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  1. The Logic of Hyperlogic. Part A: Foundations.Alexander W. Kocurek - forthcoming - Review of Symbolic Logic:1-27.
    Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., "Intuitionistic logic is correct" or "The law of excluded middle holds") into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical interpretation of the (...)
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  2. How to Adopt a Logic.Daniel Cohnitz & Carlo Nicolai - forthcoming - Dialectica.
    What is commonly referred to as the Adoption Problem is a challenge to the idea that the principles of logic can be rationally revised. The argument is based on a reconstruction of unpublished work by Saul Kripke. As the reconstruction has it, Kripke extends the scope of Willard van Orman Quine's regress argument against conventionalism to the possibility of adopting new logical principles. In this paper we want to discuss the scope of this challenge. Are all revisions of logic subject (...)
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  3. $$\mathrm {ZF}$$ ZF Between Classicality and Non-classicality.Sourav Tarafder & Giorgio Venturi - 2022 - Studia Logica 110 (1):189-218.
    We present a generalization of the algebra-valued models of \ where the axioms of set theory are not necessarily mapped to the top element of an algebra, but may get intermediate values, in a set of designated values. Under this generalization there are many algebras which are neither Boolean, nor Heyting, but that still validate \.
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  4. The Orthologic of Epistemic Modals.Wesley H. Holliday & Matthew Mandelkern - manuscript
    Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form ‘p, but it might be that not p’ appears to be a contradiction, 'might not p' does not entail 'not p', which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. Some theories predict that (...)
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  5. Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism.Gerhard Schurz - 2022 - Journal of Philosophical Logic 51 (1):27-55.
    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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  6. An Axiomatic Approach to the Quantified Argument Calculus.Matteo Pascucci - forthcoming - Erkenntnis:1-26.
    The present article employs a model-theoretic semantics to interpret a fragment of the language of the Quantified Argument Calculus (Quarc), a recently introduced logical system whose main aim is capturing the structure of natural language sentences in a closer way than does the language of classical logic. The main contribution is an axiomatization for the set of formulas that are valid in all standard interpretations within the employed semantics.
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  7. Moral Principles: Hedged, Contributory, Mixed.Aleks Knoks - 2021 - In Deontic Logic and Normative Systems 2020/21.
    It's natural to think that the principles expressed by the statements "Promises ought to be kept" and "We ought to help those in need" are defeasible. But how are we to make sense of this defeasibility? On one proposal, moral principles have hedges or built-in unless clauses specifying the conditions under which the principle doesn't apply. On another, such principles are contributory and, thus, do not specify which actions ought to be carried out, but only what counts in favor or (...)
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  8. Nonclassical Logics and Their Applications: Post-Proceedings of the 8th International Workshop on Logic and Cognition.Shier Ju, Alessandra Palmigiano & Minghui Ma (eds.) - 2020 - Singapore: Springer.
    This edited book focuses on non-classical logics and their applications, highlighting the rapid advances and the new perspectives that are emerging in this area. Non-classical logics are logical formalisms that violate or go beyond classical logic laws, and their specific features make them particularly suited to describing and reason about aspects of social interaction. The richness and diversity of non-classical logics mean that this area is a natural catalyst for ideas and insights from many different fields, from information theory to (...)
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  9. Residuated Structures and Orthomodular Lattices.D. Fazio, A. Ledda & F. Paoli - 2021 - Studia Logica 109 (6):1201-1239.
    The variety of residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., \-groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated \-groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated \-groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some (...)
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  10. Deductive Cardinality Results and Nuisance-Like Principles.Sean C. Ebels-Duggan - 2021 - Review of Symbolic Logic 14 (3):592-623.
    The injective version of Cantor’s theorem appears in full second-order logic as the inconsistency of the abstraction principle, Frege’s Basic Law V (BLV), an inconsistency easily shown using Russell’s paradox. This incompatibility is akin to others—most notably that of a (Dedekind) infinite universe with the Nuisance Principle (NP) discussed by neo-Fregean philosophers of mathematics. This paper uses the Burali–Forti paradox to demonstrate this incompatibility, and another closely related, without appeal to principles related to the axiom of choice—a result hitherto unestablished. (...)
