Results for 'Para-consistent Logic'

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  1. Translations between logical systems: a manifesto.Walter A. Carnielli & Itala Ml D'Ottaviano - 1997 - Logique Et Analyse 157:67-81.
    The main objective o f this descriptive paper is to present the general notion of translation between logical systems as studied by the GTAL research group, as well as its main results, questions, problems and indagations. Logical systems here are defined in the most general sense, as sets endowed with consequence relations; translations between logical systems are characterized as maps which preserve consequence relations (that is, as continuous functions between those sets). In this sense, logics together with translations form a (...)
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  2. “Fuzzy time”, a Solution of Unexpected Hanging Paradox (a Fuzzy interpretation of Quantum Mechanics).Farzad Didehvar - manuscript
    Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to (...)
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  3. Minimal inconsistency-tolerant logics: a quantitative approach.Christian Strasser & Sanderson Molick - forthcoming - Australasian Journal of Logic.
    In order to reason in a non-trivializing way with contradictions, para- consistent logics reject some classically valid inferences. As a way of re- covering some of these inferences, Graham Priest ([Priest, 1991]) proposed to nonmonotonically strengthen the Logic of Paradox by allowing the se- lection of “less inconsistent” models via a comparison of their respective inconsistent parts. This move recaptures a good portion of classical logic in that it does not block, e.g., disjunctive syllogism, unless it (...)
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  4. Hegel and the Sciences. [REVIEW]Sergio Cremaschi - 1989 - The Owl of Minerva 20 (2):224-228.
    I discuss this collection of essays on Hegel and the sciences while stressing the interest of Hegel's philosophy of nature in the light of later non-mainstream developments in the life-sciences and medicine. I compare then the chapters dedicated to Hegel's logic with recent literature on para-consistent logic and re-interpretations of Hegel's own logic.
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  5. (1 other version) “Fuzzy time”, from paradox to paradox (Does it solve the contradiction between Quantum Mechanics & General Relativity?).Farzad Didehvar - manuscript
    Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to (...)
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  6. Wittgenstein contra la Metamatemática.Axel Barceló - manuscript
    En este texto retomo una pregunta importante que había quedado abierta al final del segundo capítulo de mi (2019): ¿cuáles son los límites del análisis? Sabemos que por obvias limitaciones materiales, todo análisis siempre será incompleto y por lo tanto, limitado. A estos límites les hemos llamado “metodológicos”, para distinguirlos de los metafísicos. Si el análisis tiene límites en este segundo sentido, aun si termináramos de analizar por completo un concepto, no podremos estar seguros de conocer todas sus propiedades (...)
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  7. Redução Plena do Deôntico ao Ôntico.Diogo Lindner - 2008 - Dissertation, Universidade Federal de Santa Maria
    A presente dissertação tem como objetivo uma apresentação da proposta de Charles Kielkopf, de tradução da lógica deôntica standard em uma lógica normal alética e de seusresultados quanto à construção de um sistema de lógica deôntica que capture conceitos eprincípios kantianos como necessidade causal e as formulações do Imperativo Categórico acerca do Reino da Natureza e do Reino dos Fins. Uma vez que este processo resulta em uma interpretação de aspectos da filosofia kantiana, optou-se inicialmente por uma apresentação em linhas (...)
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  8. Logically-consistent hypothesis testing and the hexagon of oppositions.Julio Michael Stern, Rafael Izbicki, Luis Gustavo Esteves & Rafael Bassi Stern - 2017 - Logic Journal of the IGPL 25 (5):741-757.
    Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for these modalities to be (...)
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  9. Acerca de la interpretación de Landgrebe sobre el cartesianismo de Husserl.Patricio Agustin Perkins - 2014 - Investigaciones Fenomenológicas 11:203-222.
    Critico la teoría hermenéutica de Landgrebe sobre el cartesianismo de Husserl mostrando la estructura argumentativa en la que se inserta, lo que pretende y lo que está forzada a pretender. Su núcleo duro radica en los conceptos de crítica inmanente y lógica interna y tiene como meta final promover una idea de trascendental no-entitativa voluntarista y correlacional opuesta a la de un yo absoluto. Para probar esto, analizo tres niveles del cartesianismo de Landgrebe: primero, la síntesis contradictoria entre apodicticidad (...)
