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6345 found
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1 — 50 / 6345
  1. Algunos tópicos de Lógica matemática y los Fundamentos de la matemática.Franklin Galindo - manuscript
    En este trabajo matemático-filosófico se estudian cuatro tópicos de la Lógica matemática: El método de construcción de modelos llamado Ultraproductos, la Propiedad de Interpolación de Craig, las Álgebras booleanas y los Órdenes parciales separativos. El objetivo principal del mismo es analizar la importancia que tienen dichos tópicos para el estudio de los fundamentos de la matemática, desde el punto de vista del platonismo matemático. Para cumplir con tal objetivo se trabajará en el ámbito de la Matemática, de la Metamatemática y (...)
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  2. Nota: ¿CUÁL ES EL CARDINAL DEL CONJUNTO DE LOS NÚMEROS REALES?Franklin Galindo - manuscript
    ¿Qué ha pasado con el problema del cardinal del continuo después de Gödel (1938) y Cohen (1964)? Intentos de responder esta pregunta pueden encontrarse en los artículos de José Alfredo Amor (1946-2011), "El Problema del continuo después de Cohen (1964-2004)", de Carlos Di Prisco , "Are we closer to a solution of the continuum problem", y de Joan Bagaria, "Natural axioms of set and the continuum problem" , que se pueden encontrar en la biblioteca digital de mi blog de Lógica (...)
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  3. A statistical learning approach to a problem of induction.Kino Zhao - manuscript
    At its strongest, Hume's problem of induction denies the existence of any well justified assumptionless inductive inference rule. At the weakest, it challenges our ability to articulate and apply good inductive inference rules. This paper examines an analysis that is closer to the latter camp. It reviews one answer to this problem drawn from the VC theorem in statistical learning theory and argues for its inadequacy. In particular, I show that it cannot be computed, in general, whether we are in (...)
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  4. Two notes on abstract model theory. I. properties invariant on the range of definable relations between structures.Solomon Feferman with with R. L. Vaught - manuscript
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  5. Two notes on abstract model theory. II. languages for which the set of valid sentences is semi-invariantly implicitly definable.Solomon Feferman with with R. L. Vaught - manuscript
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  6. Rijke. PDL for ordered trees.Loredana Afanasiev, Patrick Blackburn, Ioanna Dimitriou, Gaiffe Evan, Goris Maarten & Marx Maarten - forthcoming - Journal of Applied Non-Classical Logics.
  7. Dependent choice, properness, and generic absoluteness.David Asperó & Asaf Karagila - forthcoming - Review of Symbolic Logic:1-25.
    We show that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the presence of large cardinals, even with respect to $\mathsf {DC}$ -preserving symmetric submodels of forcing extensions. Hence, $\mathsf {ZF}+\mathsf {DC}$ not only provides the right framework for developing classical analysis, but is also the right base theory over which to safeguard truth in analysis from the independence phenomenon in the presence of (...)
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  8. Syntactic characterizations of first-order structures in mathematical fuzzy logic.Guillermo Badia, Pilar Dellunde, Vicent Costa & Carles Noguera - forthcoming - Soft Computing.
    This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.
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  9. Local Applications of Logics via Model-Theoretic Interpretations.Carlos Benito-Monsalvo - forthcoming - Logic and Logical Philosophy:1-22.
    This paper analyses the notion of ‘interpretation’, which is often tied to the semantic approach to logic, where it is used when referring to truth-value assignments, for instance. There are, however, other uses of the notion that raise interesting problems. These are the cases in which interpreting a logic is closely related to its justification for a given application. The paper aims to present an understanding of interpretations that supports the model-theoretic characterization of validity to the detriment of the proof-theoretic (...)
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  10. The additive groups of ℤ and ℚ with predicates for being square‐free.Neer Bhardwaj & Minh Chieu Tran - forthcoming - Journal of Symbolic Logic:1-26.