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  11. Probabilistic Inferences From Conjoined to Iterated Conditionals.Giuseppe Sanfilippo, Niki Pfeifer, D. E. Over & A. Gilio - 2018 - International Journal of Approximate Reasoning 93:103-118.
    There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, P(if A then B), is the conditional probability of B given A, P(B|A). We identify a conditional which is such that P(if A then B)=P(B|A) with de Finetti's conditional event, B|A. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, we illustrate (...)
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  12. Probability Semantics for Aristotelian Syllogisms.Niki Pfeifer & Giuseppe Sanfilippo - manuscript
    We present a coherence-based probability semantics for (categorical) Aristotelian syllogisms. For framing the Aristotelian syllogisms as probabilistic inferences, we interpret basic syllogistic sentence types A, E, I, O by suitable precise and imprecise conditional probability assessments. Then, we define validity of probabilistic inferences and probabilistic notions of the existential import which is required, for the validity of the syllogisms. Based on a generalization of de Finetti's fundamental theorem to conditional probability, we investigate the coherent probability propagation rules of argument forms (...)
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  13. 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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  14. Three Short Arguments Against Goff’s Grounding of Logical Laws in Universal Consciousness.Andrew Thomas - 2021 - Kriterion - Journal of Philosophy (3):237-246.
    In this paper, I argue that Goff's view that universal consciousness grounds logical laws such as the law of non-contradiction cannot be true on the grounds that we cannot guarantee the classical logic loving nature of universal consciousness that Goff desires in order to ground logical laws. I will present three arguments to show this.
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  15. 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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  16. Towards a Non-classical Meta-theory for Substructural Approaches to Paradox.Lucas Rosenblatt - 2021 - Journal of Philosophical Logic 50 (5):1007-1055.
    In the literature on self-referential paradoxes one of the hardest and most challenging problems is that of revenge. This problem can take many shapes, but, typically, it besets non-classical accounts of some semantic notion, such as truth, that depend on a set of classically defined meta-theoretic concepts, like validity, consistency, and so on. A particularly troubling form of revenge that has received a lot of attention lately involves the concept of validity. The difficulty lies in that the non-classical logician cannot (...)
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  17. Logic Works: A Rigorous Introduction to Formal Logic.Lorne Falkenstein, Scott Stapleford & Molly Kao - 2022 - New York: Routledge.
    Logic Works is a critical and extensive introduction to logic. It asks questions about why systems of logic are as they are, how they relate to ordinary language and ordinary reasoning, and what alternatives there might be to classical logical doctrines. It considers how logical analysis can be applied to carefully represent the reasoning employed in academic and scientific work, better understand that reasoning, and identify its hidden premises. Aiming to be as much a reference work and handbook for further, (...)
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  18. 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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  19. One Step is Enough.David Ripley - forthcoming - Journal of Philosophical Logic:1-27.
    The recent development and exploration of mixed metainferential logics is a breakthrough in our understanding of nontransitive and nonreflexive logics. Moreover, this exploration poses a new challenge to theorists like me, who have appealed to similarities to classical logic in defending the logic ST, since some mixed metainferential logics seem to bear even more similarities to classical logic than ST does. There is a whole ST-based hierarchy, of which ST itself is only the first step, that seems to become more (...)
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  20. Imperative Inference and Practical Rationality.Daniel W. Harris - 2021 - Philosophical Studies (4):1065-1090.
    Some arguments include imperative clauses. For example: ‘Buy me a drink; you can’t buy me that drink unless you go to the bar; so, go to the bar!’ How should we build a logic that predicts which of these arguments are good? Because imperatives aren’t truth apt and so don’t stand in relations of truth preservation, this technical question gives rise to a foundational one: What would be the subject matter of this logic? I argue that declaratives are used to (...)
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  21. Islamic Contradictory Theology . . . Is There Any Such Thing?Abbas Ahsan - 2021 - Logica Universalis 15 (2).
