Results for 'Tarski Undefinability'

180 found
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  1.  73
    Tarski Undefinability Theorem Succinctly Refuted.Pete Olcott - manuscript
    If the conclusion of the Tarski Undefinability Theorem was that some artificially constrained limited notions of a formal system necessarily have undecidable sentences, then Tarski made no mistake within his assumptions. When we expand the scope of his investigation to other notions of formal systems we reach an entirely different conclusion showing that Tarski's assumptions were wrong.
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  2.  63
    Tarski Undefinability Theorem Terse Refutation.P. Olcott - manuscript
    Both Tarski and Gödel “prove” that provability can diverge from Truth. When we boil their claim down to its simplest possible essence it is really claiming that valid inference from true premises might not always derive a true consequence. This is obviously impossible.
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  3.  54
    The Prolog Inference Model Refutes Tarski Undefinability.Pete Olcott - manuscript
    The generalized conclusion of the Tarski and Gödel proofs: All formal systems of greater expressive power than arithmetic necessarily have undecidable sentences. Is not the immutable truth that Tarski made it out to be it is only based on his starting assumptions. -/- When we reexamine these starting assumptions from the perspective of the philosophy of logic we find that there are alternative ways that formal systems can be defined that make undecidability inexpressible in all of these formal (...)
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  4. How Tarski Defined the Undefinable.Cezary Cieśliński - 2015 - European Review 23 (01):139 - 149.
    This paper describes Tarski’s project of rehabilitating the notion of truth, previously considered dubious by many philosophers. The project was realized by providing a formal truth definition, which does not employ any problematic concept.
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  5.  60
    Refuting Tarski and Gödel with a Sound Deductive Formalism.P. Olcott - manuscript
    The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic value of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide the valid deductive inference. Sound deductive conclusions are the result of these finite string transformation rules.
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  6. Tarski’s Convention T: Condition Beta.John Corcoran - forthcoming - South American Journal of Logic 1 (1).
    Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part (...)
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  7. Refuting Incompleteness and Undefinability.Pete Olcott - manuscript
    Within the (Haskell Curry) notion of a formal system we complete Tarski's formal correctness: ∀x True(x) ↔ ⊢ x and use this finally formalized notion of Truth to refute his own Undefinability Theorem (based on the Liar Paradox), the Liar Paradox, and the (Panu Raatikainen) essence of the conclusion of the 1931 Incompleteness Theorem.
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  8. The Inexpressibility of Validity.Julien Murzi - 2014 - Analysis 74 (1):65-81.
    Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth; and that no such theory, if sound, can even express truth. In this note, I prove corresponding limitative results for validity. While Peano Arithmetic already has the resources to define a predicate expressing logical validity, as Jeff Ketland has recently pointed out (2012, Validity as a primitive. Analysis 72: 421-30), (...)
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  9. Deductively Sound Formal Proofs.P. Olcott - manuscript
    Could the intersection of [formal proofs of mathematical logic] and [sound deductive inference] specify formal systems having [deductively sound formal proofs of mathematical logic]? All that we have to do to provide [deductively sound formal proofs of mathematical logic] is select the subset of conventional [formal proofs of mathematical logic] having true premises and now we have [deductively sound formal proofs of mathematical logic].
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  10. Eliminating Undecidability and Incompleteness in Formal Systems.Pete Olcott - manuscript
    To eliminate incompleteness, undecidability and inconsistency from formal systems we only need to convert the formal proofs to theorem consequences of symbolic logic to conform to the sound deductive inference model. -/- Within the sound deductive inference model there is a (connected sequence of valid deductions from true premises to a true conclusion) thus unlike the formal proofs of symbolic logic provability cannot diverge from truth.
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  11. Proof That Wittgenstein is Correct About Gödel.P. Olcott - manuscript
    The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic property of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide valid the deductive inference. Conclusions of sound arguments are derived from truth preserving finite string transformations applied to true premises.
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  12.  82
    Defining Gödel Incompleteness Away.P. Olcott - manuscript
    We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of self-contradictory expressions in a formal system as proof that this formal system is incomplete because self-contradictory expressions are neither provable nor disprovable in this formal system. Since self-contradictory expressions are neither provable nor disprovable (...)
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  13. The Concept of Truth in a Finite Universe.Panu Raatikainen - 2000 - Journal of Philosophical Logic 29 (6):617-633.
