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  1. Finitary Unification in Locally Tabular Modal Logics Characterized.Wojciech Dzik, Sławomir Kost & Piotr Wojtylak - 2022 - Annals of Pure and Applied Logic 173 (4):103072.
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  2. Bealer's Intensional Logic.Clarence Lewis Protin - manuscript
    Many intuitively valid arguments involving intensionality cannot be captured by first-order logic, even when extended by modal and epistemic operators. Indeed, previous attempts at providing an adequate treatment of the phenomenon of intensionality in logic and language, such as those of Frege, Church, Russell, Carnap, Quine, Montague and others are fraught with numerous philosophical and technical difficulties and shortcomings. We present Bealer's solution to this problem which hinges on an ontological commitment to theory of Properties, Propositions and Relations (PRP). At (...)
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  3. Conditional Logics Accommodating Stalnaker's Thesis.Andrew Bacon - manuscript
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  4. Axiomatization of Some Basic and Modal Boolean Connexive Logics.Mateusz Klonowski - 2021 - Logica Universalis 15 (4):517-536.
    Boolean connexive logic is an extension of Boolean logic that is closed under Modus Ponens and contains Aristotle’s and Boethius’ theses. According to these theses a sentence cannot imply its negation and the negation of a sentence cannot imply the sentence; and if the antecedent implies the consequent, then the antecedent cannot imply the negation of the consequent and if the antecedent implies the negation of the consequent, then the antecedent cannot imply the consequent. Such a logic was first introduced (...)
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  5. Quantifier-Free Epistemic Term-Modal Logic with Assignment Operator.Yanjing Wang, Yu Wei & Jeremy Seligman - 2022 - Annals of Pure and Applied Logic 173 (3):103071.
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  6. Substitution Inconsistencies in Transparent Intensional Logic.Miloš Kosterec - forthcoming - Journal of Applied Non-Classical Logics:1-17.
    This paper presents several important results for Transparent Intensional Logic. The conversions that are standardly taken to be valid – namely restricted β-conversion by name and β-reduction...
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  7. Advances in Modal Logic, Volume 3: Papers From the Third Aiml Conference, Held at the University of Leipzig, October 2000.Frank Wolter, H. Wansing, Maarten de Rijke & Michael Zakharyaschev - 2002 - Singapore: World Scientific.
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  8. Displaying Modal Logic.Heinrich Wansing - 1998 - Dordrecht, Netherland: Springer.
    The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly conceived. (...)
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  9. An Essay in Modal Logic.Georg Henrik von Wright - 1951 - Amsterdam, Netherlands: North-Holland.
    The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate in modal logic that has persisted (...)
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  10. Advances in Modal Logic, Volume 5: Papers From the Fifth Aiml Conference, Held in Manchester, 9-11 September 2004.Renate A. Schmidt, Ian Pratt-Hartmann, Mark Reynolds & Heinrich Wansing (eds.) - 2005 - London, England: King's College Publications.
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  11. Neighborhood Semantics for Modal Logic.Eric Pacuit - 2017 - Cham, Switzerland: Springer.
    This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic. In addition, the book discusses a broad range of topics, including standard modal logic results ; bisimulations for neighborhood models and other model-theoretic (...)
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  12. Advances in Modal Logic, Volume 1: Papers From the First Aiml Conference, Held at the Free University of Berlin, 1996.Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.) - 1998 - Cambridge, England: Cambridge University Press.
    Modal logic originated in philosophy as the logic of necessity and possibility. Now it has reached a high level of mathematical sophistication and has many applications in a variety of disciplines, including theoretical and applied computer science, artificial intelligence, the foundations of mathematics, and natural language syntax and semantics. This volume represents the proceedings of the first international workshop on Advances in Modal Logic, held in Berlin, Germany, October 8-10, 1996. It offers an up-to-date perspective on the field, with contributions (...)
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  13. Natural Deduction, Hybrid Systems and Modal Logics.Andrzej Indrzejczak - 2010 - Dordrecht, Netherland: Springer.
    This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.
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  14. A Companion to Modal Logic.George Edward Hughes & M. J. Cresswell - 1984 - London, England: Methuen.
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  15. An Introduction to Modal Logic.George Edward Hughes & M. J. Cresswell - 1968 - London, England: Methuen.
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  16. Advances in Modal Logic, Volume 6: Papers From the Sixth Conference on Advances in Modal Logic, Held in Noosa, Queensland, Australia, 25-28 September 2006. [REVIEW]Guido Governatori, Ian Hodkinson & Yde Venema - 2006 - London, England: College Publications.
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  17. Procedural Semantics for Hyperintensional Logic: Foundations and Applications of Transparent Intensional Logic.Marie Duží, Bjorn Jespersen & Pavel Materna - 2010 - Dordrecht, Netherland: Springer.