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  10. Ver con los dos sistemas de pensamiento: una revisión de "Ver las cosas como son: una teoría de la percepción" (Seeing Things As They Are: a Theory of Perception) de John Searle (2015).Michael Richard Starks - 2020 - In Michael Starks (ed.), Comprender las Conexiones entre Ciencia, Filosofía, Psicología, Religión, Política, Economía, Historia y Literatura - Artículos y reseñas 2006-2019. Las Vegas, NV USA: Reality Press. pp. 65-104.
    Como tantas veces en filosofía, el título no sólo establece la línea de batalla, sino que expone los prejuicios y errores del autor, ya que si podemos o no dar sentido al juego de idiomas 'Ver las cosas como son' y si es posible tener una 'teoría filosófica' de percepción' (que sólo puede ser sobre cómo funciona el lenguaje de la percepción), a diferencia de uno científico, que es una teoría sobre cómo funciona el cerebro, son exactamente los problemas. Este (...)
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  11. The Logical Consistency of Simultaneous Agnostic Hypothesis Tests.Julio Michael Stern - 2016 - Entropy 8 (256):1-22.
    Simultaneous hypothesis tests can fail to provide results that meet logical requirements. For example, if A and B are two statements such that A implies B, there exist tests that, based on the same data, reject B but not A. Such outcomes are generally inconvenient to statisticians (who want to communicate the results to practitioners in a simple fashion) and non-statisticians (confused by conflicting pieces of information). Based on this inconvenience, one might want to use tests that satisfy logical requirements. (...)
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  12. Strengthening Consistency Results in Modal Logic.Samuel Alexander & Arthur Paul Pedersen - 2023 - Tark.
    A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces generic theories (...)
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  13. Dutch Books, Coherence, and Logical Consistency.Anna Mahtani - 2014 - Noûs 49 (3):522-537.
    In this paper I present a new way of understanding Dutch Book Arguments: the idea is that an agent is shown to be incoherent iff he would accept as fair a set of bets that would result in a loss under any interpretation of the claims involved. This draws on a standard definition of logical inconsistency. On this new understanding, the Dutch Book Arguments for the probability axioms go through, but the Dutch Book Argument for Reflection fails. The question of (...)
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  14. Consistency and Permission in Deontic Justification Logic.Federico L. G. Faroldi, Thomas Studer, Meghdad Ghari & Eveline Lehmann - forthcoming - Journal of Logic and Computation 1.
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  15. Ethics, Logical Consistency and Practical Deliberation.Nancy Matchett - 2011 - Theoretical and Applied Ethics 1 (3).
    Moral conflicts are real, and while a deontic logic containing a modified "agglomeration rule" may be able to accommodate this fact, even the most sophisticated logic will still overlook much of what everyday normative reasoning involves.
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  16. A Deontic Logic for Programming Rightful Machines: Kant’s Normative Demand for Consistency in the Law.Ava Thomas Wright - 2023 - Logics for Ai and Law: Joint Proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence (Lingai) and the International Workshop on Logic, Ai and Law (Lail).
    In this paper, I set out some basic elements of a deontic logic with an implementation appropriate for handling conflicting legal obligations for purposes of programming autonomous machine agents. Kantian justice demands that the prescriptive system of enforceable public laws be consistent, yet statutes or case holdings may often describe legal obligations that contradict; moreover, even fundamental constitutional rights may come into conflict. I argue that a deontic logic of the law should not try to work around (...)
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  17. La interpretación modal de la mecánica cuántica: de la lógica cuántica al problema de la medida.Jose Alejandro Fernández Cuesta - 2023 - Revista de la Sociedad de Lógica, Metodología y Filosofía de la Ciencia En España:14-36.