    The prospects and limitations of defining truth in a finite model in the same language whose truth one is considering are thoroughly examined. It is shown that in contradistinction to Tarski's undefinability theorem for arithmetic, it is in a definite sense possible in this case to define truth in the very language whose truth is in question.
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  14. The Eternal Unprovability Filter – Part I.Kiran Pai - 2016 - Dissertation, Thinkstrike
    I prove both the mathematical conjectures P ≠ NP and the Continuum Hypothesis are eternally unprovable using the same fundamental idea. Starting with the Saunders Maclane idea that a proof is eternal or it is not a proof, I use the indeterminacy of human biological capabilities in the eternal future to show that since both conjectures are independent of Axioms and have definitions connected with human biological capabilities, it would be impossible to prove them eternally without the creation and widespread (...)
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  15. Tarski and Primitivism About Truth.Jamin Asay - 2013 - Philosophers' Imprint 13:1-18.
    Tarski’s pioneering work on truth has been thought by some to motivate a robust, correspondence-style theory of truth, and by others to motivate a deflationary attitude toward truth. I argue that Tarski’s work suggests neither; if it motivates any contemporary theory of truth, it motivates conceptual primitivism, the view that truth is a fundamental, indefinable concept. After outlining conceptual primitivism and Tarski’s theory of truth, I show how the two approaches to truth share much in common. While (...)
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  16. Tarski.Benedict Eastaugh - 2017 - In Alex Malpass & Marianna Antonutti Marfori (eds.), The History of Philosophical and Formal Logic: From Aristotle to Tarski. London: Bloomsbury. pp. 293-313.
    Alfred Tarski was one of the greatest logicians of the twentieth century. His influence comes not merely through his own work but from the legion of students who pursued his projects, both in Poland and Berkeley. This chapter focuses on three key areas of Tarski's research, beginning with his groundbreaking studies of the concept of truth. Tarski's work led to the creation of the area of mathematical logic known as model theory and prefigured semantic approaches in the (...)
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  17. Was Tarski's Theory of Truth Motivated by Physicalism?Greg Frost-Arnold - 2004 - History and Philosophy of Logic 25 (4):265-280.
    Many commentators on Alfred Tarski have, following Hartry Field, claimed that Tarski's truth-definition was motivated by physicalism—the doctrine that all facts, including semantic facts, must be reducible to physical facts. I claim, instead, that Tarski did not aim to reduce semantic facts to physical ones. Thus, Field's criticism that Tarski's truth-definition fails to fulfill physicalist ambitions does not reveal Tarski to be inconsistent, since Tarski's goal is not to vindicate physicalism. I argue that (...)'s only published remarks that speak approvingly of physicalism were written in unusual circumstances: Tarski was likely attempting to appease an audience of physicalists that he viewed as hostile to his ideas. In later sections I develop positive accounts of: (1) Tarski's reduction of semantic concepts; (2) Tarski's motivation to develop formal semantics in the particular way he does; and (3) the role physicalism plays in Tarski's thought. (shrink)
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  18. Ordinary Truth in Tarski and Næss.Joseph Ulatowski - 2016 - In Adrian Kuzniar & Joanna Odrowąż-Sypniewska (eds.), Uncovering Facts and Values. Brill. pp. 67-90.
    Alfred Tarski seems to endorse a partial conception of truth, the T-schema, which he believes might be clarified by the application of empirical methods, specifically citing the experimental results of Arne Næss (1938a). The aim of this paper is to argue that Næss’ empirical work confirmed Tarski’s semantic conception of truth, among others. In the first part, I lay out the case for believing that Tarski’s T-schema, while not the formal and generalizable Convention-T, provides a partial account (...)
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  19. What Are Logical Notions?John Corcoran & Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
    In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.
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  20. Tarski's Nominalism.Greg Frost-Arnold - 2008 - In Douglas Patterson (ed.), New Essays on Tarski and Philosophy. Oxford University Press.
    Alfred Tarski was a nominalist. But he published almost nothing on his nominalist views, and until recently the only sources scholars had for studying Tarski’s nominalism were conversational reports from his friends and colleagues. However, a recently-discovered archival resource provides the most detailed information yet about Tarski’s nominalism. Tarski spent the academic year 1940-41 at Harvard, along with many of the leading lights of scientific philosophy: Carnap, Quine, Hempel, Goodman, and (for the fall semester) Russell. This (...)
