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  1. Representing Buridan’s Divided Modal Propositions in First-Order Logic.Jonas Dagys, Živilė Pabijutaitė & Haroldas Giedra - 2021 - History and Philosophy of Logic 43 (3):264-274.
    Formalizing categorical propositions of traditional logic in the language of quantifiers and propositional functions is no straightforward matter, especially when modalities get involved. Starting...
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  2. Closed and unbounded classes and the härtig quantifier model.Philip D. Welch - 2022 - Journal of Symbolic Logic 87 (2):564-584.
    We show that assuming modest large cardinals, there is a definable class of ordinals, closed and unbounded beneath every uncountable cardinal, so that for any closed and unbounded subclasses $P, Q, {\langle L[P],\in,P \rangle }$ and ${\langle L[Q],\in,Q \rangle }$ possess the same reals, satisfy the Generalised Continuum Hypothesis, and moreover are elementarily equivalent. Examples of such P are Card, the class of uncountable cardinals, I the uniform indiscernibles, or for any n the class $C^{n}{=_{{\operatorname {df}}}}\{ \lambda \, | \, (...)
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  3. Game Semantics, Quantifiers and Logical Omniscience.Bruno Ramos Mendonça - forthcoming - Logic and Logical Philosophy:1-22.
    Logical omniscience states that the knowledge set of ordinary rational agents is closed for its logical consequences. Although epistemic logicians in general judge this principle unrealistic, there is no consensus on how it should be restrained. The challenge is conceptual: we must find adequate criteria for separating obvious logical consequences from non-obvious ones. Non-classical game-theoretic semantics has been employed in this discussion with relative success. On the one hand, with urn semantics [15], an expressive fragment of classical game semantics that (...)
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  4. Temporal interpretation of monadic intuitionistic quantifiers.Guram Bezhanishvili & Luca Carai - forthcoming - Review of Symbolic Logic:1-24.
    We show that monadic intuitionistic quantifiers admit the following temporal interpretation: “always in the future” and “sometime in the past”. It is well known that Prior’s intuitionistic modal logic ${\sf MIPC}$ axiomatizes the monadic fragment of the intuitionistic predicate logic, and that ${\sf MIPC}$ is translated fully and faithfully into the monadic fragment ${\sf MS4}$ of the predicate ${\sf S4}$ via the Gödel translation. To realize the temporal interpretation mentioned above, we introduce a new tense extension ${\sf TS4}$ of ${\sf (...)
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  5. The modal logic of stepwise removal.Johan van Benthem, Krzysztof Mierzewski & Francesca Zaffora Blando - 2022 - Review of Symbolic Logic 15 (1):36-63.
    We investigate the modal logic of stepwise removal of objects, both for its intrinsic interest as a logic of quantification without replacement, and as a pilot study to better understand the complexity jumps between dynamic epistemic logics of model transformations and logics of freely chosen graph changes that get registered in a growing memory. After introducing this logic (MLSR) and its corresponding removal modality, we analyze its expressive power and prove a bisimulation characterization theorem. We then provide a complete Hillbert-style (...)
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  6. Most-intersection of countable sets.Ahmet Çevik & Selçuk Topal - 2021 - Journal of Applied Non-Classical Logics 31 (3-4):343-354.
    We introduce a novel set-intersection operator called ‘most-intersection’ based on the logical quantifier ‘most’, via natural density of countable sets, to be used in determining the majority chara...
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  7. Against Fregean Quantification.Bryan Pickel & Brian Rabern - forthcoming - Ergo.
    There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. (...)
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  8. A Few Notes on Quantum B-algebras.Shengwei Han & Xiaoting Xu - 2021 - Studia Logica 109 (6):1423-1440.
    In order to provide a unified framework for studying non-commutative algebraic logic, Rump and Yang used three axioms to define quantum B-algebras, which can be seen as implicational subreducts of quantales. Based on the work of Rump and Yang, in this paper we shall continue to investigate the properties of three axioms in quantum B-algebras. First, using two axioms we introduce the concept of generalized quantum B-algebras and prove that the opposite of the category GqBAlg of generalized quantum B-algebras is (...)