    The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds (...)
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  18. Model Theory for Modal Logic: Kripke Models for Modal Predicate Calculi.Kenneth Alan Bowen - 1978 - Dordrecht and Boston: Reidel.
  19. Advances in Modal Logic, Volume 4: Papers From the Fourth Aiml Conference, Held in Toulouse, October 2002.Philippe Balbiani, Nobu-Yuki Suzuki & Frank Wolter (eds.) - 2003 - London, England: King's College Publications.
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  20. Advances in Modal Logic, Volume 7: Papers From the Seventh Advances in Modal Logic Conference, Held in Nancy, France, September 2008.Carlos Areces & Robert Goldblatt (eds.) - 2008 - London, England: College Publications.
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  21. Neighbourhood Semantics for FDE-Based Modal Logics.S. Drobyshevich & D. Skurt - 2021 - Studia Logica 109 (6):1273-1309.
    We investigate some non-normal variants of well-studied paraconsistent and paracomplete modal logics that are based on N. Belnap’s and M. Dunn’s four-valued logic. Our basic non-normal modal logics are characterized by a weak extensionality rule, which reflects the four-valued nature of underlying logics. Aside from introducing our basic framework of bi-neighbourhood semantics, we develop a correspondence theory in order to prove completeness results with respect to our neighbourhood semantics for non-normal variants of \, \ and \.
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  22. Essence and Necessity.Andreas Ditter - forthcoming - Journal of Philosophical Logic.
    What is the relation between metaphysical necessity and essence? This paper defends the view that the relation is one of identity: metaphysical necessity is a special case of essence. My argument consists in showing that the best joint theory of essence and metaphysical necessity is one in which metaphysical necessity is just a special case of essence. The argument is made against the backdrop of a novel, higher-order logic of essence (HLE), whose core features are introduced in the first part (...)
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  23. Reduction Techniques for Proving Decidability in Logics and Their Meet–Combination.João Rasga, Cristina Sernadas & Walter Carnielli - 2021 - Bulletin of Symbolic Logic 27 (1):39-66.
    Satisfaction systems and reductions between them are presented as an appropriate context for analyzing the satisfiability and the validity problems. The notion of reduction is generalized in order to cope with the meet-combination of logics. Reductions between satisfaction systems induce reductions between the respective satisfiability problems and (under mild conditions) also between their validity problems. Sufficient conditions are provided for relating satisfiability problems to validity problems. Reflection results for decidability in the presence of reductions are established. The validity problem in (...)
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  24. Representing Buridan’s Divided Modal Propositions in First-Order Logic.Jonas Dagys, Živilė Pabijutaitė & Haroldas Giedra - forthcoming - History and Philosophy of Logic:1-11.
    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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  25. What Can You Say? Measuring the Expressive Power of Languages.Alexander W. Kocurek - 2018 - Dissertation, University of California, Berkeley
    There are many different ways to talk about the world. Some ways of talking are more expressive than others—that is, they enable us to say more things about the world. But what exactly does this mean? When is one language able to express more about the world than another? In my dissertation, I systematically investigate different ways of answering this question and develop a formal theory of expressive power, translation, and notational variance. In doing so, I show how these investigations (...)
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  26. Understanding What We Ought and Shall Do: A Hyperstate Semantics for Descriptive, Prescriptive, and Intentional Sentences.Preston Stovall - 2020 - In Ladislav Koreň, Hans Bernhard Schmid, Preston Stovall & Leo Townsend (eds.), Groups, Norms and Practices: Essays on Inferentialism and Collective Intentionality. Cham: Springer. pp. 215-238.
    This essay is part of a larger project aimed at making sense of rational thought and agency as part of the natural world. It provides a semantic framework for thinking about the contents of: 1) descriptive thoughts and sentences having a representational or mind-to-world direction of fit, and which manifest our capacity for theoretical rationality; and 2) prescriptive and intentional sentences having an expressive or world-to-mind direction of fit, and which manifest our capacity for practical rationality. I use a modified (...)
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  27. Choice-Driven Counterfactuals.Ilaria Canavotto & Eric Pacuit - forthcoming - Journal of Philosophical Logic:1-49.
    In this paper, we investigate the semantics and logic of choice-driven counterfactuals, that is, of counterfactuals whose evaluation relies on auxiliary premises about how agents are expected to act, i.e., about their default choice behavior. To do this, we merge one of the most prominent logics of agency in the philosophical literature, namely stit logic, with the well-known logic of counterfactuals due to Stalnaker and Lewis. A key component of our semantics for counterfactuals is to distinguish between deviant and non-deviant (...)
