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  1. The Integral Construct of Science.Joseph Krecz - manuscript
    A number of general theories of physics provide a model for the fundamental rules that govern our universe, becoming a structural framework to which the new discoveries must conform. The theory of relativity is such a general theory. The theory of relativity is a complex theoretical framework that facilitates the understanding of the universal laws of physics. It is based on the curved space-time continuum fabric abstract concept, and it is well suited for interpreting cosmic events. More so, a general (...)
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  2. Not Much Higher-Order Vagueness in Williamson’s ’Logic of Clarity’.Nasim Mahoozi & Thomas Mormann - manuscript
    This paper deals with higher-order vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higher-order vagueness collapses to second-order vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with naturally defined maps h and s (...)
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  3. Qualia Logic.Paul Merriam - manuscript
    The logic of qualia is different than classical logic. We take the first steps in defining it and applying it to the Hard Problem.
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  4. M. Abad Varieties of Three-Valued.A. M. Suardiaz A. Quantifier - forthcoming - Studia Logica.
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  5. Towards World Identification in Description Logics.Farshad Badie - forthcoming - Logical Investigations.
    Logical analysis of the applicability of nominals (which are introduced by hybrid logic) in the formal descriptions of the world (within modern knowledge representation and semantics-based systems) is very important because nominals, as second sorts of propositional symbols, can support logical identification of the described world at specific [temporal and/or spacial] states. This paper will focus on answering the philosophical-logical question of ‘how a fundamental world description in description logic (DL) and a nominal can be related to each other?’. Based (...)
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  6. Logical Characterisation of Possibilistic and Probabilistic Descriptions of Events in Description Logics.Farshad Badie - forthcoming - Bulletin of the Section of Logic.
    Description Logics (DLs) are a family of formal knowledge representation formalisms and the most well-known formalisms in semantics-based systems. The central focus of this research is on logical-terminological characterisation/analysis of possibilistic and probabilistic descriptions of events in DLs. Based on a logical characterisation of the concept of `being', this paper conceptualises events within DLs world descriptions. Accordingly, it deals with the concepts of `possibility of events' and `probability of events'. The main goal of this research is to investigate how possible (...)
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  7. An Occurrence Description Logic.Farshad Badie & Hans Götzsche - forthcoming - Logical Investigations.
    Description Logics (DLs) are a family of well-known terminological knowledge representation formalisms in modern semantics-based systems. This research focuses on analysing how our developed Occurrence Logic (OccL) can conceptually and logically support the development of a description logic. OccL is integrated into the alternative theory of natural language syntax in `Deviational Syntactic Structures' under the label `EFA(X)3' (or the third version of Epi-Formal Analysis in Syntax, EFA(X), which is a radical linguistic theory). From the logical point of view, OccL is (...)
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  8. An Abductive Question-Answer System for the Minimal Logic of Formal Inconsistency $$\mathsf {mbC}$$ mbC.Szymon Chlebowski, Andrzej Gajda & Mariusz Urbański - forthcoming - Studia Logica:1-31.
    The aim in this paper is to define an Abductive Question-Answer System for the minimal logic of formal inconsistency \. As a proof-theoretical basis we employ the Socratic proofs method. The system produces abductive hypotheses; these are answers to abductive questions concerning derivability of formulas from sets of formulas. We integrated the generation of and the evaluation of hypotheses via constraints of consistency and significance being imposed on the system rules.
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  9. Priority Merge and Intersection Modalities.Zoé Christoff, Norbert Gratzl & Olivier Roy - forthcoming - Review of Symbolic Logic:1-32.
    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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  10. 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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  11. Sequent-Calculi for Metainferential Logics.Bruno Da Ré & Federico Pailos - forthcoming - Studia Logica:1-35.
    In recent years, some theorists have argued that the clogics are not only defined by their inferences, but also by their metainferences. In this sense, logics that coincide in their inferences, but not in their metainferences were considered to be different. In this vein, some metainferential logics have been developed, as logics with metainferences of any level, built as hierarchies over known logics, such as \, and \. What is distinctive of these metainferential logics is that they are mixed, i.e. (...)
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  12. Derivability and Metainferential Validity.Bruno Da Ré, Damian Szmuc & Paula Teijeiro - forthcoming - Journal of Philosophical Logic:1-27.
