La représentation des relations de cooccurrence à l’échelle d’un corpus entier sous la forme d’un graphe permet d’étudier l’organisation des mots dans le discours par des moyens lexicométriques. Cette étude révèle deux formes d’organisation complémentaires de ce lexique. En premier lieu, une organisation hiérarchique, qui donne à certains lemmes une saillance particulière du fait de leur meilleur positionnement dans le réseau de relations de cooccurrence. En second lieu, une organisation modulaire, qui montre que les liens de cooccurrence (...) dans le texte répartissent le lexique en classes de lemmes co-occurrents les uns aux autres. Ces deux formes d’organisation du lexique dans les textes donnent une image du sens général de celui-ci, et permettent d’identifier la variabilité du sens lexical des unités telles qu’elles sont employées en discours. (shrink)

La représentation des relations de cooccurrence à l’échelle d’un corpus entier sous la forme d’un graphe permet d’étudier l’organisation des mots dans le discours par des moyens lexicométriques. Cette étude révèle deux formes d’organisation complémentaires de ce lexique. En premier lieu, une organisation hiérarchique, qui donne à certains lemmes une saillance particulière du fait de leur meilleur positionnement dans le réseau de relations de cooccurrence. En second lieu, une organisation modulaire, qui montre que les liens de cooccurrence (...) dans le texte répartissent le lexique en classes de lemmes co-occurrents les uns aux autres. Ces deux formes d’organisation du lexique dans les textes donnent une image du sens général de celui-ci, et permettent d’identifier la variabilité du sens lexical des unités telles qu’elles sont employées en discours. (shrink)

A partir de l’enregistrement de discours spontanés d’enfants âgés de 3 à 8 ans dans trois conditions (psychologue, groupe, parents), l’objectif de cette recherche sera d’appréhender le développement du rapport que l’enfant entretient avec lui-même et les autres en observant la distribution et les utilisations particulières des formes personnelles chez l’enfant. Pour qualifier ces emplois, nous examinerons le détail des cooccurrents des pronoms pour chaque catégorie considérée. La situation de groupe s’étant avérée particulièrement concluante, nous lui consacrerons la dernière partie (...) de nos explorations en nous concentrant sur l’asymétrie cooccurrentielle du couple moi-je dans la continuité de nos travaux autour de l’asymétrie de la relation coocurrentielle [Luong et al. 2010] en insistant sur leurs résonances dans le développement de l’identité chez l’enfant. (shrink)

A partir de l’enregistrement de discours spontanés d’enfants âgés de 3 à 8 ans dans trois conditions (psychologue, groupe, parents), l’objectif de cette recherche sera d’appréhender le développement du rapport que l’enfant entretient avec lui-même et les autres en observant la distribution et les utilisations particulières des formes personnelles chez l’enfant. Pour qualifier ces emplois, nous examinerons le détail des cooccurrents des pronoms pour chaque catégorie considérée. La situation de groupe s’étant avérée particulièrement concluante, nous lui consacrerons la dernière partie (...) de nos explorations en nous concentrant sur l’asymétrie cooccurrentielle du couple moi-je dans la continuité de nos travaux autour de l’asymétrie de la relation coocurrentielle [Luong et al. 2010] en insistant sur leurs résonances dans le développement de l’identité chez l’enfant. (shrink)

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)

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)

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.

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)

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)

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)

Récurrente sous différentes formes dans le domaine de la lexicométrie, l’analyse cooccurrentielle vise à dévoiler les attractions lexicales qui opèrent dans un texte en restituant un état intermédiaire entre la séquence textuelle et l’inventaire lexical, état qui doit combiner l’explicitation syntagmatique de l’une avec la hiérarchisation statistique de l’autre. Pour dépasser les résultats des méthodes de cooccurrence classiques et identifier des systèmes cooccurrentiels plus complexes à l’oeuvre dans le texte, il s’avère nécessaire de substituer à l’approche analytique des associations (...) lexicales une vue synthétique de ces attractions prééminentes en contexte. (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.

