properties should be thought to have. I use Bird's graph-theoretic framework for representing dispositional structures as a starting point, before arguing that it is inadequate in certain important respects. I then propose a more parsimonious (...) graph-theoretic system, which, among other things, overhauls Bird's distinction between stimulus and manifestation relations. (shrink)

This experiment investigated the effect of format (line vs. bar), viewers’ familiarity with variables, and viewers’ graphicacy (graphical literacy) skills on the comprehension of multivariate (three variable) data presented in graphs. Fifty-five undergraduates provided written descriptions of data for a set of 14 line or bar graphs, half of which depicted variables familiar to the population and half of which depicted variables unfamiliar to the population. Participants then took a test of graphicacy skills. As predicted, the format influenced viewers’ interpretations (...) of data. Specifically, viewers were more likely to describe x–y interactions when viewing line graphs than when viewing bar graphs, and they were more likely to describe main effects and “z–y” (the variable in the legend) interactions when viewing bar graphs than when viewing line graphs. Familiarity of data presented and individuals’ graphicacy skills interacted with the influence of graph format. Specifically, viewers were most likely to generate inferences only when they had high graphicacy skills, the data were familiar and thus the information inferred was expected, and the format supported those inferences. Implications for multivariate data display are discussed. (shrink)

The primary objective of this study was to propose a functional discrete mathematical model for analyzing folklore fairy tales. Within this model, characters are denoted as vertices, and explicit instances of communication – both verbal and non-verbal – within the text are depicted as edges. Upon examining a corpus of Eastern Slavic fairy tales in comparison to Chukchi fairy tales, unforeseen outcomes emerged. Notably, the constructed models seem to evade establishing certain connections between characters. Consequently, instances where the interactions among (...) fairy tale characters would result in a non-planar graph structure are notably absent. To put it differently, the models refrain from incorporating sub-graphs delineated by the Kuratowski theorem governing planar graphs, specifically the minimal non-planar graphs Κ5 and Κ3,3. Remarkably, even in more extensive texts featuring a larger cast of characters, connections that would yield a non-planar graph pattern are consistently avoided. This leads to the formulation of a hypothesis positing that traditional folk tales adhere to a “planar narrative” design – an identifiable narrative variant characterized by inherent limitations in complexity. This design, in turn, appears deeply entrenched within the societal framework of the cultures that produced these folk narratives. (shrink)

Many contemporary proponents of hylomorphism endorse a version of hylomorphism according to which the form of a material object is a certain kind of complex relation or structure. Structural approaches to form, however, seem not to capture form’s traditional role as the guarantor of diachronic identity, since more “dynamically complex” material objects, such as living organisms, seem to undergo, and survive, various structural changes over the course of their existence. As a result, some contemporary hylomorphists have looked to alternative, non-structural (...) approaches to form. One of the leading non-structural approaches is the powers approach, according to which the form of a material object is a certain kind of power continuously activated in the object or in its material parts. In this paper, I begin by offering an overview and assessment of this powers approach to form. I argue that while the powers approach captures some crucial elements for understanding the nature of more dynamically complex material objects, when we press on the details of the view we find that it actually points to a related, but importantly distinct, third approach to understanding form, according to which the form of a material object is a certain kind of activity or process in which the material object or its parts are continuously engaged. I call this third approach “Hyloenergeism”. In the second half of the paper, I consider what such a view of material objects might look like and what its principal virtues might be. (shrink)

This article considers the sexual politics of animal evidence in the context of German sexology around 1920. In the 1910s, the German-Jewish geneticist Richard B. Goldschmidt conducted experiments on the moth Lymantria dispar, and discovered individuals that were no longer clearly identifiable as male or female. When he published an article tentatively arguing that his research on ‘intersex butterflies’ could be used to inform concurrent debates about human homosexuality, he triggered a flurry of responses from Berlin-based sexologists. In this article, (...) I examine how a number of well-known sexologists affiliated with Magnus Hirschfeld, his Scientific-Humanitarian Committee, and later his Institute of Sexology attempted to incorporate Goldschmidt’s experiments into their sexological work between 1917 and 1923. Intersex butterflies were used to discuss issues at the heart of German sexology: the legal debate about the criminalisation of homosexuality under paragraph 175; the scientific methodology of sexology, caught between psychiatric, biological, and sociological approaches to the study of sexual and gender diversity; and the status of sexology as natural science, able to contribute knowledge about the sexual Konstitution of the organism. This article thus shows that butterfly experiments function as important and politically charged evidence for a discussion at the heart of the sexological project of those involved in the founding of the Institute of Sexology: the question of the nature and naturalness of homosexuality (and sexual intermediacy more broadly) and its political consequences. In doing so, this article makes a case for paying attention to non-human actors in the history of sexology. (shrink)