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  11. Transmission of Verification.Ethan Brauer & Neil Tennant - forthcoming - Review of Symbolic Logic:1-16.
    This paper clarifies, revises, and extends the account of the transmission of truthmakers by core proofs that was set out in chap. 9 of Tennant. Brauer provided two kinds of example making clear the need for this. Unlike Brouwer’s counterexamples to excluded middle, the examples of Brauer that we are dealing with here establish the need for appeals to excluded middle when applying, to the problem of truthmaker-transmission, the already classical metalinguistic theory of model-relative evaluations.
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  12. Inferential Quantification and the ω-rule.Constantin C. Brîncuș - forthcoming - In Antonio D’Aragona (ed.), Perspectives on Deduction.
    Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...)
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  13. Genericity.and Fabio Del Prete C. Beyssade /Alda Mari (ed.) - forthcoming - Oxford University Press.
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  14. Twist-Valued Models for Three-Valued Paraconsistent Set Theory.Walter A. Carnielli & Marcelo E. Coniglio - forthcoming - Logic and Logical Philosophy:1.
    We propose in this paper a family of algebraic models of ZFC based on the three-valued paraconsistent logic LPT0, a linguistic variant of da Costa and D’Ottaviano’s logic J3. The semantics is given by twist structures defined over complete Boolean agebras. The Boolean-valued models of ZFC are adapted to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. This allows for inconsistent sets w satisfying ‘not (w = w)’, where ‘not’ stands for the paraconsistent negation. Finally, our (...)
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  15. Games and cardinalities in inquisitive first-order logic.Ivano Ciardelli & Gianluca Grilletti - forthcoming - Review of Symbolic Logic:1-28.
    Inquisitive first-order logic, InqBQ, is a system which extends classical first-order logic with formulas expressing questions. From a mathematical point of view, formulas in this logic express properties of sets of relational structures. This paper makes two contributions to the study of this logic. First, we describe an Ehrenfeucht–Fraïssé game for InqBQ and show that it characterizes the distinguishing power of the logic. Second, we use the game to study cardinality quantifiers in the inquisitive setting. That is, we study what (...)
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  16. Domain Formula Circumscription.Tom Costello - forthcoming - Journal of Logic Language and Information.
  17. Sur quelques relations entre Les zéros et Les poLes Des fonctions méromorphes. Applications au developpement de Mittag-Leffler.Jeanne Férentinou-Nicolacopoulou - forthcoming - Eleutheria.
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  18. Bisimulations for Knowing How Logics.Raul Fervari, Fernando R. Velázquez-Quesada & Yanjing Wang - forthcoming - Review of Symbolic Logic:1-37.
    As a new type of epistemic logics, the logics of knowing how capture the high-level epistemic reasoning about the knowledge of various plans to achieve certain goals. Existing work on these logics focuses on axiomatizations; this paper makes the first study of their model theoretical properties. It does so by introducing suitable notions of bisimulation for a family of five knowing how logics based on different notions of plans. As an application, we study and compare the expressive power of these (...)
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  19. Absoluteness and the Skolem Paradox.Michael Hallett - forthcoming - Unpublished.
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  20. Model Theory of Fields with Finite Group Scheme Actions.Daniel Max Hoffmann & Piotr Kowalski - forthcoming - Journal of Symbolic Logic:1-26.
    We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative Hasse–Schmidt derivations [13] and about Galois actions [14]. As an application of our methods, we obtain a new model complete theory of actions of a finite group on fields of finite imperfection degree.
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  21. The Taming of Content: Some Thoughts About Domains and Modules.Keith J. Holyoak & Patricia W. Cheng - forthcoming - Thinking and Reasoning.
  22. A bounded arithmetictheory for LOGCFL.S. Kuroda - forthcoming - Archive for Mathematical Logic.
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  23. Maximal Towers and Ultrafilter Bases in Computability Theory.Steffen Lempp, Joseph S. Miller, André Nies & Mariya I. Soskova - forthcoming - Journal of Symbolic Logic:1-21.
