40 found
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  1.  3
    Truth and Falsehood: An Inquiry Into Generalized Logical Values.Yaroslav Shramko & Heinrich Wansing - 2011 - Dordrecht, Netherland: Springer.
    The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...)
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  2. Some Useful 16-Valued Logics: How a Computer Network Should Think.Yaroslav Shramko & Heinrich Wansing - 2005 - Journal of Philosophical Logic 34 (2):121-153.
    In Belnap's useful 4-valued logic, the set 2 = {T, F} of classical truth values is generalized to the set 4 = í ”íČ«(2) = {Ø, {T}, {F}, {T, F}}. In the present paper, we argue in favor of extending this process to the set 16 = ᔍ (4) (and beyond). It turns out that this generalization is well-motivated and leads from the bilattice FOUR₂ with an information and a truth-and-falsity ordering to another algebraic structure, namely the trilattice SIXTEEN₃ with an (...)
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  3.  78
    Dual Intuitionistic Logic and a Variety of Negations: The Logic of Scientific Research.Yaroslav Shramko - 2005 - Studia Logica 80 (2-3):347-367.
    We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic. This logic can be labeled as “falsification logic”: it embodies the Popperian methodology of scientific discovery. Whereas intuitionistic logic deals with constructive truth and non-constructive falsity, and Nelson's logic takes both truth and falsity as constructive notions, in the falsification logic truth is essentially non-constructive as opposed to falsity that is conceived constructively. We also briefly clarify the relationships of our falsification logic to (...)
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  4.  82
    Suszko’s Thesis, Inferential Many-Valuedness, and the Notion of a Logical System.Heinrich Wansing & Yaroslav Shramko - 2008 - Studia Logica 88 (3):405-429.
    According to Suszko's Thesis, there are but two logical values, true and false. In this paper, R. Suszko's, G. Malinowski's, and M. Tsuji's analyses of logical two-valuedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation.
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  5.  76
    Hyper-Contradictions, Generalized Truth Values and Logics of Truth and Falsehood.Yaroslav Shramko & Heinrich Wansing - 2006 - Journal of Logic, Language and Information 15 (4):403-424.
    In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of “revenge Liar” arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets of (...)
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  6.  7
    The Fmla-Fmla Axiomatizations of the Exactly True and Non-falsity Logics and Some of Their Cousins.Yaroslav Shramko, Dmitry Zaitsev & Alexander Belikov - 2019 - Journal of Philosophical Logic 48 (5):787-808.
    In this paper we present a solution of the axiomatization problem for the Fmla-Fmla versions of the Pietz and Rivieccio exactly true logic and the non-falsity logic dual to it. To prove the completeness of the corresponding binary consequence systems we introduce a specific proof-theoretic formalism, which allows us to deal simultaneously with two consequence relations within one logical system. These relations are hierarchically organized, so that one of them is treated as the basic for the resulting logic, and the (...)
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  7. The Trilaticce of Constructive Truth Values.Yaroslav Shramko, J. Michael Dunn & Tatsutoshi Takenaka - 2001 - Journal of Logic and Computation 11 (1):761--788.
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  8.  3
    The Fmla-Fmla Axiomatizations of the Exactly True and Non-falsity Logics and Some of Their Cousins.Yaroslav Shramko, Dmitry Zaitsev & Alexander Belikov - 2019 - Journal of Philosophical Logic 48 (5):787-808.
    In this paper we present a solution of the axiomatization problem for the Fmla-Fmla versions of the Pietz and Rivieccio exactly true logic and the non-falsity logic dual to it. To prove the completeness of the corresponding binary consequence systems we introduce a specific proof-theoretic formalism, which allows us to deal simultaneously with two consequence relations within one logical system. These relations are hierarchically organized, so that one of them is treated as the basic for the resulting logic, and the (...)
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  9.  17
    First-Degree Entailment and its Relatives.Yaroslav Shramko, Dmitry Zaitsev & Alexander Belikov - 2017 - Studia Logica 105 (6):1291-1317.