    The aim of this article is to study the notion of derivability and its semantic counterpart in the context of non-transitive and non-reflexive substructural logics. For this purpose we focus on the study cases of the logics ST and TS. In this respect, we show that this notion doesn’t coincide, in general, with a nowadays broadly used semantic approach towards metainferential validity: the notion of local validity. Following this, and building on some previous work by Humberstone, we prove that in (...)
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  13. Aristotelian Diagrams for Semantic and Syntactic Consequence.Lorenz Demey - forthcoming - Synthese:1-21.
    Several authors have recently studied Aristotelian diagrams for various metatheoretical notions from logic, such as tautology, satisfiability, and the Aristotelian relations themselves. However, all these metalogical Aristotelian diagrams focus on the semantic perspective on logical consequence, thus ignoring the complementary, and equally important, syntactic perspective. In this paper, I propose an explanation for this discrepancy, by arguing that the metalogical square of opposition for semantic consequence exhibits a natural analogy to the well-known square of opposition for the categorical statements from (...)
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  14. Explaining Experience In Nature: The Foundations Of Logic And Apprehension.Steven Ericsson-Zenith - forthcoming - Institute for Advanced Science & Engineering.
    At its core this book is concerned with logic and computation with respect to the mathematical characterization of sentient biophysical structure and its behavior. -/- Three related theories are presented: The first of these provides an explanation of how sentient individuals come to be in the world. The second describes how these individuals operate. And the third proposes a method for reasoning about the behavior of individuals in groups. -/- These theories are based upon a new explanation of experience in (...)
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  15. Deep ST.Thomas M. Ferguson & Elisángela Ramírez-Cámara - forthcoming - Journal of Philosophical Logic:1-33.
    Many analyses of notion of metainferences in the non-transitive logic ST have tackled the question of whether ST can be identified with classical logic. In this paper, we argue that the primary analyses are overly restrictive of the notion of metainference. We offer a more elegant and tractable semantics for the strict-tolerant hierarchy based on the three-valued function for the LP material conditional. This semantics can be shown to easily handle the introduction of mixed inferences, i.e., inferences involving objects belonging (...)
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  16. Sequent Calculi for the Propositional Logic of HYPE.Martin Fischer - forthcoming - Studia Logica:1-35.
    In this paper we discuss sequent calculi for the propositional fragment of the logic of HYPE. The logic of HYPE was recently suggested by Leitgeb as a logic for hyperintensional contexts. On the one hand we introduce a simple \-system employing rules of contraposition. On the other hand we present a \-system with an admissible rule of contraposition. Both systems are equivalent as well as sound and complete proof-system of HYPE. In order to provide a cut-elimination procedure, we expand the (...)
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  17. Self-Reference Upfront: A Study of Self-Referential Gödel Numberings.Balthasar Grabmayr & Albert Visser - forthcoming - Review of Symbolic Logic:1-40.
    In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion of self-reference even for expressively weak languages. The results of this paper suggest that the question whether truly self-referential reasoning can be formalised in arithmetic is more sensitive to the underlying coding apparatus than usually believed. As a case study, we show how this sensitivity affects the formal study (...)
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  18. 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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  19. Complexity of the Infinitary Lambek Calculus with Kleene Star.Stepan Kuznetsov - forthcoming - Review of Symbolic Logic:1-27.
    We consider the Lambek calculus, or noncommutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an $\omega $ -rule, and prove that the derivability problem in this calculus is $\Pi _1^0$ -hard. This solves a problem left open by Buszkowski, who obtained the same complexity bound for infinitary action logic, which additionally includes additive conjunction and disjunction. As a by-product, we prove that any context-free language without the empty word can be generated by a (...)
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  20. Tractarian Logicism: Operations, Numbers, Induction.Gregory Landini - forthcoming - Review of Symbolic Logic:1-41.
  21. Empty Logics.Federico Pailos - forthcoming - Journal of Philosophical Logic:1-29.
    TS is a logic that has no valid inferences. But, could there be a logic without valid metainferences? We will introduce TSω, a logic without metainferential validities. Notwithstanding, TSω is not as empty—i.e., uninformative—as it gets, because it has many antivalidities. We will later introduce the two-standard logic [TSω, STω], a logic without validities and antivalidities. Nevertheless, [TSω, STω] is still informative, because it has many contingencies. The three-standard logic [\] that we will further introduce, has no validities, no antivalidities (...)