    The tower number ${\mathfrak t}$ and the ultrafilter number $\mathfrak {u}$ are cardinal characteristics from set theory. They are based on combinatorial properties of classes of subsets of $\omega $ and the almost inclusion relation $\subseteq ^*$ between such subsets. We consider analogs of these cardinal characteristics in computability theory. We say that a sequence $(G_n)_{n \in {\mathbb N}}$ of computable sets is a tower if $G_0 = {\mathbb N}$, $G_{n+1} \subseteq ^* G_n$, and $G_n\smallsetminus G_{n+1}$ is infinite for each (...)
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  24. Badiou, Mathematics, and Model Theory.Paul Livingston - forthcoming - MonoKL.
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  25. Hyperbolic towers and independent generic sets in the theory of free groups, to appear in the Proceedings of the conference" Recent developments in Model Theory.Lars Louder, Chloé Perin & Rizos Sklinos - forthcoming - Notre Dame Journal of Formal Logic.
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  26. Groups of Worldview Transformations Implied by Einstein’s Special Principle of Relativity over Arbitrary Ordered Fields.Judit X. Madarász, Mike Stannett & Gergely Székely - forthcoming - Review of Symbolic Logic:1-28.
    In 1978, Yu. F. Borisov presented an axiom system using a few basic assumptions and four explicit axioms, the fourth being a formulation of the relativity principle; and he demonstrated that this axiom system had (up to choice of units) only two models: a relativistic one in which worldview transformations are Poincaré transformations and a classical one in which they are Galilean. In this paper, we reformulate Borisov’s original four axioms within an intuitively simple, but strictly formal, first-order logic framework, (...)
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  27. Definability in valued Ore modules.Françoise Point - forthcoming - Bulletin of Symbolic Logic.
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  28. Quine’s fluted fragment revisited.Ian Pratt-Hartmann, Wiesław Szwast & Lidia Tendera - forthcoming - Journal of Symbolic Logic:1-30.
  29. Special Issue on Recent Advances in Logical and Algebraic Approaches to Grammar, volume 7 (4) of.C. Retoré - forthcoming - Journal of Logic Language and Information.
    This a special issue of the Journal of Logic Language and Information that I edited.
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  30. Variations on determinacy and.Ramez L. Sami - forthcoming - Journal of Symbolic Logic:1-10.
  31. A Fully Model-Theoretic Semantics for Model-Preference Default Systems', Istituto di Elaborazione dell'Informazione, Pisa.F. Sebastiani - forthcoming - Studia Logica.
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  32. On the notion of Guessing model.Matteo Viale - forthcoming - Annals of Pure and Applied Logic.
  33. Model Theory and Proof Theory of the Global Reflection Principle.Mateusz Zbigniew Łełyk - forthcoming - Journal of Symbolic Logic:1-42.
    The current paper studies the formal properties of the Global Reflection Principle, to wit the assertion “All theorems of $\mathrm {Th}$ are true,” where $\mathrm {Th}$ is a theory in the language of arithmetic and the truth predicate satisfies the usual Tarskian inductive conditions for formulae in the language of arithmetic. We fix the gap in Kotlarski’s proof from [15], showing that the Global Reflection Principle for Peano Arithmetic is provable in the theory of compositional truth with bounded induction only (...)
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  34. Admissibility of Π2-Inference Rules: interpolation, model completion, and contact algebras.Nick Bezhanishvili, Luca Carai, Silvio Ghilardi & Lucia Landi - 2023 - Annals of Pure and Applied Logic 174 (1):103169.
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  35. On the proof complexity of logics of bounded branching.Emil Jeřábek - 2023 - Annals of Pure and Applied Logic 174 (1):103181.
  36. A Modern Rigorous Approach to Stratification in NF/NFU.Tin Adlešić & Vedran Čačić - 2022 - Logica Universalis 16 (3):451-468.