    We consider a family of logical systems for representing entailment relations of various kinds. This family has its root in the logic of first-degree entailment formulated as a binary consequence system, i.e. a proof system dealing with the expressions of the form \, where both \ and \ are single formulas. We generalize this approach by constructing consequence systems that allow manipulating with sets of formulas, either to the right or left of the turnstile. In this way, it is possible (...)
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  10.  16
    Modal Multilattice Logic.Norihiro Kamide & Yaroslav Shramko - 2017 - Logica Universalis 11 (3):317-343.
    A modal extension of multilattice logic, called modal multilattice logic, is introduced as a Gentzen-type sequent calculus \. Theorems for embedding \ into a Gentzen-type sequent calculus S4C and vice versa are proved. The cut-elimination theorem for \ is shown. A Kripke semantics for \ is introduced, and the completeness theorem with respect to this semantics is proved. Moreover, the duality principle is proved as a characteristic property of \.
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  11.  49
    Truth Values.Yaroslav Shramko - 2010 - Stanford Encyclopedia of Philosophy.
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  12.  33
    A Modal Translation for Dual-Intuitionistic Logic.Yaroslav Shramko - 2016 - Review of Symbolic Logic 9 (2):251-265.
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  13.  24
    Kripke Completeness of Bi-Intuitionistic Multilattice Logic and its Connexive Variant.Norihiro Kamide, Yaroslav Shramko & Heinrich Wansing - 2017 - Studia Logica 105 (6):1193-1219.
    In this paper, bi-intuitionistic multilattice logic, which is a combination of multilattice logic and the bi-intuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzen-type sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into bi-intuitionistic logic. The logic proposed is an extension of first-degree entailment logic and can be regarded as a bi-intuitionistic variant of the original classical multilattice logic (...)
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  14. The Slingshot Argument and Sentential Identity.Yaroslav Shramko & Heinrich Wansing - 2009 - Studia Logica 91 (3):429-455.
    The famous “slingshot argument” developed by Church, Gödel, Quine and Davidson is often considered to be a formally strict proof of the Fregean conception that all true sentences, as well as all false ones, have one and the same denotation, namely their corresponding truth value: the true or the false . In this paper we examine the analysis of the slingshot argument by means of a non-Fregean logic undertaken recently by A.WĂłitowicz and put to the test her claim that the (...)
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  15.  35
    Bi-Facial Truth: A Case for Generalized Truth Values.Dmitry Zaitsev & Yaroslav Shramko - 2013 - Studia Logica 101 (6):1299-1318.
    We explore a possibility of generalization of classical truth values by distinguishing between their ontological and epistemic aspects and combining these aspects within a joint semantical framework. The outcome is four generalized classical truth values implemented by Cartesian product of two sets of classical truth values, where each generalized value comprises both ontological and epistemic components. This allows one to define two unary twin connectives that can be called “semi-classical negations”. Each of these negations deals only with one of the (...)
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  16.  24
    The Nature of Scientific Philosophy.Yaroslav Shramko - forthcoming - Logic and Logical Philosophy:1.
    The goal of this paper is to explain the nature of philosophy as a distinct science with its own subject-matter. This is achieved through a comparative analysis of mathematical and philosophical knowledge that reveals a profound similarity between mathematics and philosophy as mutually complementary sciences exploring the field of abstract entities that can be comprehended only by purely a priori theoretical inquiry. By considering this complementarity, a general definition of philosophy can be obtained by dualizing the traditional Aristotelian definition of (...)
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  17.  44
    The Logical Way of Being True: Truth Values and the Ontological Foundation of Logic.Yaroslav Shramko - 2014 - Logic and Logical Philosophy 23 (2):119-131.
    In this paper I reject the normative interpretation of logic and give reasons for a realistic account based on the ontological treatment of logical values.
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  18. What is a Genuine Intuitionistic Notion of Falsity?Yaroslav Shramko - 2012 - Logic and Logical Philosophy 21 (1):3-23.