    El presente trabajo pretende explicitar que los operadores modales, como construcciones lógicas, insertos en las interpretaciones modales (MI) de la mecánica cuántica son usados de manera informal sin una semántica modal adecuada. Primero se estudiarán en detalle los motivos por los que ninguna lógica cuántica puede ofrecer una base apropiada para formalizar estos operadores en contextos mecánico-cuánticos. A continuación, se presentará el enfoque de las historias cuánticas como una nueva lógica cuántica (NQL) intrínsecamente booleana como posible herramienta para (...)
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  18. New foundations for imperative logic I: Logical connectives, consistency, and quantifiers.Peter B. M. Vranas - 2008 - Noûs 42 (4):529-572.
    Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much (...)
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  19. Consistency proof of a fragment of pv with substitution in bounded arithmetic.Yoriyuki Yamagata - 2018 - Journal of Symbolic Logic 83 (3):1063-1090.
    This paper presents proof that Buss's S22 can prove the consistency of a fragment of Cook and Urquhart's PV from which induction has been removed but substitution has been retained. This result improves Beckmann's result, which proves the consistency of such a system without substitution in bounded arithmetic S12. Our proof relies on the notion of "computation" of the terms of PV. In our work, we first prove that, in the system under consideration, if an equation is proved and either (...)
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  20. On the philosophical motivations for the logics of formal consistency and inconsistency.Walter Carnielli & Rodrigues Abilio - manuscript
    We present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language. We shall defend the view according to which logics of formal inconsistency are theories of logical consequence of normative and epistemic character. This approach not only allows us to make inferences in the presence of contradictions, but offers a philosophically acceptable account of paraconsistency.
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  21. Logic in mathematics and computer science.Richard Zach - forthcoming - In Filippo Ferrari, Elke Brendel, Massimiliano Carrara, Ole Hjortland, Gil Sagi, Gila Sher & Florian Steinberger (eds.), Oxford Handbook of Philosophy of Logic. Oxford, UK: Oxford University Press.
    Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, (...)
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  22. (1 other version)I.W.Kelly Logical consistency and the child.I. W. Kelly - 1981 - Philosophy of the Social Sciences 11 (1):15-18.
    The Swiss psychologist Jean Piaget contends that children below the age of 12 see no necessity for the logical law of non-contradiction. I argue this view is problematic. First of all, Piaget's dialogues with children which are considered supportive of this position are not clearly so. Secondly, Piaget underestimates the necessary nature of following the logical law of non-contradiction in everyday discourse. The mere possibility of saying something significant and informative at all presupposes that the law of non-contradiction is enforced.
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  23. Book of Abstracts: Trends in Logic XVI: Consistency, Contradiction, Paraconsistency and Reasoning.Walter A. Carnielli, Rafael Testa & Juliana Bueno-Soler - 2016 - Campinas, SP, Brasil: CLE-Unicamp.
    “Trends in Logic XVI: Consistency, Contradiction, Paraconsistency, and Reasoning - 40 years of CLE” is being organized by the Centre for Logic, Epistemology and the History of Science at the State University of Campinas (CLEUnicamp) from September 12th to 15th, 2016, with the auspices of the Brazilian Logic Society, Studia Logica and the Polish Academy of Sciences. The conference is intended to celebrate the 40th anniversary of CLE, and is centered around the areas of logic, epistemology, (...)
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  24. The Consistency Argument for Ranking Functions.Franz Huber - 2007 - Studia Logica 86 (2):299-329.
    The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem. The latter says that an agent’s belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update rules.
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  25. The consistent histories interpretation of quantum mechanics.Edward MacKinnon - unknown
    The consistent histories reformulation of quantum mechanics was developed by Robert Griffiths, given a formal logical systematization by Roland Omn\`{e}s, and under the label `decoherent histories', was independently developed by Murray Gell-Mann and James Hartle and extended to quantum cosmology. Criticisms of CH involve issues of meaning, truth, objectivity, and coherence, a mixture of philosophy and physics. We will briefly consider the original formulation of CH and some basic objections. The reply to these objections, like the objections themselves, involves (...)