Récurrente sous différentes formes dans le domaine de la lexicométrie, l’analyse cooccurrentielle vise à dévoiler les attractions lexicales qui opèrent dans un texte en restituant un état intermédiaire entre la séquence textuelle et l’inventaire lexical, état qui doit combiner l’explicitation syntagmatique de l’une avec la hiérarchisation statistique de l’autre. Pour dépasser les résultats des méthodes de cooccurrence classiques et identifier des systèmes cooccurrentiels plus complexes à l’oeuvre dans le texte, il s’avère nécessaire de substituer à l’approche analytique des associations (...) lexicales une vue synthétique de ces attractions prééminentes en contexte. (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)

Cet article montre ce que la cooccurrence peut nous apprendre sur la monosémie et comment on peut exploiter l’analyse des cooccurrences de deuxième ordre pour quantifier l’analyse sémantique. Les analyses sont conduites sur un corpus technique (1,7 million d’occurrences) relevant du domaine spécialisé des machines-outils pour l’usinage des métaux. Dans cet article, nous expliquons la méthodologie adoptée pour déterminer le degré de monosémie d’un mot technique à partir de l’analyse du recoupement de ses cooccurrences de deuxième ordre. Dans le (...) but d’affiner les résultats de la mesure de recoupement, nous procédons également à quelques expérimentations qui vont au-delà du simple repérage statistique des cooccurrences et qui font varier différents paramètres, tels que la fenêtre d’observation, le seuil de significativité et la forme graphique ou le lemme des cooccurrences de premier et deuxième ordre. Finalement, nous abordons l’importance de l’intégration des étiquettes morphosyntaxiques dans l’analyse des cooccurrences. (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)

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)

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)

Cet article montre ce que la cooccurrence peut nous apprendre sur la monosémie et comment on peut exploiter l’analyse des cooccurrences de deuxième ordre pour quantifier l’analyse sémantique. Les analyses sont conduites sur un corpus technique (1,7 million d’occurrences) relevant du domaine spécialisé des machines-outils pour l’usinage des métaux. Dans cet article, nous expliquons la méthodologie adoptée pour déterminer le degré de monosémie d’un mot technique à partir de l’analyse du recoupement de ses cooccurrences de deuxième ordre. Dans le (...) but d’affiner les résultats de la mesure de recoupement, nous procédons également à quelques expérimentations qui vont au-delà du simple repérage statistique des cooccurrences et qui font varier différents paramètres, tels que la fenêtre d’observation, le seuil de significativité et la forme graphique ou le lemme des cooccurrences de premier et deuxième ordre. Finalement, nous abordons l’importance de l’intégration des étiquettes morphosyntaxiques dans l’analyse des cooccurrences. (shrink)

Cet article essaye d’évaluer l’impact de la lemmatisation, ou, inversement, de la flexion casuelle sur les réseaux cooccurrentiels d’un mot-pôle en latin. Conjointement, il exploite cet impact pour approfondir l’examen de l’asymétrie des relations de cooccurrence.Nos précédents articles méthodologiques, consacrés notamment à l’asymétrie de la cooccurrence, reposaient en effet sur le dénombrement des cooccurrents d’un mot-pôle considéré et décompté sous sa forme de lemme. Or, si la cooccurrence est bien la « forme minimale du contexte » [Mayaffre (...) 2008] qui contribue à construire le sens textuel, la question se pose alors de la pertinence de l’abstraction opérée par la lemmatisation. Les différentes formes fléchies d’un mot en latin sont porteuses non seulement des catégories du nombre (et, pour les adjectifs et les pronoms, du genre), mais aussi de marques casuelles étroitement reliées à la fonction syntaxique et l’ensemble est susceptible d’avoir une influence sur le contexte immédiat du mot, y compris dans sa dimension thématique.Nous montrons donc dans un premier temps que la forme casuelle d’un mot latin détermine pour une bonne part la liste de ses cooccurrents spécifiques. Nous exploitons ensuite ce constat pour confirmer, au moyen de deux tests différents qui utilisent le réseau cooccurrentiel des diverses formes fléchies d’un même lemme, une hypothèse précédemment avancée [Luong et al. 2010] selon laquelle l’asymétrie des cooccurrences est, pour partie au moins, une image de la double insertion d’une forme, d’une part, dans un paradigme lexico-sémantique stabilisée en langue, d’autre part, dans un réseau de relations syntagmatiques actualisées en discours. (shrink)