    I highlight the importance of the notion of falsity for a semantical consideration of intuitionistic logic. One can find two principal (and non-equivalent) versions of such a notion in the literature, namely, falsity as non-truth and falsity as truth of a negative proposition. I argue in favor of the first version as the genuine intuitionistic notion of falsity.
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  19.  7
    Truth Values. Part I.Yaroslav Shramko & Heinrich Wansing - 2009 - Studia Logica 91 (3):429-455.
    The famous “slingshot argument” developed by Church, Gödel, Quine and Davidson is often considered to be a formally strict proof of the Fregean conception that all true sentences, as well as all false ones, have one and the same denotation, namely their corresponding truth value: the true or the false. In this paper we examine the analysis of the slingshot argument by means of a non-Fregean logic undertaken recently by A.WĂłitowicz and put to the test her claim that the slingshot (...)
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  20.  17
    Entailment Relations and/as Truth Values.Yaroslav Shramko & Heinrich Wansing - 2007 - Bulletin of the Section of Logic 36 (3/4):131-143.
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  21.  37
    Editorial Introduction. Truth Values: Part II. [REVIEW]Yaroslav Shramko & Heinrich Wansing - 2009 - Studia Logica 92 (2):143-146.
  22. A Philosophically Plausible Modified Grzegorczyk Semantics for First-Degree Intuitionistic Entailment.Yaroslav Shramko - 1998 - Logique Et Analyse 161:162-163.
  23.  6
    Between Hilbert and Gentzen: four-valued consequence systems and structural reasoning.Yaroslav Shramko - forthcoming - Archive for Mathematical Logic:1-25.
    Structural reasoning is simply reasoning that is governed exclusively by structural rules. In this context a proof system can be said to be structural if all of its inference rules are structural. A logic is considered to be structuralizable if it can be equipped with a sound and complete structural proof system. This paper provides a general formulation of the problem of structuralizability of a given logic, giving specific consideration to a family of logics that are based on the Dunn–Belnap (...)
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  24.  8
    Hilbert-Style Axiomatization of First-Degree Entailment and a Family of its Extensions.Yaroslav Shramko - 2021 - Annals of Pure and Applied Logic 172 (9):103011.
  25. A Theory of Relevant Properties 1: Reflections and Definitions.Yaroslav Shramko - 1999 - Theoria 14 (1):63-81.
    In the paper a theory of relevant properties is developed. The theory permits us to distinguish between properties that are relevant to an object and the properties that are irrelevant to it. Predication is meaningful only if a property is relevant to an object. On the base of introducing a special negative type of predication as opposed to usual sentential negation, a new notion of generalization for properties is defined. Context-free, as weIl as context-depended relevance of properties are considered.
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  26.  36
    Editorial Introduction. Truth Values: Part I. [REVIEW]Yaroslav Shramko & Heinrich Wansing - 2009 - Studia Logica 91 (3):295-304.
  27.  35
    Presentation.Olga Korpalo, Valentin Omelyantchik & Yaroslav Shramko - 1999 - Theoria: Revista de TeorĂ­a, Historia y Fundamentos de la Ciencia 14 (1):5-9.
    The paper discusses interpretations of Aristotle’s modal notions by modern commentators. It is shown that the semantics of modal notions which the above mentioned authors attribute to Aristotle is based on the algebraic idea of multiplier.
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  28.  28
    A Theory of Relevant Properties 1: Reflections and Definitions.Yaroslav Shramko - 1999 - Theoria: Revista de TeorĂ­a, Historia y Fundamentos de la Ciencia 14 (1):63-81.
    In the paper a theory of relevant properties is developed. The theory permits us to distinguish between properties that are relevant to an object and the properties that are irrelevant to it. Predication is meaningful only if a property is relevant to an object. On the base of introducing a special negative type of predication as opposed to usual sentential negation, a new notion of generalization for properties is defined. Context-free, as weIl as context-depended relevance of properties are considered.