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  22. A Note on the Sequent Calculi.Franco Parlamento & Flavio Previale - forthcoming - Review of Symbolic Logic:1-15.
    We show that the replacement rule of the sequent calculi ${\bf G3[mic]}^= $ in [8] can be replaced by the simpler rule in which one of the principal formulae is not repeated in the premiss.
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  23. Dialogue Games for Minimal Logic.Alexandra Pavlova - forthcoming - Logic and Logical Philosophy:1.
    In this paper, we define a class of dialogue games for Johansson’s minimal logic and prove that it corresponds to the validity of minimal logic. Many authors have stated similar results for intuitionistic and classical logic either with or without actually proving the correspondence. Rahman, Clerbout and Keiff [17] have already specified dialogues for minimal logic; however, they transformed it into Fitch-style natural deduction only. We propose a different specification for minimal logic with the proof of correspondence between the existence (...)
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  24. From Semantic Games to Provability: The Case of Gödel Logic.Alexandra Pavlova, Robert Freiman & Timo Lang - forthcoming - Studia Logica:1-28.
    We present a semantic game for Gödel logic and its extensions, where the players’ interaction stepwise reduces arbitrary claims about the relative order of truth degrees of complex formulas to atomic ones. The paper builds on a previously developed game for Gödel logic with projection operator in Fermüller et al., Information processing and management of uncertainty in knowledge-based systems, Springer, Cham, 2020, pp. 257–270). This game is extended to cover Gödel logic with involutive negations and constants, and then lifted to (...)
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  25. Abstract Forms of Quantification in the Quantified Argument Calculus.Edi Pavlović & Norbert Gratzl - forthcoming - Review of Symbolic Logic:1-32.
    The Quantified argument calculus (Quarc) has received a lot of attention recently as an interesting system of quantified logic which eschews the use of variables and unrestricted quantification, but nonetheless achieves results similar to the Predicate calculus (PC) by employing quantifiers applied directly to predicates instead. Despite this noted similarity, the issue of the relationship between Quarc and PC has so far not been definitively resolved. We address this question in the present paper, and then expand upon that result. Utilizing (...)
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  26. Supervaluations and the Strict-Tolerant Hierarchy.Brian Porter - forthcoming - Journal of Philosophical Logic:1-20.
    In a recent paper, Barrio, Pailos and Szmuc show that there are logics that have exactly the validities of classical logic up to arbitrarily high levels of inference. They suggest that a logic therefore must be identified by its valid inferences at every inferential level. However, Scambler shows that there are logics with all the validities of classical logic at every inferential level, but with no antivalidities at any inferential level. Scambler concludes that in order to identify a logic, we (...)
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  27. The Lattice of Super-Belnap Logics.Adam Přenosil - forthcoming - Review of Symbolic Logic:1-50.
  28. On the Methods of Constructing Hilbert-Type Axiom Systems for Finite-Valued Propositional Logics of Łukasiewicz.Mateusz M. Radzki - forthcoming - History and Philosophy of Logic:1-10.
    The article explores the following question: which among the most often examined in the literature method of constructing Hilbert-type axiom systems for finite-valued propositional logics of Łukasi...
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  29. Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism.Gerhard Schurz - forthcoming - Journal of Philosophical Logic:1-29.
    In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value. Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic and quantum logics, (...)
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  30. The Ontological Innocence of Schematic Logic.Oliver William Tatton-Brown - forthcoming - Logic and Logical Philosophy:1.
    This paper gives a semantics for schematic logic, proving soundness and completeness. The argument for soundness is carried out in ontologically innocent fashion, relying only on the existence of formulae which are actually written down in the course of a derivation in the logic. This makes the logic available to a nominalist, even a nominalist who does not wish to rely on modal notions, and who accepts the possibility that the universe may in fact be finite.
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  31. Questions in Two-Dimensional Logic.Thom van Gessel - forthcoming - Review of Symbolic Logic:1-30.
    Since Kripke, philosophers have distinguished a priori true statements from necessarily true ones. A statement is a priori true if its truth can be established before experience, and necessarily true if it could not have been false according to logical or metaphysical laws. This distinction can be captured formally using two-dimensional semantics. There is a natural way to extend the notions of apriority and necessity so they can also apply to questions. Questions either can or cannot be resolved before experience, (...)