    The main feature of NF/NFU is the notion of stratification, which sets it apart from other set theories. We define stratification and prove constructively that every stratified formula has the (unique) least assignment of types. The basic notion of stratification is concerned only with variables, but we extend it to abstraction terms in order to simplify further development. We reflect on nested abstraction terms, proving that they get the expected types. These extensions enable us to check whether some complex formula (...)
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  37. Copying One of a Pair of Structures.Rachael Alvir, Hannah Burchfield & Julia F. Knight - 2022 - Journal of Symbolic Logic 87 (3):1201-1214.
    We ask when, for a pair of structures $\mathcal {A}_1,\mathcal {A}_2$, there is a uniform effective procedure that, given copies of the two structures, unlabeled, always produces a copy of $\mathcal {A}_1$. We give some conditions guaranteeing that there is such a procedure. The conditions might suggest that for the pair of orderings $\mathcal {A}_1$ of type $\omega _1^{CK}$ and $\mathcal {A}_2$ of Harrison type, there should not be any such procedure, but, in fact, there is one. We construct an (...)
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  38. The Non-categoricity of Logic (I). The Problem of a Full Formalization.Constantin C. Brîncuș - 2022 - In Probleme de Logică/Problems of Logic. București, România: pp. 137-156.
    A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires in addition the preservation of the standard (...)
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  39. Model theory of monadic predicate logic with the infinity quantifier.Facundo Carreiro, Alessandro Facchini, Yde Venema & Fabio Zanasi - 2022 - Archive for Mathematical Logic 61 (3):465-502.
    This paper establishes model-theoretic properties of \, a variation of monadic first-order logic that features the generalised quantifier \. We will also prove analogous versions of these results in the simpler setting of monadic first-order logic with and without equality and \, respectively). For each logic \ we will show the following. We provide syntactically defined fragments of \ characterising four different semantic properties of \-sentences: being monotone and continuous in a given set of monadic predicates; having truth preserved under (...)
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  40. Model theory and combinatorics of banned sequences.Hunter Chase & James Freitag - 2022 - Journal of Symbolic Logic 87 (1):1-20.
    We set up a general context in which one can prove Sauer-Shelah type lemmas. We apply our general results to answer a question of Bhaskar [1] and give a slight improvement to a result of Malliaris and Terry [7]. We also prove a new Sauer-Shelah type lemma in the context of op-rank, a notion of Guingona and Hill [4].
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  41. Priority merge and intersection modalities.Zoé Christoff, Norbert Gratzl & Olivier Roy - 2022 - Review of Symbolic Logic 15 (1):165-196.
    We study the logic of so-called lexicographic or priority merge for multi-agent plausibility models. We start with a systematic comparison between the logical behavior of priority merge and the more standard notion of pooling through intersection, used to define, for instance, distributed knowledge. We then provide a sound and complete axiomatization of the logic of priority merge, as well as a proof theory in labeled sequents that admits cut. We finally study Moorean phenomena and define a dynamic resolution operator for (...)
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  42. Model theory of adeles I.Jamshid Derakhshan & Angus Macintyre - 2022 - Annals of Pure and Applied Logic 173 (3):103074.
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  43. Model-Theoretic Properties of Dynamics on the Cantor Set.Christopher J. Eagle & Alan Getz - 2022 - Notre Dame Journal of Formal Logic 63 (3):357-371.
    We examine topological dynamical systems on the Cantor set from the point of view of the continuous model theory of commutative C*-algebras. After some general remarks, we focus our attention on the generic homeomorphism of the Cantor set, as constructed by Akin, Glasner, and Weiss. We show that this homeomorphism is the prime model of its theory. We also show that the notion of “generic” used by Akin, Glasner, and Weiss is distinct from the notion of “generic” encountered in Fraïssé (...)