    The application of paraconsistent logics to theological contradictions is a fascinating move. Jc Beall’s (J Anal Theol, 7(1): 400–439, 2019) paper entitled ‘Christ—A Contradiction: A Defense of ‘Contradictory Christology’ is a notable example. Beall proposes a solution to the fundamental problem of Christology. His solution aims at making the case, and defending the viability of, what he has termed, ‘Contradictory Christology’. There are at least two essential components of Beall’s ‘Contradictory Christology’. These include the dogmatic statements of Chalcedon and FDE (...)
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  22. 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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  23. Natural Implicative Expansions of Variants of Kleene's Strong 3-Valued Logic with Gödel-Type and Dual Gödel-Type Negation.Gemma Robles & José M. Méndez - 2021 - Journal of Applied Non-Classical Logics 31 (2):130-153.
    Let MK3 I and MK3 II be Kleene's strong 3-valued matrix with only one and two designated values, respectively. Next, let MK3 G be defined exactly as MK3 I, except th...
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  24. An Approach to Stochastic Processes Via Non-Classical Logic.Antonio Di Nola, Anatolij Dvurečenskij & Serafina Lapenta - 2021 - Annals of Pure and Applied Logic 172 (9):103012.
  25. Heterodox Logics and the Problem of the Unity of Logic.Francisco Miró Quesada Cantuarias - manuscript
    The present paper is an essay on what, in the last years, has begun to be called, "philosophical logic". Philosophical logic originates as a consequence of the progressive formal rigour of traditional logic. This rigour had led, contrary to what was excepted, to problems of fundamental philosophical meaning and of abysmatic depth. There are many problems which are of interest to philosophical logic, but, in the author's opinion, the most important one has hardly been approached. This problem is the relation (...)
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  26. 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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  27. 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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  28. Questions in Two-Dimensional Logic.Thom van Gessel - forthcoming - Review of Symbolic Logic:1-21.
    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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  29. An Implicative Expansion of Belnap’s Four-Valued Matrix: A Modal Four-Valued Logic Without Strong Modal Lukasiewicz-Type Paradoxes.José Miguel Blanco - 2020 - Bulletin of Symbolic Logic 26 (3-4):297-298.
  30. The Fundamental Theorem of Central Element Theory.Mariana Vanesa Badano & Diego Jose Vaggione - 2020 - Journal of Symbolic Logic 85 (4):1599-1606.
    We give a short proof of the fundamental theorem of central element theory. The original proof is constructive and very involved and relies strongly on the fact that the class be a variety. Here we give a more direct nonconstructive proof which applies for the more general case of a first-order class which is both closed under the formation of direct products and direct factors.
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  31. On the Correspondence Between Nested Calculi and Semantic Systems for Intuitionistic Logics.Tim Lyon - 2021 - Journal of Logic and Computation 31 (1):213-265.
    This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as (...)
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  32. G. Priest's An Introduction to Non-Classical Logic (2001). [REVIEW]Hans-Peter Leeb - 2003 - History and Philosophy of Logic 24:65-66.
    The review gives a short description of the content of the book and discusses the treatment of conditionals in it.
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  33. El lugar de la lógica en el razonamiento jurídico.Miguel Garcia-Godinez - 2019 - In Gerardo Ramirez & Manuel Jimenez (eds.), Ensayos de retórica jurídica. Mexico City, CDMX, Mexico: pp. 171-180.
  34. Extended Syllogistics in Calculus CL.Jens Lemanski - 2021 - Journal of Applied Logics 8 (2):557-577.
    Extensions of traditional syllogistics have been increasingly researched in philosophy, linguistics, and areas such as artificial intelligence and computer science in recent decades. This is mainly due to the fact that syllogistics is seen as a logic that comes very close to natural language abilities. Various forms of extended syllogistics have become established. This paper deals with the question to what extent a syllogistic representation in CL diagrams can be seen as a form of extended syllogistics. It will be shown (...)
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  35. An Algebraic Study of Tense Operators on Nelson Algebras.A. V. Figallo, G. Pelaitay & J. Sarmiento - 2021 - Studia Logica 109 (2):285-312.
    Ewald considered tense operators G, H, F and P on intuitionistic propositional calculus and constructed an intuitionistic tense logic system called IKt. In 2014, Figallo and Pelaitay introduced the variety IKt of IKt-algebras and proved that the IKt system has IKt-algebras as algebraic counterpart. In this paper, we introduce and study the variety of tense Nelson algebras. First, we give some examples and we prove some properties. Next, we associate an IKt-algebra to each tense Nelson algebras. This result allowed us (...)