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  26. A calculus for Belnap's logic in which each proof consists of two trees.Stefan Wintein & Reinhard Muskens - 2012 - Logique Et Analyse 220:643-656.
    In this paper we introduce a Gentzen calculus for (a functionally complete variant of) Belnap's logic in which establishing the provability of a sequent in general requires \emph{two} proof trees, one establishing that whenever all premises are true some conclusion is true and one that guarantees the falsity of at least one premise if all conclusions are false. The calculus can also be put to use in proving that one statement \emph{necessarily approximates} another, where necessary approximation is a natural (...)
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  27. Elements of Mathematical Logic for Consistency Analysis of Axiomatic Sets in the Mind-Body Problem.David Tomasi - 2020 - In David Låg Tomasi (ed.), Critical Neuroscience and Philosophy. A Scientific Re-Examination of the Mind-Body Problem. London, England, UK: Palgrave MacMillan Springer.
    (...) However, whether we chose a weak or strong approximation, the set would not make any sense at all, if (once more) this choice would not be justified in either temporal or spatial sense or given the context of possible applicability of the set in different circumstances. This would obviously represent a dualism in itself as we would (for instance) posit and apply a full identity-equality-equivalence of x and y when applying Newtonian physics to certain observations we make (it would (...)
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  28. Consistency of belief.Howard Darmstadter - 1971 - Journal of Philosophy 68 (10):301-310.
    A rational man’s beliefs are not logically consistent, and he does not believe all the logical consequences of his beliefs. This is because in any situational context, we only accept certain believed sentences. Within that context, we insist that sentences be logically consistent, and we accept the logical consequences of the other sentences we accept in that context. But such sentences do not have to be consistent with sentences we accept in other contexts, nor will we always (...)
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  29. Consistency and the theory of truth.Richard Heck - 2015 - Review of Symbolic Logic 8 (3):424-466.
    This paper attempts to address the question what logical strength theories of truth have by considering such questions as: If you take a theory T and add a theory of truth to it, how strong is the resulting theory, as compared to T? Once the question has been properly formulated, the answer turns out to be about as elegant as one could want: Adding a theory of truth to a finitely axiomatized theory T is more or less equivalent to a (...)
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  30. The Logicality of Language: A new take on Triviality, “Ungrammaticality”, and Logical Form.Guillermo Del Pinal - 2017 - Noûs 53 (4):785-818.
    Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth-conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the `logicality of language', accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter-examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired (...)
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  31. The Logic of Opacity.Andrew Bacon & Jeffrey Sanford Russell - 2017 - Philosophy and Phenomenological Research 99 (1):81-114.
    We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide (...)
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  32. Modal-Logical Reconstructions of Thought Experiments.Ruward Mulder & F. A. Muller - 2023 - Erkenntnis 2023 (7):2835-2847.
    Sorensen (1992) has provided two modal-logical schemas to reconstruct the logical structure of two types of destructive thought experiments: the Necessity Refuter and the Possibility Refuter. The schemas consist of five propositions which Sorensen claims but does not prove to be inconsistent.We show that the five propositions, as presented by Sorensen, are not inconsistent, but by adding a premise (and a logical truth), we prove that the resulting sextet of premises is inconsistent. Häggqvist (2009) has provided a different modal-logical schema (...)
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  33. Metodologias para o Ensino de Lógica em Libras: Notas sobre o desenvolvimento de uma aula de Lógica para o projeto IFSP FILOLIBRAS.Rafael Testa, Lucimar Bizio & João Antonio de Moraes - 2022 - CLE E-Prints 20 (3).
    Resumo -/- A partir da experiência de produção de uma videoaula de Lógica em Libras (Testa, Moraes, Bizio e Caló, 2021) para o IFSP FILOLIBRAS, inserida no contexto do projeto ‘O Ensino de Filosofia para Surdos: elaboração de material didático em uma perspectiva de inclusão escolar’ (Moraes e Bizio, 2021), levantamos algumas questões relativas ao arcabouço teórico do projeto. Após introduzirmos as motivações do projeto, explicamos como sua metodologia foi tratada no contexto da aula de Lógica, expondo as (...)