The problem of when a recursive graph has a recursive k-coloring has been extensively studied by Bean, Schmerl, Kierstead, Remmel, and others. In this paper, we study the polynomial time analogue of that problem. We develop a number of negative and positive results about colorings of polynomial time graphs. For example, we show that for any recursive graph G and for any k, there is a polynomial time graph G′ whose vertex set is {0,1}* such that there (...) is an effective degree preserving correspondence between the set of k-colorings of G and the set of k-colorings of G′ and hence there are many examples of k-colorable polynomial time graphs with no recursive k-colorings. Moreover, even though every connected 2-colorable recursive graph is recursively 2-colorable, there are connected 2-colorable polynomial time graphs which have no primitive recursive 2-coloring. We also give some sufficient conditions which will guarantee that a polynomial time graph has a polynomial time or exponential time coloring. (shrink)

We compared the ability of three different contextual models of lexical semantic memory and of a simple associative model to predict the properties of semantic networks derived from word association norms. None of the semantic models were able to accurately predict all of the network properties. All three contextual models over-predicted clustering in the norms, whereas the associative model under-predicted clustering. Only a hybrid model that assumed that some of the responses were based on a contextual model and others on (...) an associative network successfully predicted all of the network properties and predicted a word's top five associates as well as or better than the better of the two constituent models. The results suggest that participants switch between a contextual representation and an associative network when generating free associations. We discuss the role that each of these representations may play in lexical semantic memory. Concordant with recent multicomponent theories of semantic memory, the associative network may encode coordinate relations between concepts, and contextual representations may be used to process information about more abstract concepts. (shrink)

Recently developed theory using directed graphs permits simple and precise statements about the validity of causal inferences in most cases. Applying this while reading econometric papers can make it easy to understand assumptions that are vague in prose, and to isolate those assumptions that are crucial to support the main causal claims. The method is illustrated here alongside a close reading of the paper that introduced the use of settler mortality to instrument the impact of institutions on economic development. Two (...) causal pathways that invalidate the instrument are found not to be blocked by satisfactory strategies. The estimates in the original paper, and in many that have used the instrument since, should be considered highly suspect. (shrink)

Peirce considered the principal business of logic to be the analysis of reasoning. He argued that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries the logical analysis of reasoning to the furthest point possible. The present paper investigates the analytic virtues of the Alpha part of the system, which corresponds to the sentential calculus. We examine Peirce’s proposal that the relation of illation is the primitive relation of logic and defend the view that this idea (...) constitutes the fundamental motive of philosophy of notation both in algebraic and graphical logic. We explain how in his algebras and graphs Peirce arrived at a unifying notation for logical constants that represent both truth-function and scope. Finally, we show that Shin’s argument for multiple readings of Alpha graphs is circular. (shrink)

The graph edit distance (GED) measures the dissimilarity between two graphs as the minimal cost of a sequence of elementary operations transforming one graph into another. This measure is fundamental in many areas such as structural pattern recognition or classification. However, exactly computing GED is NP-hard. Among different classes of heuristic algorithms that were proposed to compute approximate solutions, local search based algorithms provide the tightest upper bounds for GED. In this paper, we present K-REFINE and RANDPOST. K-REFINE (...) generalizes and improves an existing local search algorithm and performs particularly well on small graphs. RANDPOST is a general warm start framework that stochastically generates promising initial solutions to be used by any local search based GED algorithm. It is particularly efficient on large graphs. An extensive empirical evaluation demonstrates that both K-REFINE and RANDPOST perform excellently in practice. (shrink)

The authors consider reflexive games that describe the interaction of subjects making decisions based on an awareness structure, i.e., a hierarchy of beliefs about essential parameters, beliefs about beliefs, and so on. It was shown that the language of graphs of reflexive games represents a convenient uniform description method for reflexion effects in bélles-léttres.

