Search results for: Yaroslav Shramko

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The Fmla-Fmla Axiomatizations of the Exactly True and Non-falsity Logics and Some of Their Cousins

Yaroslav Shramko, Dmitry Zaitsev, Alexander Belikov

Journal of Philosophical Logic > 2019 > 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...

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Kripke Completeness of Bi-intuitionistic Multilattice Logic and its Connexive Variant

Norihiro Kamide, Yaroslav Shramko, Heinrich Wansing

Studia Logica > 2017 > 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...

article

First-Degree Entailment and its Relatives

Yaroslav Shramko, Dmitry Zaitsev, Alexander Belikov

Studia Logica > 2017 > 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 $$\varphi \vdash \psi $$ φ ⊢ ψ , where both $$\varphi $$ φ and $$\psi $$ ψ are single formulas. We generalize...

article

Modal Multilattice Logic

Norihiro Kamide, Yaroslav Shramko

Logica Universalis > 2017 > 11 > 3 > 317-343

A modal extension of multilattice logic, called modal multilattice logic, is introduced as a Gentzen-type sequent calculus $$\hbox {MML}_n$$ MML n . Theorems for embedding $$\hbox {MML}_n$$ MML n into a Gentzen-type sequent calculus S4C (an extended S4-modal logic) and vice versa are proved. The cut-elimination theorem for $$\hbox {MML}_n$$ MML n is shown. A Kripke...

article

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.

Yaroslav Shramko

Studia Logica > 2017 > 105 > 3 > 665-668

article

Принцип дуальності в логіці і філософії

Yaroslav Shramko

Філософська Думка > 2016 > 3 > 47-63

Сер Майкл Атія, визначний сучасний математик, лауреат медалі Філдса й Абелівської премії 1, в одній зі своїх недавніх статей схарактеризував дуальність як потужний евристичний принцип, що дозволяє розглянути один і той самий об’єкт із двох різних точок зору. У згаданій статті йдеться про застосування цього фундаментального принципу в математиці й фізиці і наведено численні приклади його надзвичайної...

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Логічна термінологія: проблема кодифікації

Vakhtang Kebuladze, Nadia Kazachenko, Anatolii Konverskyi, Anna Laktionova, more

Філософська Думка > 2016 > 3 > 6-33

Я дуже радий вітати у стінах Інституту філософії представників нашої логічної спільноти і всіх колег, хто братиме участь у сьогоднішній дискусії. Тема, яку ми маємо намір обговорити, є вкрай важливою. Кожен, хто здійснював дослідження в галузі логіки або викладав логіку в університетській аудиторії, знає, наскільки актуальним є питання розробки логічної термінології. Тут виникає багато супутніх проблем...

article

Is time reversible?

Yaroslav Shramko

Logic and Logical Philosophy > 2015 > 24 > 2 > 143–153

This paper presents an elementary logical proof of time irreversibility. To this effect, we construct a simple mathematical model of a process, which can demonstrably be shown to be irreversible in the sense that it cannot be reproduced in a backward direction by the very conditions of its construction. To model this process we employ a puzzle problem (paradox) referred to in the literature as “Austin’s...

article

The logical way of being true: Truth values and the ontological foundation of logic

Yaroslav Shramko

Logic and Logical Philosophy > 2014 > 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.

article

Bi-facial Truth: a Case for Generalized Truth Values

Dmitry Zaitsev, Yaroslav Shramko

Studia Logica > 2013 > 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...

article

What is a Genuine Intuitionistic Notion of Falsity?

Yaroslav Shramko

Logic and Logical Philosophy > 2012 > 21 > 1 > 3-23

I highlight the importance of the notion of falsity for a seman- tical 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.

article

Що таке аналітична філософія?

Yaroslav Shramko

Філософська Думка > 2011 > 3 > 10-27

The paper elucidates some characteristic features of analytic philosophy as a specific direction in modern philosophical thought. The initial point of the investigation is a definition of analytic philosophy given by Michael Dummett and its critical consideration in the literature of last two decades. Summing up, one can state that analytic philosophy in one way or another is bound to the following...

article

Editorial Introduction. Truth Values: Part II

Yaroslav Shramko, Heinrich Wansing

Studia Logica > 1-4

article

Editorial Introduction. Truth Values: Part I

Yaroslav Shramko, Heinrich Wansing

Studia Logica > 2009 > 91 > 3 > 295-304

article

The Slingshot Argument and Sentential Identity

Yaroslav Shramko, Heinrich Wansing

Studia Logica > 2009 > 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...

article

Editorial Introduction. Truth Values: Part II

Yaroslav Shramko, Heinrich Wansing

Studia Logica > 2009 > 92 > 2 > 143-146

article

Erratum to Suszko’s Thesis, Inferential Many-valuedness, and the Notion of a Logical System Studia Logica, 88:405–429, 2008

Heinrich Wansing, Yaroslav Shramko

Studia Logica > 2008 > 89 > 1 > 147-147

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Suszko’s Thesis, Inferential Many-valuedness, and the Notion of a Logical System

Heinrich Wansing, Yaroslav Shramko

Studia Logica > 2008 > 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 twovaluedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation. [A] fundamental problem concerning many-valuedness is to know what...

article

Hyper-Contradictions, Generalized Truth Values and Logics of Truth and Falsehood

Yaroslav Shramko, Heinrich Wansing

Journal of Logic, Language and Information > 2006 > 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...

article

Some Useful 16-Valued Logics: How a Computer Network Should Think

Yaroslav Shramko, Heinrich Wansing

Journal of Philosophical Logic > 2005 > 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=℘(2)={∅,{T},{F},{T,F}}. In the present paper, we argue in favor of extending this process to the set 16=℘(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,...

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Search results for: Yaroslav Shramko

The Fmla-Fmla Axiomatizations of the Exactly True and Non-falsity Logics and Some of Their Cousins

Kripke Completeness of Bi-intuitionistic Multilattice Logic and its Connexive Variant

First-Degree Entailment and its Relatives

Modal Multilattice Logic

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.

Принцип дуальності в логіці і філософії

Логічна термінологія: проблема кодифікації

Is time reversible?

The logical way of being true: Truth values and the ontological foundation of logic

Bi-facial Truth: a Case for Generalized Truth Values

What is a Genuine Intuitionistic Notion of Falsity?

Що таке аналітична філософія?

Editorial Introduction. Truth Values: Part II

Editorial Introduction. Truth Values: Part I

The Slingshot Argument and Sentential Identity

Editorial Introduction. Truth Values: Part II

Erratum to Suszko’s Thesis, Inferential Many-valuedness, and the Notion of a Logical System Studia Logica, 88:405–429, 2008

Suszko’s Thesis, Inferential Many-valuedness, and the Notion of a Logical System

Hyper-Contradictions, Generalized Truth Values and Logics of Truth and Falsehood

Some Useful 16-Valued Logics: How a Computer Network Should Think

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