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  34. Referential consistency as a a criterion of meaning.Steven James Bartlett - 1982 - Synthese 52 (2):267 - 282.
    NOTE TO THE READER - December, 2021 ●●●●● -/- After a long period of time devoted to research in other areas, the author returned to the subject of this paper in a book-length study, CRITIQUE OF IMPURE REASON: Horizons of Possibility and Meaning. In this book (Chapter 11, “The Metalogic of Meaning”), the position developed in the 1982 paper, "Referential Consistency as a Criterion of Meaning", has been substantively revised and several important corrections made. It is recommended that readers read (...)
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  35. Para-quantitative Methodology: Reclaiming experimentalism in educational research.Bakhtiar Shabani Varaki - 2015 - Open Review of Educational Research 1 (2):26-41.
    This article focuses on the criticisms of current approaches in educational research methodology. Itsummarizes rationales for mixed methods and argues that the mixing quantitative paradigm andqualitative paradigm is problematic due to practical and philosophical arguments. It is alsoindicated that the current rise of mixed methods work has increased problems with quantitativeand qualitative methods. In this article we offer a different symbolic system, with differentlogical form for describing educational phenomena based on the philosophical assumptions andnew mathematical reasoning: para-quantitativism. Para-quantitative (...)
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  36. Ideal rationality and logical omniscience.Declan Smithies - 2015 - Synthese 192 (9):2769-2793.
    Does rationality require logical omniscience? Our best formal theories of rationality imply that it does, but our ordinary evaluations of rationality seem to suggest otherwise. This paper aims to resolve the tension by arguing that our ordinary evaluations of rationality are not only consistent with the thesis that rationality requires logical omniscience, but also provide a compelling rationale for accepting this thesis in the first place. This paper also defends an account of apriori justification for logical beliefs that is (...)
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  37. Logic, Ethics and the Ethics of Logic.Catherine Legg - 2014 - In T. Thellefsen B. Sorensen (ed.), Charles Sanders Peirce in His Own Words. pp. 271-278.
    This piece explores the meaning of the following quote from Charles Peirce (1902), ". . . the main reason logic is unsettled is that thirteen different opinions are current as to the true aim of the science. Now this is not a logical difficulty, but an ethical difficulty; for ethics is the science of aims. Secondly, it is true that ethics has been, and always must be, a theatre of discussion for the reason that its study consists in the (...)
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  38. First-order swap structures semantics for some Logics of Formal Inconsistency.Marcelo E. Coniglio, Aldo Figallo-Orellano & Ana Claudia Golzio - 2020 - Journal of Logic and Computation 30 (6):1257-1290.
    The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of QmbC, (...)
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  39. Book review: Carnielli, W., Coniglio, M. paraconsistent logic: Consistency, contradiction and negation. Logic, epistemology, and the unity of science series. [REVIEW]Henrique Antunes & Vincenzo Ciccarelli - 2018 - Manuscrito 41 (2):111-122.
    Review of the book "Paraconsistent Logic: Consistency, Contradiction, and Negation by Water Carnielli and Marcelo Coniglio.
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  40. Stoic Logic.Susanne Bobzien - 2003 - In Brad Inwood (ed.), The Cambridge Companion to Stoic Philosophy. Cambridge University Press.
    ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic principles of (...)
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  41. Logic and the Structure of the Web of Belief.Matthew Carlson - 2015 - Journal for the History of Analytical Philosophy 3 (5).
    In this paper, I examine Quine's views on the epistemology of logic. According to Quine's influential holistic account, logic is central in the “web of belief” that comprises our overall theory of the world. Because of this, revisions to logic would have devastating systematic consequences, and this explains why we are loath to make such revisions. In section1, I clarify this idea and thereby show that Quine actually takes the web of belief to have asymmetrical internal structure. (...)
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  42. Logics for modelling collective attitudes.Daniele Porello - 2018 - Fundamenta Informaticae 158 (1-3):239-27.
    We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal (...)