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  21. More on Putnam and Tarski.Panu Raatikainen - 2003 - Synthese 135 (1):37 - 47.
    Hilary Putnam's famous arguments criticizing Tarski's theory of truth are evaluated. It is argued that they do not succeed to undermine Tarski's approach. One of the arguments is based on the problematic idea of a false instance of T-schema. The other ignores various issues essential for Tarski's setting such as language-relativity of truth definition.
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  22. Truth, Correspondence, Models, and Tarski.Panu Raatikainen - 2007 - In Approaching Truth: Essays in Honour of Ilkka Niiniluoto. London: College Press. pp. 99-112.
    In the early 20th century, scepticism was common among philosophers about the very meaningfulness of the notion of truth – and of the related notions of denotation, definition etc. (i.e., what Tarski called semantical concepts). Awareness was growing of the various logical paradoxes and anomalies arising from these concepts. In addition, more philosophical reasons were being given for this aversion.1 The atmosphere changed dramatically with Alfred Tarski’s path-breaking contribution. What Tarski did was to show that, assuming that (...)
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  23. REVIEW OF Alfred Tarski, Collected Papers, Vols. 1-4 (1986) Edited by Steven Givant and Ralph McKenzie. [REVIEW]John Corcoran - 1991 - MATHEMATICAL REVIEWS 91 (h):01101-4.
    Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but most of the Aristotelian corpus is not about (...)
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  24. The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper.John Corcoran & José Miguel Sagüillo - 2011 - History and Philosophy of Logic 32 (4):359 - 374.
    This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes (...)
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  25. The Development of Mathematical Logic From Russell to Tarski, 1900-1935.Paolo Mancosu, Richard Zach & Calixto Badesa - 2009 - In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press.
    The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...)
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  26.  13
    Alfred Tarski - człowiek, który zdefiniował prawdę.Urszula Wybraniec-Skardowska - 2007 - Ruch Filozoficzny 4 (4).
    This article is a characteristic of Alfred Tarski's profile, seen from a personal perspective after a long visit to Berkeley, at the invitation of Jan Tarski, in the house where Alfred Tarski lived. It takes into account the scientific achievements and research results of Tarski, as well as certain impressions of the author of these memories concerning the exotic life of this great Polish logician and mathematician of the 20th century.
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  27.  98
    Alfred Tarski - the Man Who Defined Truth.Urszula Wybraniec-Skardowska - 2008 - Filozofia, Scientific Works of Jan Długosz Academy, Częstochowa:67-71.
    This article is a translation of the paper in Polish (Alfred Tarski - człowiek, który zdefiniował prawdę) published in Ruch Filozoficzny 4 (4) (2007). It is a personal Alfred Tarski memories based on my stay in Berkeley and visit the Alfred Tarski house for the invitation of Janusz Tarski.
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  28. Book Reviews: Anita Burdman Feferman and Solomon Feferman, "Alfred Tarski: Life and Logic", Cambridge University Press, Cambridge.Walter Carnielli - 2006 - Logic and Logical Philosophy 15 (1):91-96.
    Anita Burdman Feferman and Solomon Feferman, "Alfred Tarski: Life and Logic", Cambridge University Press, Cambridge, UK, 2004, pp. 432.
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  29. Process Tracing: Defining the Undefinable.Christopher Clarke - forthcoming - In The Oxford Handbook of Philosophy of Political Science.
    A good definition of process tracing should highlight what is distinctive about process tracing as a methodology of causal inference. I look at eight criteria that are used to define process tracing in the methodological literature, and I dismiss all eight criteria as unhelpful (some because they are too restrictive, and others because they are vacuous). In place of these criteria, I propose four alternative criteria, and I draw a distinction between process tracing for the ultimate aim of testing a (...)
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  30. Nihilism and Tarski's truth definition: an interests incompatibility.Maurilio Lovatti - 1998 - Per la Filosofia (43):46-56.
    In this paper the importance of Tarski's truth definition is evaluated like a productive resource to criticize Nietzsche's nihilistic view and any pragmatic understanding of truth.
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  31. Brentano's Criticism of the Correspondence Conception of Truth and Tarski's Semantic Theory.Jan Woleński - 1989 - Topoi 8 (2):105-110.