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  9. Immediate Negation.Adrian Kreutz - 2021 - History and Philosophy of Logic 42 (4):398-410.
    At Kyoto, there is something peculiar going on with negations, or so it seems: A is A, and yet A is immediately not A, and therefore A is A. Without a doubt, this looks a lot like a paradoxical inf...
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  10. Categorical Propositions and Existential Import: A Post-modern Perspective.Byeong-Uk Yi - 2021 - History and Philosophy of Logic 42 (4):307-373.
    This article examines the traditional and modern doctrines of categorical propositions and argues that both doctrines have serious problems. While the doctrines disagree about existential imports...
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  11. Operands and Instances.Peter Fritz - 2021 - Review of Symbolic Logic:1-22.
    Can conjunctive propositions be identical without their conjuncts being identical? Can universally quantified propositions be identical without their instances being identical? On a common conception of propositions, on which they inherit the logical structure of the sentences which express them, the answer is negative both times. Here, it will be shown that such a negative answer to both questions is inconsistent, assuming a standard type-theoretic formalization of theorizing about propositions. The result is not specific to conjunction and universal quantification, but (...)
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  12. One Modal Logic to Rule Them All?Wesley H. Holliday & Tadeusz Litak - 2018 - In Guram Bezhanishvili, Giovanna D'Agostino, George Metcalfe & Thomas Studer (eds.), Advances in Modal Logic, Vol. 12. London: College Publications. pp. 367-386.
    In this paper, we introduce an extension of the modal language with what we call the global quantificational modality [∀p]. In essence, this modality combines the propositional quantifier ∀p with the global modality A: [∀p] plays the same role as the compound modality ∀pA. Unlike the propositional quantifier by itself, the global quantificational modality can be straightforwardly interpreted in any Boolean Algebra Expansion (BAE). We present a logic GQM for this language and prove that it is complete with respect to (...)
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  13. The fluted fragment with transitive relations.Ian Pratt-Hartmann & Lidia Tendera - 2022 - Annals of Pure and Applied Logic 173 (1):103042.
    The fluted fragment is a fragment of first-order logic (without equality) in which, roughly speaking, the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that this fragment has the finite model property. We consider extensions of the fluted fragment with various numbers of transitive relations, as well as the equality predicate. In the presence of one transitive relation (together with equality), the finite model property is lost; nevertheless, (...)
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  14. What’s Positive and Negative about Generics: A Constrained Indexical Approach.Junhyo Lee & Anthony Nguyen - 2021 - Philosophical Studies 179 (5):1739-1761.
    Nguyen argues that only his radically pragmatic account and Sterken’s indexical account can capture what we call the positive data. We present some new data, which we call the negative data, and argue that no theory of generics on the market is compatible with both the positive data and the negative data. We develop a novel version of the indexical account and show that it captures both the positive data and the negative data. In particular, we argue that there is (...)
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  15. Positive Monotone Modal Logic.Jim de Groot - 2021 - Studia Logica 109 (4):829-857.
    Positive monotone modal logic is the negation- and implication-free fragment of monotone modal logic, i.e., the fragment with connectives and. We axiomatise positive monotone modal logic, give monotone neighbourhood semantics based on posets, and prove soundness and completeness. The latter follows from the main result of this paper: a duality between so-called \-spaces and the algebraic semantics of positive monotone modal logic. The main technical tool is the use of coalgebra.
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  16. Grounding, Quantifiers, and Paradoxes.Francesco A. Genco, Francesca Poggiolesi & Lorenzo Rossi - 2021 - Journal of Philosophical Logic 50 (6):1417-1448.
    The notion of grounding is usually conceived as an objective and explanatory relation. It connects two relata if one—the ground—determines or explains the other—the consequence. In the contemporary literature on grounding, much effort has been devoted to logically characterize the formal aspects of grounding, but a major hard problem remains: defining suitable grounding principles for universal and existential formulae. Indeed, several grounding principles for quantified formulae have been proposed, but all of them are exposed to paradoxes in some very natural (...)
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  17. Identity in Mares-Goldblatt Models for Quantified Relevant Logic.Shawn Standefer - 2021 - Journal of Philosophical Logic 50 (6):1389-1415.