Multi-Task Learning tries to improve the learning process of different tasks by solving them simultaneously. A popular Multi-Task Learning formulation for SVM is to combine common and task-specific parts. Other approaches rely on using a Graph Laplacian regularizer. Here we propose a combination of these two approaches that can be applied to L1, L2 and LS-SVMs. We also propose an algorithm to iteratively learn the graph adjacency matrix used in the Laplacian regularization. We test our proposal with synthetic (...) and real problems, both in regression and classification settings. When the task structure is present, we show that our model is able to detect it, which leads to better results, and we also show it to be competitive even when this structure is not present. (shrink)

We performed an EEG graph analysis on data from 31 typical readers (22.27 ± 2.53 y/o) and 24 dyslexics (22.99 ± 2.29 y/o), recorded while they were engaged in an audiovisual task and during resting-state. The task simulates reading acquisition as participants learned new letter-sound mappings via feedback. EEG data was filtered for the delta (0.5–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), and beta (13–30 Hz) bands. We computed the Phase Lag Index (PLI) to provide an estimate of (...) the functional connectivity between all pairs of electrodes per band. Then, networks were constructed using a Minimum Spanning Tree (MST), a unique sub-graph connecting all nodes (electrodes) without loops, aimed at minimizing bias in between groups and conditions comparisons. Both groups showed a comparable accuracy increase during task blocks, indicating that they correctly learned the new associations. The EEG results revealed lower task-specific theta connectivity, and lower theta degree correlation over both rest and task recordings, indicating less network integration in dyslexics compared to typical readers. This pattern suggests a role of theta oscillations in dyslexia and may reflect differences in task engagement between the groups, although robust correlations between MST metrics and performance indices were lacking. (shrink)

I argue that Frege Problems in thought are best modeled using graph-theoretic machinery; and that these problems can arise even when subjects associate all the same qualitative properties to the object they’re thinking of twice. I compare the proposed treatment to similar ideas by Heck, Ninan, Recanati, Kamp and Asher, Fodor, and others.

This paper examines the contemporary philosophical and cognitive relevance of Charles Peirce's diagrammatic logic of existential graphs (EGs), the ‘moving pictures of thought’. The first part brings to the fore some hitherto unknown details about the reception of EGs in the early 1900s that took place amidst the emergence of modern conceptions of symbolic logic. In the second part, philosophical aspects of EGs and their contributions to contemporary logical theory are pointed out, including the relationship between iconic logic and images, (...) the problem of the meaning of logical constants, the cognitive economy of iconic logic, the failure of the Frege–Russell thesis, and the failure of the Language of Thought hypothesis. (shrink)

Fried and Kollár constructed a fully faithful functor from the category of graphs to the category of fields. We give a new construction of such a functor and use it to resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure${\cal S}$, there exists a countable field${\cal F}$of arbitrary characteristic with the same essential computable-model-theoretic properties as${\cal S}$. Along the way, we develop a new “computable category theory”, and prove that our functor and (...) its partially defined inverse are computable functors. (shrink)

In organisms, ribonucleic acid plays an essential role. Its function is being discovered more and more. Due to the conserved nature of RNA sequences, its function mainly depends on the RNA secondary structure. The discovery of an approximate relationship between two RNA secondary structures helps to understand their functional relationship better. It is an important and urgent task to explore structural similarities from the graphical representation of RNA secondary structures. In this paper, a novel graphical analysis method based on the (...) triple vector curve representation of RNA secondary structures is proposed. A combinational method involving a discrete wavelet transform and fractal dimension with sliding window is introduced to analyze and compare the graphs derived from feature extraction; after that, the distance matrix is generated. Then, the distance matrix is analyzed by clustering and visualized as a clustering tree. RNA virus and noncoding RNA datasets are applied to perform experiments and analyze the clustering tree. The results show that the proposed method yields more accurate results in the comparison of RNA secondary structures. (shrink)