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  44. First-Order Axiomatisations of Representable Relation Algebras Need Formulas of Unbounded Quantifier Depth.Rob Egrot & Robin Hirsch - 2022 - Journal of Symbolic Logic 87 (3):1283-1300.
    Using a variation of the rainbow construction and various pebble and colouring games, we prove that RRA, the class of all representable relation algebras, cannot be axiomatised by any first-order relation algebra theory of bounded quantifier depth. We also prove that the class At(RRA) of atom structures of representable, atomic relation algebras cannot be defined by any set of sentences in the language of RA atom structures that uses only a finite number of variables.
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  45. Embeddings Into Outer Models.Monroe Eskew & Sy-David Friedman - 2022 - Journal of Symbolic Logic 87 (4):1301-1321.
    We explore the possibilities for elementary embeddings $j : M \to N$, where M and N are models of ZFC with the same ordinals, $M \subseteq N$, and N has access to large pieces of j. We construct commuting systems of such maps between countable transitive models that are isomorphic to various canonical linear and partial orders, including the real line ${\mathbb R}$.
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  46. Poset Products as Relational Models.Wesley Fussner - 2022 - Studia Logica 110 (1):95-120.
    We introduce a relational semantics based on poset products, and provide sufficient conditions guaranteeing its soundness and completeness for various substructural logics. We also demonstrate that our relational semantics unifies and generalizes two semantics already appearing in the literature: Aguzzoli, Bianchi, and Marra’s temporal flow semantics for Hájek’s basic logic, and Lewis-Smith, Oliva, and Robinson’s semantics for intuitionistic Łukasiewicz logic. As a consequence of our general theory, we recover the soundness and completeness results of these prior studies in a uniform (...)
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  47. El Axioma de elección en el quehacer matemático contemporáneo.Franklin Galindo & Randy Alzate - 2022 - Aitías 2 (3):49-126.
    Para matemáticos interesados en problemas de fundamentos, lógico-matemáticos y filósofos de la matemática, el axioma de elección es centro obligado de reflexión, pues ha sido considerado esencial en el debate dentro de las posiciones consideradas clásicas en filosofía de la matemática (intuicionismo, formalismo, logicismo, platonismo), pero también ha tenido una presencia fundamental para el desarrollo de la matemática y metamatemática contemporánea. Desde una posición que privilegia el quehacer matemático, nos proponemos mostrar los aportes que ha tenido el axioma en varias (...)
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  48. The σ1-definable universal finite sequence.Joel David Hamkins & Kameryn J. Williams - 2022 - Journal of Symbolic Logic 87 (2):783-801.
    We introduce the $\Sigma _1$ -definable universal finite sequence and prove that it exhibits the universal extension property amongst the countable models of set theory under end-extension. That is, the sequence is $\Sigma _1$ -definable and provably finite; the sequence is empty in transitive models; and if M is a countable model of set theory in which the sequence is s and t is any finite extension of s in this model, then there is an end-extension of M to a (...)
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  49. Approximate counting and NP search problems.Leszek Aleksander Kołodziejczyk & Neil Thapen - 2022 - Journal of Mathematical Logic 22 (3).
    Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. We study a new class of NP search problems, those which can be proved total using standard combinatorial reasoning based on approximate counting. Our model for this kind of reasoning is the bounded arithmetic theory [math] of [E. Jeřábek, Approximate counting by hashing in bounded arithmetic, J. Symb. Log. 74(3) (2009) 829–860]. In particular, the Ramsey and weak pigeonhole search problems lie in the new class. We give a purely computational (...)
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  50. Combing Graphs and Eulerian Diagrams in Eristic.Jens Lemanski & Reetu Bhattacharjee - 2022 - In Valeria Giardino, Sven Linker, Tony Burns, Francesco Bellucci, J. M. Boucheix & Diego Viana (eds.), Diagrammatic Representation and Inference. 13th International Conference, Diagrams 2022, Rome, Italy, September 14–16, 2022, Proceedings. Cham: pp. 97–113.
    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 (...)
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