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  32. Lies, Half-Truths, and Falsehoods About Tarski’s 1933 “Liar” Antinomies.John Corcoran & Joaquin Miller - 2012 - Bulletin of Symbolic Logic 18 (1):140-141.
    We discuss misinformation about “the liar antinomy” with special reference to Tarski’s 1933 truth-definition paper [1]. Lies are speech-acts, not merely sentences or propositions. Roughly, lies are statements of propositions not believed by their speakers. Speakers who state their false beliefs are often not lying. And speakers who state true propositions that they don’t believe are often lying—regardless of whether the non-belief is disbelief. Persons who state propositions on which they have no opinion are lying as much as those (...)
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  33.  27
    Normalisation and Subformula Property for a System of Classical Logic with Tarski’s Rule.Nils Kürbis - forthcoming - Archive for Mathematical Logic:1-25.
    This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system, and gives reduction procedures for them. It is then shown that deductions in the system convert into normal form, i.e. deductions that contain neither maximal formulas nor maximal segments, and that deductions in normal form satisfy the subformula property. Tarski’s Rule is treated as a general introduction rule for (...)
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  34. Elementare ma complessa: la prospettiva della complessità computazionale attraverso il caso studio della geometria di Tarski.Pierluigi Graziani - 2012 - In Vincenzo Fano, Enrico Giannetto, Giulia Giannini & Pierluigi Graziani (eds.), Complessità e Riduzionismo. © ISONOMIA – Epistemologica, University of Urbino. pp. 66-81.
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  35. Il Concetto di Verità' di Tarski.Carlotta Pavese - 2020 - In Guido Bonino, Carlo Gabbani & Paolo Tripodi (eds.), Biblioteca Analitica. pp. 91-102.
    In questo capitolo racconto l'articolo classico sulla verità' di Tarski.
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  36. CORCORAN REVIEWS THE 4 VOLUMES OF TARSKI's COLLECTED PAPERS.John Corcoran - 1991 - MATHEMATICAL REVIEWS 91 (I):110-114.
    CORCORAN REVIEWS THE 4 VOLUMES OF TARSKI’S COLLECTED PAPERS Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in (...)
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  37. 2007. Notes on the Founding of Logics and Metalogic: Aristotle, Boole, and Tarski. Eds. C. Martínez Et Al. Current Topics in Logic and Analytic Philosophy / Temas Actuales de Lógica y Filosofía Analítica. Imprenta Univeridade Santiago de Compostela.John Corcoran - 2007 - In C. Martínez (ed.), Current Topics in Logic and Analytic Philosophy /. pp. 145-178.
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  38. La Forma della Verità. Logica e filosofia nell'opera di Alfred Tarski.Ciro De Florio - 2013 - Italy: Mimesis.
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  39. Logical Indefinites.Jack Woods - 2014 - Logique Et Analyse -- Special Issue Edited by Julien Murzi and Massimiliano Carrara 227: 277-307.
    I argue that we can and should extend Tarski's model-theoretic criterion of logicality to cover indefinite expressions like Hilbert's ɛ operator, Russell's indefinite description operator η, and abstraction operators like 'the number of'. I draw on this extension to discuss the logical status of both abstraction operators and abstraction principles.
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  40.  50
    Gómez-Torrente on Modality and Tarskian Logical Consequence.Manuel García-Carpintero - 2010 - Theoria : An International Journal for Theory, History and Fundations of Science 18 (2):159-170.
    Gómez-Torrente’s papers have made important contributions to vindicate Tarski’s model-theoretic account of the logical properties in the face of Etchemendy’s criticisms. However, at some points his vindication depends on interpreting the Tarskian account as purportedly modally deflationary, i.e., as not intended to capture the intuitive modal element in the logical properties, that logical consequence is (epistemic or alethic) necessary truth-preservation. Here it is argued that the views expressed in Tarski’s seminal work do not support this modally deflationary interpretation, (...)
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  41. Logicality and Invariance.Denis Bonnay - 2006 - Bulletin of Symbolic Logic 14 (1):29-68.
    What is a logical constant? The question is addressed in the tradition of Tarski's definition of logical operations as operations which are invariant under permutation. The paper introduces a general setting in which invariance criteria for logical operations can be compared and argues for invariance under potential isomorphism as the most natural characterization of logical operations.