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  32. Infinitary Action Logic with Exponentiation.Stepan L. Kuznetsov & Stanislav O. Speranski - 2022 - Annals of Pure and Applied Logic 173 (2):103057.
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  33. Lindström Theorems in Graded Model Theory.Guillermo Badia & Carles Noguera - 2021 - Annals of Pure and Applied Logic 172 (3):102916.
    Stemming from the works of Petr Hájek on mathematical fuzzy logic, graded model theory has been developed by several authors in the last two decades as an extension of classical model theory that studies the semantics of many-valued predicate logics. In this paper we take the first steps towards an abstract formulation of this model theory. We give a general notion of abstract logic based on many-valued models and prove six Lindström-style characterizations of maximality of first-order logics in terms of (...)
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  34. Nominal Conceptualism and Logical Modelling of Agents’ Conceptions.Farshad Badie - 2021 - Логико-Философские Штудии 1 (19):95-100.
    In the view of my philosophical position “nominal conceptualism”, cognitive/knowledge agents, who are in some way aware of expressing the world based on their mental concepts, deal with their linguistic and/or symbolic expressions. In this paper I rely on nominal conceptualism to logically characterise agents’ concept-based descriptions of the world and analyse a fundamental logical system for conception representation.
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  35. 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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  36. Team Semantics for Interventionist Counterfactuals: Observations vs. Interventions.Fausto Barbero & Gabriel Sandu - 2021 - Journal of Philosophical Logic 50 (3):471-521.
    Team semantics is a highly general framework for logics which describe dependencies and independencies among variables. Typically, the dependencies considered in this context are properties of sets of configurations or data records. We show how team semantics can be further generalized to support languages for the discussion of interventionist counterfactuals and causal dependencies, such as those that arise in manipulationist theories of causation. We show that the “causal teams” we introduce in the present paper can be used for modelling some (...)
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  37. CRITIQUE OF IMPURE REASON: Horizons of Possibility and Meaning.Steven James Bartlett - 2021 - Salem, USA: Studies in Theory and Behavior.
    PLEASE NOTE: This is the corrected 2nd eBook edition, 2021. ●●●●● _Critique of Impure Reason_ has now also been published in a printed edition. To reduce the otherwise high price of this scholarly, technical book of nearly 900 pages and make it more widely available beyond university libraries to individual readers, the non-profit publisher and the author have agreed to issue the printed edition at cost. ●●●●● The printed edition was released on September 1, 2021 and is now available through (...)
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  38. Endogenizing Epistemic Actions.Adam Bjorndahl & Will Nalls - 2021 - Studia Logica 109 (5):1049-1091.
    Through a series of examples, we illustrate some important drawbacks that the action model logic framework suffers from in its ability to represent the dynamics of information updates. We argue that these problems stem from the fact that the action model, a central construct designed to encode agents’ uncertainty about actions, is itself effectively common knowledge amongst the agents. In response to these difficulties, we motivate and propose an alternative semantics that avoids them by endogenizing the action model. We discuss (...)
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  39. A Logical Theory of Causality.Alexander Bochman - 2021 - Cambridge, Massachusetts: MIT Press.
    "The first book that provides a systematic and rigorous logical theory of causality"--.
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  40. Containment Logics: Algebraic Completeness and Axiomatization.Stefano Bonzio & Michele Pra Baldi - 2021 - Studia Logica 109 (5):969-994.
    The paper studies the containment companion of a logic \. This consists of the consequence relation \ which satisfies all the inferences of \, where the variables of the conclusion are contained into those of the set of premises, in case this is not inconsistent. In accordance with the work started in [10], we show that a different generalization of the Płonka sum construction, adapted from algebras to logical matrices, allows to provide a matrix-based semantics for containment logics. In particular, (...)
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  41. Incompleteness and the Halting Problem.Cristian S. Calude - 2021 - Studia Logica 109 (5):1159-1169.
    We present an abstract framework in which we give simple proofs for Gödel’s First and Second Incompleteness Theorems and obtain, as consequences, Davis’, Chaitin’s and Kritchman-Raz’s Theorems.
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  42. An Algebraic Study of S5-Modal Gödel Logic.Diego Castaño, Cecilia Cimadamore, José Patricio Díaz Varela & Laura Rueda - 2021 - Studia Logica 109 (5):937-967.