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  29.  47
    Tautologien und TrivialitĂ€ten? Logische Methoden in der Philosophie.Fabian Neuhaus, Uwe Scheffler & Yaroslav Shramko - 2003 - Zeitschrift fĂŒr Philosophische Forschung 57 (3):412 - 430.
    Logiker wĂŒrden doch nur Tautologien und TrivialitĂ€ten produzieren. Mit dieser Kritik werden Logiker an philosophischen Instituten oft konfrontiert. Es wird ebenfalls eingewendet, daß mathematische Methoden in der Philosophie unangemessen seien, daß man durch die Verwendung dieser Methoden auf eine bestimmte philosophische Position festgelegt sei und daß der philosophische Gewinn den mit einem logischen Apparat verbundenen Aufwand nicht rechtfertige. In der Arbeit wird dargelegt, inwieweit diese vier VorwĂŒrfe berechtigt sind und inwieweit sie auf Mißver- stĂ€ndnissen beruhen. Dazu werden folgende Fragen beantwortet: (...)
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  30.  8
    Correction To: The Nature of Entailment: An Informational Approach.Yaroslav Shramko & Heinrich Wansing - 2020 - Synthese 198 (S22):5263-5264.
    The paragraph starting with “By accepting condition only,...” should be read as follows.
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  31.  2
    The Nature of Entailment: An Informational Approach.Yaroslav Shramko & Heinrich Wansing - 2019 - Synthese 198 (S22):5241-5261.
    In this paper we elaborate a conception of entailment based on what we call the Ackermann principle, which explicates valid entailment through a logical connection between sentences depending on their informational content. We reconstruct Dunn’s informational semantics for entailment on the basis of Restall’s approach, with assertion and denial as two independent speech acts, by introducing the notion of a ‘position description’. We show how the machinery of position descriptions can effectively be used to define the positive and the negative (...)
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  32.  31
    From the Editors.Heinrich Wansing, Sergei Odintsov & Yaroslav Shramko - 2005 - Studia Logica 80 (2-3):153-157.
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  33.  12
    Review of Walter P. Van Stigt: Brouwer's Intuitionism. [REVIEW]Yaroslav Shramko - 1996 - Journal of Applied Non-Classical Logics 6 (3):292-295.
  34.  7
    Norihiro Kamide and Heinrich Wansing, Proof Theory of N4-Related Paraconsistent Logics. Studies in Logic Vol. 54. College Publications, 2015, Pp. 414. ISBN-13: 978-1848901674 (Paperback) $20.50. [REVIEW]Yaroslav Shramko - 2017 - Studia Logica 105 (3):665-668.
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  35.  9
    Is Time Reversible?Yaroslav Shramko - 2015 - Logic and Logical Philosophy 24 (2).
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  36.  4
    Analytical Philosophy and Epistemology in Ukraine: Presentation.ValentĂ­n Omelyantchik, Yaroslav Shramko & Olga Korpalo - 1999 - Theoria: Revista de TeorĂ­a, Historia y Fundamentos de la Ciencia 14 (1):5-9.
    The paper discusses interpretations of Aristotle’s modal notions by modern commentators. It is shown that the semantics of modal notions which the above mentioned authors attribute to Aristotle is based on the algebraic idea of multiplier.
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  37.  16
    Relevant Properties.Yaroslav Shramko - 1994 - Logic and Logical Philosophy 2 (5):103-115.
    I would like to start my paper with the following statement of Barry Smith: “Relevance logic has become ontologically fertile.”.
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  38.  18
    The Logical Ontology of Negative Facts: On What is Not.Uwe Scheffler & Yaroslav Shramko - 2000 - In Jan Faye, Uwe Scheffler & Max Urchs (eds.), Things, Facts and Events. Rodopi. pp. 76--109.
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  39.  3
    Relevant Variants of Intuitionistic Logic.Yaroslav Shramko - 1994 - Logic Journal of the IGPL 2 (1):47-53.
  40.  1
    Truth Values. Part II.Yaroslav Shramko & Heinrich Wansing - 2009 - Studia Logica 92 (2).