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  36. Double Negation Semantics for Generalisations of Heyting Algebras.Rob Arthan & Paulo Oliva - 2021 - Studia Logica 109 (2):341-365.
    This paper presents an algebraic framework for investigating proposed translations of classical logic into intuitionistic logic, such as the four negative translations introduced by Kolmogorov, Gödel, Gentzen and Glivenko. We view these as variant semantics and present a semantic formulation of Troelstra’s syntactic criteria for a satisfactory negative translation. We consider how each of the above-mentioned translation schemes behaves on two generalisations of Heyting algebras: bounded pocrims and bounded hoops. When a translation fails for a particular class of algebras, we (...)
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  37. Kripke Semantics for Intuitionistic Łukasiewicz Logic.A. Lewis-Smith, P. Oliva & E. Robinson - 2021 - Studia Logica 109 (2):313-339.
    This paper proposes a generalization of the Kripke semantics of intuitionistic logic IL appropriate for intuitionistic Łukasiewicz logic IŁL — a logic in the intersection between IL and (classical) Łukasiewicz logic. This generalised Kripke semantics is based on the poset sum construction, used in Bova and Montagna (Theoret Comput Sci 410(12):1143–1158, 2009) to show the decidability (and PSPACE completeness) of the quasiequational theory of commutative, integral and bounded GBL algebras. The main idea is that w \Vdash \sigma—which for IL is (...)
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  38. A Conservative Negation Extension of Positive Semilattice Logic Without the Finite Model Property.Yale Weiss - 2021 - Studia Logica 109 (1):125-136.
    In this article, I present a semantically natural conservative extension of Urquhart’s positive semilattice logic with a sort of constructive negation. A subscripted sequent calculus is given for this logic and proofs of its soundness and completeness are sketched. It is shown that the logic lacks the finite model property. I discuss certain questions Urquhart has raised concerning the decision problem for the positive semilattice logic in the context of this logic and pose some problems for further research.
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  39. Semi De Morgan Logic Properly Displayed.Giuseppe Greco, Fei Liang, M. Andrew Moshier & Alessandra Palmigiano - 2021 - Studia Logica 109 (1):1-45.
    In the present paper, we endow semi De Morgan logic and a family of its axiomatic extensions with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis of the variety of semi De Morgan algebras, and applies the guidelines of the multi-type methodology in the design of display calculi.
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  40. Routley Star and Hyperintensionality.Sergei Odintsov & Heinrich Wansing - 2021 - Journal of Philosophical Logic 50 (1):33-56.
    We compare the logic HYPE recently suggested by H. Leitgeb as a basic propositional logic to deal with hyperintensional contexts and Heyting-Ockham logic introduced in the course of studying logical aspects of the well-founded semantics for logic programs with negation. The semantics of Heyting-Ockham logic makes use of the so-called Routley star negation. It is shown how the Routley star negation can be obtained from Dimiter Vakarelov’s theory of negation and that propositional HYPE coincides with the logic characterized by the (...)
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  41. Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey.Peter Fletcher - 2020 - Journal of Philosophical Logic 49 (6):1111-1157.
    I survey Brouwer’s weak counterexamples to classical theorems, with a view to discovering what useful mathematical work is done by weak counterexamples; whether they are rigorous mathematical proofs or just plausibility arguments; the role of Brouwer’s notion of the creative subject in them, and whether the creative subject is really necessary for them; what axioms for the creative subject are needed; what relation there is between these arguments and Brouwer’s theory of choice sequences. I refute one of Brouwer’s claims with (...)
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  42. Transfinite Meta-inferences.Chris Scambler - 2020 - Journal of Philosophical Logic 49 (6):1079-1089.
    In Barrio et al. Barrio Pailos and Szmuc prove that there are systems of logic that agree with classical logic up to any finite meta-inferential level, and disagree with it thereafter. This article presents a generalized sense of meta-inference that extends into the transfinite, and proves analogous results to all transfinite orders.