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  28. On the Modal Interpretation of the Connective of Realisation.A. M. Karczewska - forthcoming - Journal of Applied Non-Classical Logics:1-13.
    The connective of realisation associates propositions with names of contexts, at which they are said to be realised. Realisation is usually understood as relativised truth-connective, thus under mo...
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  29. Substitution Inconsistencies in Transparent Intensional Logic.Miloš Kosterec - forthcoming - Tandf: Journal of Applied Non-Classical Logics:1-17.
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  30. Advances in Modal Logic, Vol. 12.Guram Bezhanishvili, Giovanna D'Agostino, George Metcalfe & Thomas Studer (eds.) - 2018 - College Publications.
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  31. Logic Talk.Alexander W. Kocurek - 2021 - Synthese 199 (5-6):13661-13688.
    Sentences about logic are often used to show that certain embedding expressions are hyperintensional. Yet it is not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. In this paper, I develop a formal system called hyperlogic that is designed to do just that. I provide a hyperintensional semantics for hyperlogic that doesn’t appeal to logically impossible worlds, as traditionally understood, but instead uses a shiftable parameter that determines the (...)
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  32. One-Step Modal Logics, Intuitionistic and Classical, Part 1.Harold T. Hodes - 2021 - Journal of Philosophical Logic 50 (5):837-872.
    This paper and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 presents (...)
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  33. A Simple Logic of Functional Dependence.Alexandru Baltag & Johan van Benthem - 2021 - Journal of Philosophical Logic 50 (5):939-1005.
    This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized assignment semantics for first order logic. The expressive strength, complete proof calculus and meta-properties of LFD are explored. Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models. Finally, more concrete settings for dependence are discussed: continuous (...)
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  34. Can All Things Be Counted?Chris Scambler - 2021 - Journal of Philosophical Logic 50 (5):1079-1106.
    In this paper, I present and motivate a modal set theory consistent with the idea that there is only one size of infinity.
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  35. On the Logic of Belief and Propositional Quantification.Yifeng Ding - 2021 - Journal of Philosophical Logic 50 (5):1143-1198.
    We consider extending the modal logic KD45, commonly taken as the baseline system for belief, with propositional quantifiers that can be used to formalize natural language sentences such as “everything I believe is true” or “there is something that I neither believe nor disbelieve.” Our main results are axiomatizations of the logics with propositional quantifiers of natural classes of complete Boolean algebras with an operator validating KD45. Among them is the class of complete, atomic, and completely multiplicative BAOs validating KD45. (...)
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  36. One-Step Modal Logics, Intuitionistic and Classical, Part 2.Harold T. Hodes - 2021 - Journal of Philosophical Logic 50 (5):873-910.
    Hodes “looked under the hood” of the familiar versions of the classical propositional modal logic K and its intuitionistic counterpart. This paper continues that project, addressing some familiar classical strengthenings of K and GL), and their intuitionistic counterparts. Section 9 associates two intuitionistic one-step proof-theoretic systems to each of the just mentioned intuitionistic logics, this by adding for each a new rule to those which generated IK in Hodes. For the systems associated with the intuitionistic counterparts of D and T, (...)
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  37. Modes of Truth: The Unified Approach to Truth, Modality, and Paradox.Carlo Nicolai & Johannes Stern (eds.) - 2021 - Routledge.
    The aim of this volume is to open up new perspectives and to raise new research questions about a unified approach to truth, modalities, and propositional attitudes. The volume's essays are grouped thematically around different research questions. The first theme concerns the tension between the theoretical role of the truth predicate in semantics and its expressive function in language. The second theme of the volume concerns the interaction of truth with modal and doxastic notions. The third theme covers higher-order solutions (...)
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  38. On Blass Translation for Leśniewski’s Propositional Ontology and Modal Logics.Takao Inoué - forthcoming - Studia Logica:1-25.
    In this paper, we shall give another proof of the faithfulness of Blass translation of the propositional fragment \ of Leśniewski’s ontology in the modal logic \ by means of Hintikka formula. And we extend the result to von Wright-type deontic logics, i.e., ten Smiley-Hanson systems of monadic deontic logic. As a result of observing the proofs we shall give general theorems on the faithfulness of B-translation with respect to normal modal logics complete to certain sets of well-known accessibility relations (...)
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  39. The Vietoris Functor and Modal Operators on Rings of Continuous Functions.G. Bezhanishvili, L. Carai & P. J. Morandi - 2022 - Annals of Pure and Applied Logic 173 (1):103029.
  40. Unification in Pretabular Extensions of S4.Stepan I. Bashmakov - 2021 - Logica Universalis 15 (3):381-397.
    L.L. Maksimova and L. Esakia, V. Meskhi showed that the modal logic \ has exactly 5 pretabular extensions PM1–PM5. In this paper, we study the problem of unification for all given logics. We showed that PM2 and PM3 have finitary, and PM1, PM4, PM5 have unitary types of unification. Complete sets of unifiers in logics are described.