    Mares and Goldblatt, 163–187, 2006) provided an alternative frame semantics for two quantified extensions of the relevant logic R. In this paper, I show how to extend the Mares-Goldblatt frames to accommodate identity. Simpler frames are provided for two zero-order logics en route to the full logic in order to clarify what is needed for identity and substitution, as opposed to quantification. I close with a comparison of this work with the Fine-Mares models for relevant logics with identity and a (...)
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  18. A Note on Logicality of Generalized Quantifiers.Tin Perkov - 2021 - Logica Universalis 15 (2):149-152.
    This note follows up an earlier paper in which a possibility of defining logical constants within abstract logical frameworks was discussed, by using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality. In the present note, this approach is applied to the discussion on logicality of generalized quantifiers. It is demonstrated that generalized quantifiers are logical constants by this criterion.
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  19. On Negation for Non-classical Set Theories.S. Jockwich Martinez & G. Venturi - 2021 - Journal of Philosophical Logic 50 (3):549-570.
    We present a case study for the debate between the American and the Australian plans, analyzing a crucial aspect of negation: expressivity within a theory. We discuss the case of non-classical set theories, presenting three different negations and testing their expressivity within algebra-valued structures for ZF-like set theories. We end by proposing a minimal definitional account of negation, inspired by the algebraic framework discussed.
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  20. Peirce’s Triadic Logic and Its (Overlooked) Connexive Expansion.Alex Belikov - forthcoming - Logic and Logical Philosophy:1.
    In this paper, we present two variants of Peirce’s Triadic Logic within a language containing only conjunction, disjunction, and negation. The peculiarity of our systems is that conjunction and disjunction are interpreted by means of Peirce’s mysterious binary operations Ψ and Φ from his ‘Logical Notebook’. We show that semantic conditions that can be extracted from the definitions of Ψ and Φ agree (in some sense) with the traditional view on the semantic conditions of conjunction and disjunction. Thus, we support (...)
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  21. Quantified Modal Relevant Logics.Nicholas Ferenz - forthcoming - Review of Symbolic Logic:1-32.
  22. 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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  23. Graded Structures of Opposition in Fuzzy Natural Logic.Petra Murinová - 2020 - Logica Universalis 14 (4):495-522.
    The main objective of this paper is devoted to two main parts. First, the paper introduces logical interpretations of classical structures of opposition that are constructed as extensions of the square of opposition. Blanché’s hexagon as well as two cubes of opposition proposed by Morreti and pairs Keynes–Johnson will be introduced. The second part of this paper is dedicated to a graded extension of the Aristotle’s square and Peterson’s square of opposition with intermediate quantifiers. These quantifiers are linguistic expressions such (...)
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  24. Ramsey transfer to semi-retractions.Lynn Scow - 2021 - Annals of Pure and Applied Logic 172 (3):102891.
  25. Where is ‘There is’ in ‘∃’?Richard Davies - forthcoming - Tandf: History and Philosophy of Logic:1-16.
    The paper offers a survey of four key moments in which symbolisms for quantification were first introduced: §§11–2 of Frege’s Begriffsschrift (1879); Peirce’s ‘Algebra of Logic’ (1885); Peano’s ‘Studii di Logica matematica’ (1897); and *9 (‘replaced’ by *8 in the second edition) of Whitehead and Russell’s Principia Mathematica (1910). Despite their divergent aims, these authors present substantially equivalent visions of what their differing symbolisms express. In each case, some passage suggests that one (but not the only) way to render one (...)
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  26. Complexity of syntactical tree fragments of Independence-Friendly logic.Fausto Barbero - 2021 - Annals of Pure and Applied Logic 172 (1):102859.
    A dichotomy result of Sevenster (2014) [29] completely classified the quantifier prefixes of regular Independence-Friendly (IF) logic according to the patterns of quantifier dependence they contain. On one hand, prefixes that contain “Henkin” or “signalling” patterns were shown to characterize fragments of IF logic that capture NP-complete problems; all the remaining prefixes were shown instead to be essentially first-order. In the present paper we develop the machinery which is needed in order to extend the results of Sevenster to non-prenex, regular (...)