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  43. Two Adaptive Logics of Norm-Propositions.Mathieu Beirlaen & Christian Straßer - 2013 - Journal of Applied Logic 11 (2):147-168.
    We present two defeasible logics of norm-propositions (statements about norms) that (i) consistently allow for the possibility of normative gaps and normative conflicts, and (ii) map each premise set to a sufficiently rich consequence set. In order to meet (i), we define the logic LNP, a conflict- and gap-tolerant logic of norm-propositions capable of formalizing both normative conflicts and normative gaps within the object language. Next, we strengthen LNP within the adaptive logic framework for non-monotonic reasoning in (...)
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  44. Evitable iterates of the consistency operator.James Walsh - 2023 - Computability 12 (1):59--69.
    Why are natural theories pre-well-ordered by consistency strength? In previous work, an approach to this question was proposed. This approach was inspired by Martin's Conjecture, one of the most prominent conjectures in recursion theory. Fixing a reasonable subsystem $T$ of arithmetic, the goal was to classify the recursive functions that are monotone with respect to the Lindenbaum algebra of $T$. According to an optimistic conjecture, roughly, every such function must be equivalent to an iterate $\mathsf{Con}_T^\alpha$ of the consistency operator ``in (...)
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  45. The logic of viewpoints.Antti Hautamäki - 1983 - Studia Logica 42 (2-3):187 - 196.
    In this paper a propositional logic of viewpoints is presented. The language of this logic consists of the usual modal operatorsL (of necessity) andM (of possibility) as well as of two new operatorsA andR. The intuitive interpretations ofA andR are from all viewpoints and from some viewpoint, respectively. Semantically the language is interpreted by using Kripke models augmented with sets of viewpoints and with a new alternativeness relation for the operatorA. Truth values of formulas are evaluated with respect (...)
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  46. The Logic of Hyperlogic. Part A: Foundations.Alexander W. Kocurek - 2024 - Review of Symbolic Logic 17 (1):244-271.
    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 (...)
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  47. The logic of systems of granular partitions.Thomas Bittner, Barry Smith & Maureen Donnelly - 2005 - IFOMIS Reports.
    The theory of granular partitions is designed to capture in a formal framework important aspects of the selective character of common-sense views of reality. It comprehends not merely the ways in which we can view reality by conceiving its objects as gathered together not merely into sets, but also into wholes of various kinds, partitioned into parts at various levels of granularity. We here represent granular partitions as triples consisting of a rooted tree structure as first component, a domain satisfying (...)
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  48. Symbolic Logic Study Guide (a textbook).Xinli Wang - 2009 - University Readers.
    The Symbolic Logic Study Guide is designed to accompany the widely used symbolic logic textbook Language, Proof and Logic (LPL), by Jon Barwise and John Etchemendy (CSLI Publications 2003). The guide has two parts. The first part contains condensed, essential lecture notes, which streamline and systematize the first fourteen chapters of the book into seven teaching sections, and thus provide a clear, well-designed roadmap for the understanding of the text. The second part consists of twelve sample quizzes (...)
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  49. Inductive Logic.Franz Huber - 2008 - In J. Lachs R. Talisse (ed.), Encyclopedia of American Philosophy. Routledge.
    Logic is the study of the quality of arguments. An argument consists of a set of premises and a conclusion. The quality of an argument depends on at least two factors: the truth of the premises, and the strength with which the premises confirm the conclusion. The truth of the premises is a contingent factor that depends on the state of the world. The strength with which the premises confirm the conclusion is supposed to be independent of the state (...)
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  50. How to prove the consistency of arithmetic.Jaakko Hintikka & Besim Karakadilar - 2006 - Acta Philosophica Fennica 78:1.
    It is argued that the goal of Hilbert's program was to prove the model-theoretical consistency of different axiom systems. This Hilbert proposed to do by proving the deductive consistency of the relevant systems. In the extended independence-friendly logic there is a complete proof method for the contradictory negations of independence-friendly sentences, so the existence of a single proposition that is not disprovable from arithmetic axioms can be shown formally in the extended independence-friendly logic. It can also be proved (...)
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