    In this paper we continue the study of the variety \ of monadic Gödel algebras. These algebras are the equivalent algebraic semantics of the S5-modal expansion of Gödel logic, which is equivalent to the one-variable monadic fragment of first-order Gödel logic. We show three families of locally finite subvarieties of \ and give their equational bases. We also introduce a topological duality for monadic Gödel algebras and, as an application of this representation theorem, we characterize congruences and give characterizations of (...)
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  43. Paraconsistent Orbits of Logics.Edelcio G. de Souza, Alexandre Costa-Leite & Diogo H. B. Dias - 2021 - Logica Universalis 15 (3):271-289.
    Some strategies to turn any logic into a paraconsistent system are examined. In the environment of universal logic, we show how to paraconsistentize logics at the abstract level using a transformation in the class of all abstract logics called paraconsistentization by consistent sets. Moreover, by means of the notions of paradeduction and paraconsequence we go on applying the process of changing a logic converting it into a paraconsistent system. We also examine how this transformation can be performed using multideductive abstract (...)
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  44. Two Applications of Topology to Model Theory.Christopher J. Eagle, Clovis Hamel & Franklin D. Tall - 2021 - Annals of Pure and Applied Logic 172 (5):102907.
    By utilizing the topological concept of pseudocompactness, we simplify and improve a proof of Caicedo, Dueñez, and Iovino concerning Terence Tao's metastability. We also pinpoint the exact relationship between the Omitting Types Theorem and the Baire Category Theorem by developing a machine that turns topological spaces into abstract logics.
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  45. De Finettian Logics of Indicative Conditionals Part I: Trivalent Semantics and Validity.Paul Égré, Lorenzo Rossi & Jan Sprenger - 2021 - Journal of Philosophical Logic 50 (2):187-213.
    This paper explores trivalent truth conditions for indicative conditionals, examining the “defective” truth table proposed by de Finetti and Reichenbach. On their approach, a conditional takes the value of its consequent whenever its antecedent is true, and the value Indeterminate otherwise. Here we deal with the problem of selecting an adequate notion of validity for this conditional. We show that all standard validity schemes based on de Finetti’s table come with some problems, and highlight two ways out of the predicament: (...)
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  46. Variable Sharing in Connexive Logic.Luis Estrada-González & Claudia Lucía Tanús-Pimentel - 2021 - Journal of Philosophical Logic 50 (6):1377-1388.
    However broad or vague the notion of connexivity may be, it seems to be similar to the notion of relevance even when relevance and connexive logics have been shown to be incompatible to one another. Relevance logics can be examined by suggesting syntactic relevance principles and inspecting if the theorems of a logic abide to them. In this paper we want to suggest that a similar strategy can be employed with connexive logics. To do so, we will suggest some properties (...)
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  47. Two Pretabular Linear Extensions of Relevance Logic R.Asadollah Fallahi - 2021 - Journal of Applied Non-Classical Logics 31 (2):154-179.
    Pretabularity is the attribute of logics that are not characterised by finite matrices, but all of whose proper extensions are. Two of the first-known pretabular logics were Dummett’s famous super-...
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  48. On a Logico-Algebraic Approach to AGM Belief Contraction Theory.D. Fazio & M. Pra Baldi - 2021 - Journal of Philosophical Logic 50 (5):911-938.
    In this paper we investigate AGM belief contraction operators by using the tools of algebraic logic. We generalize the notion of contraction to arbitrary finitary propositional logics, and we show how to switch from a syntactic-based approach to a semantic one. This allows to build a solid bridge between the validity of AGM postulates in a propositional logic and specific algebraic properties of its intended algebraic counterpart. Such a connection deserves particular attention when we deal with maxichoice contractions, as studied (...)
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  49. 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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  50. Hyper-MacNeille Completions of Heyting Algebras.J. Harding & F. M. Lauridsen - 2021 - Studia Logica 109 (5):1119-1157.
    A Heyting algebra is supplemented if each element a has a dual pseudo-complement \, and a Heyting algebra is centrally supplement if it is supplemented and each supplement is central. We show that each Heyting algebra has a centrally supplemented extension in the same variety of Heyting algebras as the original. We use this tool to investigate a new type of completion of Heyting algebras arising in the context of algebraic proof theory, the so-called hyper-MacNeille completion. We show that the (...)
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