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  43. Reasoning Continuously: A Formal Construction of Continuous Proofs.T. D. P. Brunet & E. Fisher - 2020 - Studia Logica 108 (6):1145-1160.
    We begin with the idea that lines of reasoning are continuous mental processes and develop a notion of continuity in proof. This requires abstracting the notion of a proof as a set of sentences ordered by provability. We can then distinguish between discrete steps of a proof and possibly continuous stages, defining indexing functions to pick these out. Proof stages can be associated with the application of continuously variable rules, connecting continuity in lines of reasoning with continuously variable reasons. Some (...)
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  44. Definable Operators on Stable Set Lattices.Robert Goldblatt - 2020 - Studia Logica 108 (6):1263-1280.
    A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We generalise this to the level of non-distributive logics that have a relational semantics provided by structures based on polarities. Such structures have associated complete lattices of stable subsets, and these have been used to construct canonical extensions of lattice-based algebras. We study classes of structures that are closed under ultraproducts and whose (...)
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  45. A Canonical Model for Constant Domain Basic First-Order Logic.Ben Middleton - 2020 - Studia Logica 108 (6):1307-1323.
    I build a canonical model for constant domain basic first-order logic (BQLCD), the constant domain first-order extension of Visser’s basic propositional logic, and use the canonical model to verify that BQLCD satisfies the disjunction and existence properties.
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  46. Supervaluationism, Subvaluationism and the Sorites Paradox.Pablo Cobreros & Luca Tranchini - 2019 - In Elia Zardini & Sergi Oms (eds.), The Sorites Paradox. Cambridge, Reino Unido: pp. 38-62.
    One way in which we might approach the challenge posed by the Sorites Paradox is considering that Sorites-susceptible predicates have several candidate extensions, or several ways in which these expressions can be made precise. For example, a candidate extension for the predicate ‘is a baby’ is the set of humans of less than two years, but also the set of those less than two years and one second, and of those less than two years and two seconds. In this chapter (...)
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  47. The Quantified Argument Calculus and Natural Logic.Hanoch Ben-Yami - 2020 - Dialectica 74 (2).
    The formalisation of Natural Language arguments in a formal language close to it in syntax has been a central aim of Moss’s Natural Logic. I examine how the Quantified Argument Calculus (Quarc) can handle the inferences Moss has considered. I show that they can be incorporated in existing versions of Quarc or in straightforward extensions of it, all within sound and complete systems. Moreover, Quarc is closer in some respects to Natural Language than are Moss’s systems – for instance, is (...)
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  48. Intuitionistic Non-normal Modal Logics: A General Framework.Tiziano Dalmonte, Charles Grellois & Nicola Olivetti - 2020 - Journal of Philosophical Logic 49 (5):833-882.
    We define a family of intuitionistic non-normal modal logics; they can be seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only Necessity or Possibility. We then consider the more important case of bimodal logics, which contain both modal operators. In this case we define several interactions between Necessity and Possibility of increasing strength, although weaker than duality. We thereby obtain a lattice of 24 distinct bimodal logics. For all logics we provide both a Hilbert (...)
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  49. A Paraconsistent Conditional Logic.Minghui Ma & Chun-Ting Wong - 2020 - Journal of Philosophical Logic 49 (5):883-903.
    We develop a paraconsistent logic by introducing new models for conditionals with acceptive and rejective selection functions which are variants of Chellas’ conditional models. The acceptance and rejection conditions are substituted for truth conditions of conditionals. The paraconsistent conditional logic is axiomatized by a sequent system \ which is an extension of the Belnap-Dunn four-valued logic with a conditional operator. Some acceptive extensions of \ are shown to be sound and complete. We also show the finite acceptive model property and (...)
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  50. A Relevant Logic of Questions.Vít Punčochář - 2020 - Journal of Philosophical Logic 49 (5):905-939.
    This paper introduces the inquisitive extension of R, denoted as InqR, which is a relevant logic of questions based on the logic R as the background logic of declaratives. A semantics for InqR is developed, and it is shown that this semantics is, in a precisely defined sense, dual to Routley-Meyer semantics for R. Moreover, InqR is axiomatized and completeness of the axiomatic system is established. The philosophical interpretation of the duality between Routley-Meyer semantics and the semantics for InqR is (...)
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