Cet article essaye d’évaluer l’impact de la lemmatisation, ou, inversement, de la flexion casuelle sur les réseaux cooccurrentiels d’un mot-pôle en latin. Conjointement, il exploite cet impact pour approfondir l’examen de l’asymétrie des relations de cooccurrence.Nos précédents articles méthodologiques, consacrés notamment à l’asymétrie de la cooccurrence, reposaient en effet sur le dénombrement des cooccurrents d’un mot-pôle considéré et décompté sous sa forme de lemme. Or, si la cooccurrence est bien la « forme minimale du contexte » [Mayaffre (...) 2008] qui contribue à construire le sens textuel, la question se pose alors de la pertinence de l’abstraction opérée par la lemmatisation. Les différentes formes fléchies d’un mot en latin sont porteuses non seulement des catégories du nombre (et, pour les adjectifs et les pronoms, du genre), mais aussi de marques casuelles étroitement reliées à la fonction syntaxique et l’ensemble est susceptible d’avoir une influence sur le contexte immédiat du mot, y compris dans sa dimension thématique.Nous montrons donc dans un premier temps que la forme casuelle d’un mot latin détermine pour une bonne part la liste de ses cooccurrents spécifiques. Nous exploitons ensuite ce constat pour confirmer, au moyen de deux tests différents qui utilisent le réseau cooccurrentiel des diverses formes fléchies d’un même lemme, une hypothèse précédemment avancée [Luong et al. 2010] selon laquelle l’asymétrie des cooccurrences est, pour partie au moins, une image de la double insertion d’une forme, d’une part, dans un paradigme lexico-sémantique stabilisée en langue, d’autre part, dans un réseau de relations syntagmatiques actualisées en discours. (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 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.

Les coocurrences ont surtout servi jusqu’ici à établir les relations, principalement sémantiques, que les mots ont entre eux. On les relevait certes dans un corpus, mais de façon indifférenciée, sans opposer les textes les uns aux autres. Or la comparaison des textes est la démarche habituelle quand la lexicométrie s’occupe des mots simples. On se propose ici d’étendre aux données cooccurrentielles les méthodes et les outils statistiques qui ont fait leurs preuves au niveau lexical. New Statistical Processing of Co-occurences by (...) HYPERBASE. The co-occurrences have mainly been studied to establish semantic relations, i.e., the relation in-between words. Certainly, they use to be extracted from a corpus, but indiscriminately, without taking into consideration the text divisions. When dealing with simple words, the usual approach is the comparison of texts. Here, we propose to extend those methods, approved at the lexical level, and to enlarge the application of statistical tools even to co-occurrential data. (shrink)

Nicholas Shackel (2011) has proposed a number of arguments to save the Dipert–Bird model of physical reality from the sorts of unpalatable consequence I identified in Oderberg 2011. Some consequences, he thinks, are only apparent; others are real but palatable. In neither case does he seem to me to have deflected the concerns I raised, leaving graph structuralism on Dipert–Bird lines as problematic as ever.

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)

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.

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)

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 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)

We investigate dependence of recursively enumerable graphs on the equality relation given by a specific r.e. equivalence relation on ω. In particular we compare r.e. equivalence relations in terms of graphs they permit to represent. This defines partially ordered sets that depend on classes of graphs under consideration. We investigate some algebraic properties of these partially ordered sets. For instance, we show that some of these partial ordered sets possess atoms, minimal and maximal elements. We also fully describe the isomorphism (...) types of some of these partial orders. (shrink)

Les coocurrences ont surtout servi jusqu’ici à établir les relations, principalement sémantiques, que les mots ont entre eux. On les relevait certes dans un corpus, mais de façon indifférenciée, sans opposer les textes les uns aux autres. Or la comparaison des textes est la démarche habituelle quand la lexicométrie s’occupe des mots simples. On se propose ici d’étendre aux données cooccurrentielles les méthodes et les outils statistiques qui ont fait leurs preuves au niveau lexical. New Statistical Processing of Co-occurences by (...) HYPERBASE. The co-occurrences have mainly been studied to establish semantic relations, i.e., the relation in-between words. Certainly, they use to be extracted from a corpus, but indiscriminately, without taking into consideration the text divisions. When dealing with simple words, the usual approach is the comparison of texts. Here, we propose to extend those methods, approved at the lexical level, and to enlarge the application of statistical tools even to co-occurrential data. (shrink)

Improving a theorem of Gasarch and Hirst, we prove that if 2 ≤ k ≤ m < ω, then the following is equivalent to WKL0 over RCA0 Every locally k-colorable graph is m-colorable.