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  27. An Inferential Impasse in the Theory of Implicatures.Savas L. Tsohatzidis - manuscript
  28. Response to William Lane Craig’s God over All.Peter van Inwagen - 2019 - Philosophia Christi 21 (2):267-275.
    In contrast to William Lane Craig’s view this article presents a sort of precis of my position on ontological commitment—whether you call it neo-Quineanism or not—and its implications for the nominalism-realism debate, a precis that proceeds from first principles.
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  29. Existential Import, Aristotelian Logic, and its Generalizations.Corina Strößner - 2020 - Logica Universalis 14 (1):69-102.
    The paper uses the theory of generalized quantifiers to discuss existential import and its implications for Aristotelian logic, namely the square of opposition, conversions and the assertoric syllogistic, as well as for more recent generalizations to intermediate quantifiers like “most”. While this is a systematic discussion of the semantic background one should assume in order to obtain the inferences and oppositions Aristotle proposed, it also sheds some light on the interpretation of his writings. Moreover by applying tools from modern formal (...)
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  30. Invariance and Necessity.Gila Sher - 2019 - In Bernhard Ritter, Paul Weingartner & Gabriele M. Mras (eds.), Philosophy of logic and Mathematics. Berlin, Boston: De Gruyter. pp. 55-70.
    Properties and relations in general have a certain degree of invariance, and some types of properties/relations have a stronger degree of invariance than others. In this paper I will show how the degrees of invariance of different types of properties are associated with, and explain, the modal force of the laws governing them. This explains differences in the modal force of laws/principles of different disciplines, starting with logic and mathematics and proceeding to physics and biology.
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  31. Gebhard Furhken. Languages with added quantifier “there exist at least Nα.”The theory of models, Proceedings of the 1963 International Symposium at Berkeley, edited by J. W. Addison, Leon Henkin, and Alfred Tarski, Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam1965, pp. 121–131. [REVIEW]A. B. Slomson - 1970 - Journal of Symbolic Logic 35 (2):342.
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  32. Per Lindström. First order predicate logic with generalized quantifiers. Theoria, vol. 32 , pp. 186–195.G. Fuhrken - 1969 - Journal of Symbolic Logic 34 (4):650.
  33. R. H. Thomason and H. Leblanc. All or none: a novel choice of primitives for elementary logic. The journal of symbolic logic, vol. 32 , pp. 345–351.Mitsuru Yasuhara - 1969 - Journal of Symbolic Logic 34 (1):124-125.
  34. H. Jerome Keisler. Logic with the quantifier “there exist uncountably many.”Annals of mathematical logic, vol. 1 no. 1 , pp. 1–93. [REVIEW]Gebhard Fuhrken - 1971 - Journal of Symbolic Logic 36 (4):685-687.
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  35. Karp Carol R.. Finite-quantifier equivalence. The theory of models, Proceedings of the 1963 International Symposium at Berkeley, edited by Addison J. W., Henkin Leon, and Tarski Alfred, Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam 1965, pp. 407–412. [REVIEW]H. Jerome Keisler - 1971 - Journal of Symbolic Logic 36 (1):158.
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  36. Finite partially-ordered quantification.Wilbur John Walkoe - 1970 - Journal of Symbolic Logic 35 (4):535-555.
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  37. G. J. Warnock. Metaphysics in logic. A revised reprint of XXXV 455. Essays in conceptual analysis, selected and edited by Antony Flew, Macmillan & Co. Ltd., London, and St. Martin's Press, New York, 1956, pp. 75–93. [REVIEW]Anders Wedberg - 1972 - Journal of Symbolic Logic 37 (4):750.
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  38. Timothy Smiley. Sense without denotation. Analysis , n.s. no. 78 , pp. 125–135.Bas C. van Fraassen - 1972 - Journal of Symbolic Logic 37 (2):423.
  39. Rolf Schock. Logics without existence assumptions. Almqvist & Wiksell, Stockholm1968, 134 pp. [REVIEW]Theodore Hailperin - 1972 - Journal of Symbolic Logic 37 (2):424.