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  42. Truth, Meaning, and Translation.Panu Raatikainen - 2008 - In Douglas Patterson (ed.), New essays on Tarski and philosophy. O.University Press. pp. 247.
    Philosopher’s judgements on the philosophical value of Tarski’s contributions to the theory of truth have varied. For example Karl Popper, Rudolf Carnap, and Donald Davidson have, in their different ways, celebrated Tarski’s achievements and have been enthusiastic about their philosophical relevance. Hilary Putnam, on the other hand, pronounces that “[a]s a philosophical account of truth, Tarski’s theory fails as badly as it is possible for an account to fail.” Putnam has several alleged reasons for his dissatisfaction,1 but (...)
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  43. The Antinomy of the Variable: A Tarskian Resolution.Bryan Pickel & Brian Rabern - 2016 - Journal of Philosophy 113 (3):137-170.
    Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables ‘x’ (...)
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  44. Truth, Proof and Gödelian Arguments: A Defence of Tarskian Truth in Mathematics.Markus Pantsar - 2009 - Dissertation, University of Helsinki
    One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to (...)
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  45. Swap Structures Semantics for Ivlev-Like Modal Logics.Marcelo E. Coniglio & Ana Claudia Golzio - 2019 - Soft Computing 23 (7):2243-2254.
    In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally a (...)
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  46. Conceptual Structure of Classical Logic.John Corcoran - 1972 - Philosophy and Phenomenological Research 33 (1):25-47.
    One innovation in this paper is its identification, analysis, and description of a troubling ambiguity in the word ‘argument’. In one sense ‘argument’ denotes a premise-conclusion argument: a two-part system composed of a set of sentences—the premises—and a single sentence—the conclusion. In another sense it denotes a premise-conclusion-mediation argument—later called an argumentation: a three-part system composed of a set of sentences—the premises—a single sentence—the conclusion—and complex of sentences—the mediation. The latter is often intended to show that the conclusion follows from (...)
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  47. Thinking dynamic fragments of the infinite.Fabio Scorza - 2014 - SOCRATES 2 (1):270-308.
    ABSTRACT: Compilation of eleven short essays that reflect authors view on various themes. Themes covered under this compilation are: • Right or wrong, good or bad, beautiful or ugly, these are all undefined and indefinable abstractions. • Communication: we're losing this ability; we are hiding behind a screen. • Ecology and environment: what can we do? • From kings to subjects: a society founded on the principle of dishonesty, arrogance and inequality. • Globalization and constraints, we must respect and protect (...)
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  48. Truth-Makers and Convention T.Jan Woleński - 2011 - Philosophical Papers Dedicated to Kevin Mulligan.
    This papers discuss the place, if any, of Convention T (the condition of material adequacy of the proper definition of truth formulated by Tarski) in the truth-makers account offered by Kevin Mulligan, Peter Simons and Barry Smith. It is argued that although Tarski’s requirement seems entirely acceptable in the frameworks of truth-makers theories for the first-sight, several doubts arise under a closer inspection. In particular, T-biconditionals have no clear meaning as sentences about truth-makers. Thus, truth-makers theory cannot be (...)
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  49. The History and Prehistory of Natural-Language Semantics.Daniel W. Harris - 2017 - In Sandra Lapointe & Christopher Pincock (eds.), Innovations in the History of Analytical Philosophy. Palgrave-MacMillan. pp. 149--194.
    Contemporary natural-language semantics began with the assumption that the meaning of a sentence could be modeled by a single truth condition, or by an entity with a truth-condition. But with the recent explosion of dynamic semantics and pragmatics and of work on non- truth-conditional dimensions of linguistic meaning, we are now in the midst of a shift away from a truth-condition-centric view and toward the idea that a sentence’s meaning must be spelled out in terms of its various roles in (...)
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  50. On the Mutual Definability of the Notions of Entailment, Rejection, and Inconsistency.Urszula Wybraniec-Skardowska - 2016 - Axioms 5 (15).
    In this paper, two axiomatic theories T− and T′ are constructed, which are dual to Tarski’s theory T+ (1930) of deductive systems based on classical propositional calculus. While in Tarski’s theory T+ the primitive notion is the classical consequence function (entailment) Cn+, in the dual theory T− it is replaced by the notion of Słupecki’s rejection consequence Cn− and in the dual theory T′ it is replaced by the notion of the family Incons of inconsistent sets. The author (...)
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