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  41. Copy and Remove as Dynamic Operators.Carlos Areces, Hans van Ditmarsch, Raul Fervari, Bastien Maubert & François Schwarzentruber - forthcoming - Tandf: Journal of Applied Non-Classical Logics:1-40.
  42. Did Descartes make a Diagonal Argument?Toby Meadows - forthcoming - Journal of Philosophical Logic:1-29.
    This paper explores the idea that Descartes’ cogito is a kind of diagonal argument. Using tools from modal logic, it reviews some historical antecedents of this idea from Slezak and Boos and culminates in an orginal result classifying the exact structure of belief frames capable of supporting diagonal arguments and our reconstruction of the cogito.
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  43. 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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  44. Belnap–Dunn Modal Logic with Value Operators.Yuanlei Lin & Minghui Ma - 2020 - Studia Logica 109 (4):759-789.
    The language of Belnap–Dunn modal logic \ expands the language of Belnap–Dunn four-valued logic with the modal operator \. We introduce the polarity semantics for \ and its two expansions \ and \ with value operators. The local finitary consequence relation \ in the language \ with respect to the class of all frames is axiomatized by a sequent system \ where \. We prove by using translations between sequents and formulas that these languages under the polarity semantics have the (...)
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  45. Labelled Sequent Calculi for Lewis’ Non-normal Propositional Modal Logics.Matteo Tesi - 2020 - Studia Logica 109 (4):725-757.
    C. I. Lewis’ systems were the first axiomatisations of modal logics. However some of those systems are non-normal modal logics, since they do not admit a full rule of necessitation, but only a restricted version thereof. We provide G3-style labelled sequent calculi for Lewis’ non-normal propositional systems. The calculi enjoy good structural properties, namely admissibility of structural rules and admissibility of cut. Furthermore they allow for straightforward proofs of admissibility of the restricted versions of the necessitation rule. We establish completeness (...)
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  46. Inductive Plausibility and Certainty.Ricardo Sousa Silvestre - 2021 - In Marcin Trepczyński (ed.), Philosophical Approaches to the Foundations of Logics and Mathematics. Leiden, Países Baixos: pp. 193-210.
    Is it possible to combine different logics into a coherent system with the goal of applying it to specific problems so that it sheds some light on foundational aspects of those logics? These are two of the most basic issues of combining logics. Paranormal modal logic is a combination of paraconsistent logic and modal logic. In this paper, I propose two further combinatory developments, focusing on each one of these two issues. On the foundational side, I combine paranormal modal logic (...)
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  47. Paraconsistent Logic as Model Building.Ricardo Sousa Silvestre - 2018 - South American Journal of Logic 1 (4):195-217.
    The terms “model” and “model-building” have been used to characterize the field of formal philosophy, to evaluate philosophy’s and philosophical logic’s progress and to define philosophical logic itself. A model is an idealization, in the sense of being a deliberate simplification of something relatively complex in which several important aspects are left aside, but also in the sense of being a view too perfect or excellent, not found in reality, of this thing. Paraconsistent logic is a branch of philosophical logic. (...)
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  48. A Note on the Complexity of S4.2.Aggeliki Chalki, Costas D. Koutras & Yorgos Zikos - 2021 - Journal of Applied Non-Classical Logics 31 (2):108-129.
    S4.2 is the modal logic of directed partial pre-orders and/or the modal logic of reflexive and transitive relational frames with a final cluster. It holds a distinguished position in philosophical...
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  49. Characterizing Existence of a Measurable Cardinal Via Modal Logic.Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan & Jan van Mill - 2021 - Journal of Symbolic Logic 86 (1):162-177.
    We prove that the existence of a measurable cardinal is equivalent to the existence of a normal space whose modal logic coincides with the modal logic of the Kripke frame isomorphic to the powerset of a two element set.
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  50. The Modal Logic of -Centered Forcing and Related Forcing Classes.Ur Ya’Ar - 2021 - Journal of Symbolic Logic 86 (1):1-24.
    We consider the modality “ $\varphi $ is true in every $\sigma $ -centered forcing extension,” denoted $\square \varphi $, and its dual “ $\varphi $ is true in some $\sigma $ -centered forcing extension,” denoted $\lozenge \varphi $, which give rise to the notion of a principle of $\sigma $ -centered forcing. We prove that if ZFC is consistent, then the modal logic of $\sigma $ -centered forcing, i.e., the ZFC-provable principles of $\sigma $ -centered forcing, is exactly $\mathsf (...)
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