  40. A. N. Prior. Existence in Leśniewski and in Russell. Formal systems and recursive functions, Proceedings of the Eighth Logic Colloquium, Oxford, July 1963, edited by J. N. Crossley and M. A. E. Dummett, Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam1965, pp. 149–155. [REVIEW]C. Lejewski - 1975 - Journal of Symbolic Logic 40 (3):458.
  41. Czesław Lejewski. Logic and existence. The British journal for the philosophy of science, vol. 5 , pp. 104–119. - A. N. Prior. English and ontology. The British journal for the philosophy of science, vol. 6 , pp. 64–65. [REVIEW]Bogusław Iwanuś - 1975 - Journal of Symbolic Logic 40 (1):102-103.
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  42. Baudisch Andreas, Seese Detlef, Tuschik Hans-Peter, and Weese Martin. Decidability and generalized quantifiers. Mathematical research-Mathematische Forschung, vol. 3. Akademie-Verlag, Berlin 1980, XII + 235 pp. [REVIEW]John Cowles - 1982 - Journal of Symbolic Logic 47 (4):907-908.
  43. Saharon Shelah. There are just four second-order quantifiers. Israel journal of mathematics, vol. 15 , pp. 282–300.John T. Baldwin - 1986 - Journal of Symbolic Logic 51 (1):234.
  44. Jouko Väänänen, A hierarchy theorem for Lindstrom quantifiers, Logic and abstraction, Essays dedicated to Per Lindström on his fiftieth birthday, edited by Mats Furberg, Thomas Wetterström, and Claes Åberg, Acta philosophica Gothoburgensia, no. 1, Acta Universitatis Gothobargensis, Göteborg1986, pp. 317–323. [REVIEW]Juha Oikkonen - 1989 - Journal of Symbolic Logic 54 (2):631-631.
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  45. Kolaitis Phokion G. and Väänänen Jouko A.. Generalized quantifiers and pebble games on finite structures. Annals of pure and applied logic, vol. 74 pp. 23–75. [REVIEW]I. A. Stewart - 1996 - Journal of Symbolic Logic 61 (4):1387-1388.
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  46. Everyone knows that someone knows: Quantifiers over epistemic agents.Pavel Naumov & Jia Tao - 2019 - Review of Symbolic Logic 12 (2):255-270.
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  47. Prior A. N.. Negative quantifiers. The Australasian journal of philosophy, vol. 31 , pp. 107–123.A. R. Turquette - 1955 - Journal of Symbolic Logic 20 (2):166-167.
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  48. Existential Sentences without Existential Quantification.Louise McNally - 1998 - Linguistics and Philosophy 21 (4):353-392.
    Presents a set-theoretic version of the analysis of "there be" as predicating instantiation of a property, a property-theoretic version of which was developed in McNally 1992. This paper provides a solution to the criticism that McNally 1992's analysis could not account for sentences in which postverbal nominal contains a monotone decreasing or nonmonotonic determiner.
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  49. Polarity in Natural Language: Predication, Quantification and Negation in Particular and Characterizing Sentences.Sebastian Löbner - 2000 - Linguistics and Philosophy 23 (3):213-308.
    The present paper is an attempt at the investigation of the nature of polarity contrast in natural languages. Truth conditions for natural language sentences are incomplete unless they include a proper definition of the conditions under which they are false. It is argued that the tertium non datur principle of classical bivalent logical systems is empirically invalid for natural languages: falsity cannot be equated with non-truth. Lacking a direct intuition about the conditions under which a sentence is false, we need (...)
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  50. Contraction, Infinitary Quantifiers, and Omega Paradoxes.Lucas Rosenblatt & Bruno Ré - 2018 - Journal of Philosophical Logic 47 (4):611-629.
    Our main goal is to investigate whether the infinitary rules for the quantifiers endorsed by Elia Zardini in a recent paper are plausible. First, we will argue that they are problematic in several ways, especially due to their infinitary features. Secondly, we will show that even if these worries are somehow dealt with, there is another serious issue with them. They produce a truth-theoretic paradox that does not involve the structural rules of contraction.
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