The paper is concerned with the existence of a universal graph at the successor of a strong limit singular μ of cofinality ℵ0. Starting from the assumption of the existence of a supercompact cardinal, a model is built in which for some such μ there are $\mu^{++}$ graphs on μ+ that taken jointly are universal for the graphs on μ+, while $2^{\mu^+} \gg \mu^{++}$ . The paper also addresses the general problem of obtaining a framework for consistency results at (...) the successor of a singular strong limit starting from the assumption that a supercompact cardinal κ exists. The result on the existence of universal graphs is obtained as a specific application of a more general method. (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)

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.

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)

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)

Peirce and Frege both distinguished between the propositional content of an assertion and the assertion of a propositional content, but with different notational means. We present a modification of Peirce’s graphical method of logic that can be used to reason about assertions in a manner similar to Peirce’s original method. We propose a new system of Assertive Graphs, which unlike the tradition that follows Frege involves no ad hoc sign of assertion. We show that axioms of intuitionistic logic can be (...) derived from AGs, and argue that AGs analyse and represent assertions and illocutionary content in a way which is motivated both by its logical properties and its historical connection with the ideas that led to the development of the graphical method. (shrink)

The semantic paradoxes are often associated with self-reference or referential circularity. Yablo (Analysis 53(4):251–252, 1993), however, has shown that there are infinitary versions of the paradoxes that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality. In this essay, we lay the groundwork for a general investigation into the nature of reference structures that support the semantic paradoxes and the semantic hypodoxes. We develop (...) a functionally complete infinitary propositional language endowed with a denotation assignment and extract the reference structural information in terms of graph-theoretic properties. We introduce the new concepts of dangerous and precarious reference graphs, which allows us to rigorously define the task: classify the dangerous and precarious directed graphs purely in terms of their graph-theoretic properties. Ungroundedness will be shown to fully characterize the precarious reference graphs and fully characterize the dangerous finite graphs. We prove that an undirected graph has a dangerous orientation if and only if it contains a cycle, providing some support for the traditional idea that cyclic structure is required for paradoxicality. This leaves the task of classifying danger for infinite acyclic reference graphs. We provide some compactness results, which give further necessary conditions on danger in infinite graphs, which in conjunction with a notion of self-containment allows us to prove that dangerous acyclic graphs must have infinitely many vertices with infinite out-degree. But a full characterization of danger remains an open question. In the appendices we relate our results to the results given in Cook (J Symb Log 69(3):767–774, 2004) and Yablo (2006) with respect to more restricted sentences systems, which we call $\mathcal{F}$ -systems. (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)

In this paper, I sketch a new model for the format of the content of understanding states, Compressible Graph Maximalism (CGM). In this model, the format of the content of understanding is graphical, and compressible. It thus combines ideas from approaches that stress the link between understanding and holistic structure (like as reported by Grimm (in: Ammon SGCBS (ed) Explaining Understanding: New Essays in Epistemollogy and the Philosophy of Science, Routledge, New York, 2016)), and approaches that emphasize the connection (...) between understanding and compression (like Wilkenfeld (Synthese 190(6):997–1016, 2018)). I argue that the combination of these ideas has several attractive features, and I defend the idea against some challenges. (shrink)

We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T.A. Knight and C. Darwin, and sketch a decomposition result (...) involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels’ question, “Can biology lead to new theorems?”. (shrink)

We performed an EEG graph analysis on data from 31 typical readers and 24 dyslexics, 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, theta, alpha, and beta bands. We computed the Phase Lag Index to provide an estimate of the functional connectivity between all pairs of electrodes per band. Then, networks were constructed using a Minimum (...) Spanning Tree, a unique sub-graph connecting all nodes 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)

In this book, the authors systematically define the new notion of linguistic graphs associated with a linguistic set of a linguistic variable. We can also define the notion of directed linguistic graphs and linguistic-weighted graphs. Chapter two discusses all types of linguistic graphs, linguistic dyads, linguistic triads, linguistic wheels, complete linguistic graphs, linguistic connected graphs, disconnected linguistic graphs, linguistic components of the graphs and so on. Further, we define the notion of linguistic subgraphs of a linguistic graph. However, like (...) usual graphs, we will not be able to arbitrarily connect any two linguistic words of a linguistic set associated with a linguistic variable. They can be related or adjacent depending on the linguistic variable associated with the linguistic set. This is an exceptional feature of a linguistic graph. (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 \ below the first fixed-point of the \-function, there exists a graph \ satisfying the following:\ has size and chromatic number \;for every infinite cardinal \, there exists a cofinality-preserving \-preserving forcing extension in which (...) \=\kappa \). (shrink)