We define a model for computing probabilities of right-nested conditionals in terms of graphs representing Markov chains. This is an extension of the model for simple conditionals from Wójtowicz and Wójtowicz. The model makes it possible to give a formal yet simple description of different interpretations of right-nested conditionals and to compute their probabilities in a mathematically rigorous way. In this study we focus on the problem of the probabilities of conditionals; we do not discuss questions concerning logical and metalogical (...) issues such as setting up an axiomatic framework, inference rules, defining semantics, proving completeness, soundness etc. Our theory is motivated by the possible-worlds approach ; however, our model is generally more flexible. In the paper we focus on right-nested conditionals, discussing them in detail. The graph model makes it possible to account in a unified way for both shallow and deep interpretations of right-nested conditionals. In particular, we discuss the status of the Import-Export Principle and PCCP. We briefly discuss some methodological constraints on admissible models and analyze our model with respect to them. The study also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues. (shrink)

Graph theory is a specific concept that has numerous applications throughout many industries. Despite the advancement of this technique, graph theory can still yield ambiguous and imprecise results. In order to cut down on these indeterminate factors, neutrosophic logic has emerged as an applicable solution that is gaining significant attention in solving many real-life decision-making problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. However, empirical research on this specific graph set is lacking. Neutrosophic Graph (...) Theory and Algorithms is a collection of innovative research on the methods and applications of neutrosophic sets and logic within various fields including systems analysis, economics, and transportation. While highlighting topics including linear programming, decision-making methods, and homomorphism, this book is ideally designed for programmers, researchers, data scientists, mathematicians, designers, educators, researchers, academicians, and students seeking current research on the various methods and applications of graph theory. (shrink)

The non-well-founded set theories described by Aczel (1988) have received attention from category theorists and computer scientists, but have been largely ignored by philosophers. At the root of this neglect might lie the impression that these theories do not embody a conception of set, but are rather of mere technical interest. This paper attempts to dispel this impression. I present a conception of set which may be taken as lying behind a non-well-founded set theory. I argue that the axiom AFA (...) is justified on the conception, which provides, contra Rieger (Mind 109:241–253, 2000), a rationale for restricting attention to the system based on this axiom. By making use of formal and informal considerations, I then make a case that most of the other axioms of this system are also justified on the conception. I conclude by commenting on the significance of the conception for the debate about the justification of the Axiom of Foundation. (shrink)

Language experience shapes the gradual maturation of speech production in both native and second languages. Structural aspects like the connectedness of spontaneous narratives reveal this maturation progress in L1 acquisition and, as it does not rely on semantics, it could also reveal structural pattern changes during L2 acquisition. The current study tested whether L2 lexical retrieval associated with vocabulary knowledge could impact the global connectedness of narratives during the initial stages of L2 acquisition. Specifically, the study evaluated the relationship between (...) graph structure and L2 learners’ oral production in the L2 and L1. Seventy-nine college-aged students who were native speakers of English and had received classroom instruction in either L2-Spanish or L2-Chinese participated in this study. Three tasks were used: semantic fluency, phonemic fluency and picture description. Measures were operationalized as the number of words per minute in the case of the semantic and phonemic fluency tasks. Graph analysis was carried out for the picture description task using the computational tool SpeechGraphs to calculate connectedness. Results revealed significant positive correlations between connectedness in the picture description task and measures of speech production in the phonemic and semantic fluency tasks. These correlations were only significant for the participants’ L2- Spanish and Chinese. Results indicate that producing low connectedness narratives in L2 may be a marker of the initial stages of L2 oral development. These findings are consistent with the pattern reported in the early stages of L1 literacy. Future studies should further explore the interactions between graph structure and second language production proficiency, including more advanced stages of L2 learning and considering the role of cognitive abilities in this process. (shrink)

When no single universal model for a set of structures exists at a given cardinal, then one may ask in which models of set theory does there exist a small family which embeds the rest. We show that for λ+-graphs (λ regular) omitting cliques of some finite or uncountable cardinality, it is consistent that there are small universal families and 2λ > λ+. In particular, we get such a result for triangle-free graphs.