Results for 'Darek ��ukasiewicz'
Epistemic Deism and Probabilistic Theism.Darek Łukasiewicz - 2018 - European Journal for Philosophy of Religion 10 (1):129-140.details
The aim of my paper is to clarify the conceptions of epistemic deism and probabilistic theism and to demonstrate that the two doctrines do not finally collapse into one. I would like also to point some reasons for the acceptance of a certain version of probabilistic theism which I will call in the last part of the article "open probabilistic theism". Open probabilistic theism is not a version of the view called "open theism". The reasons for the openness of open (...) probabilistic theism are quite different from the reasons supporting open theism. (shrink)
Divine Providence and Chance in the World: Replies.Dariusz Łukasiewicz - 2020 - Roczniki Filozoficzne 68 (3):5-34.details
Opatrzność Boża a przypadek w świecie Celem artykułu jest obrona dwóch tez: pierwszej, że istnienie zdarzeń przypadkowych jest do pogodzenia z istnieniem Boga oraz tezy drugiej, że przypadek może być częścią Bożej opatrzności. Koniunkcja obu powyższych tez nazwana jest w artykule tezą kompatybilizmu. Argumentacja w obronie kompatybilizmu opiera się na danych współczesnej nauki oraz na idei wszechmocnego Boga Stwórcy. Porządek argumentacji w artykule jest następujący. W części drugiej przedstawiony jest historyczny kontekst oraz podstawy doktrynalne pojęcia opatrzności. W części trzeciej omówiony (...) jest argument za nieistnieniem Boga oparty na założeniu głoszącym istnienie zdarzeń przypadkowych w świecie oraz przedstawiona jest krytyka tego argumentu. W części czwartej prezentowane są możliwe modele działania Boga w świecie, w ramach których przyjmuje się istnienie zdarzeń przypadkowych. W części piątej i ostatniej rozważana jest idea Bożej doskonałości obejmującej takie atrybuty jak wszechmoc, wszechwiedzę, doskonałą dobroć i suwerenną wolę Bożą. (shrink)
Łukasiewicz on the Principle of Contradiction.Venanzio Raspa - 1999 - Journal of Philosophical Research 24:57-112.details
Łukasiewicz distinguishes three formulations of the principle of contradiction in Aristotle's works: ontological, logical, and psychological. The first two formulations are equivalent though not synonymous, but neither of them is equivalent to the psychological one, which expresses not a principle but only an empirical law. Furthermore, the principle of contradiction is neither a simple and ultimate law nor is it necessary for conducting an inference, because the syllogism is independent of it. The further explanation of this concept leads Łukasiewicz to (...) formulate the idea of a non-Aristotelian logic, that is, a logic operating without the principle of contradiction. If the principle of contradiction shall be valid, it must be proved. A proof can be supplied only on the basis of a definition of object, as something that cannot have and not have the same property at the same time. However, this definition does not hold for all objects, i.e., for contradictory objects. In virtue of its ontological character the Aristotelian principle of contradiction is then different from that of symbolic logic. (shrink)
Ancient Greek and Roman Logic in Ancient Greek and Roman Philosophy
Aristotle: Non-Contradiction in Ancient Greek and Roman Philosophy
Nonclassical Logics in Logic and Philosophy of Logic
Polish Philosophy in European Philosophy
On Jan Łukasiewicz's Many-Valued Logic and His Criticism of Determinism.Dariusz Łukasiewicz - 2011 - Philosophia Scientiae 15:7-20.details
Many-Valued Logic in Logic and Philosophy of Logic
On Jan Łukasiewicz's Many-Valued Logic and His Criticism of Determinism.Dariusz Łukasiewicz - 2011 - Philosophia Scientae 15:7-20.details
Extending Łukasiewicz Logics with a Modality: Algebraic Approach to Relational Semantics.Georges Hansoul & Bruno Teheux - 2013 - Studia Logica 101 (3):505-545.details
This paper presents an algebraic approach of some many-valued generalizations of modal logic. The starting point is the definition of the [0, 1]-valued Kripke models, where [0, 1] denotes the well known MV-algebra. Two types of structures are used to define validity of formulas: the class of frames and the class of Ł n -valued frames. The latter structures are frames in which we specify in each world u the set (a subalgebra of Ł n ) of the allowed truth (...) values of the formulas in u. We apply and develop algebraic tools (namely, canonical and strong canonical extensions) to generate complete modal n + 1-valued logics and we obtain many-valued counterparts of Shalqvist canonicity result. (shrink)
Product Ł Ukasiewicz Logic.Rostislav Horčík & Petr Cintula - 2004 - Archive for Mathematical Logic 43 (4):477-503.details
Łu logic plays a fundamental role among many-valued logics. However, the expressive power of this logic is restricted to piecewise linear functions. In this paper we enrich the language of Łu logic by adding a new connective which expresses multiplication. The resulting logic, PŁ, is defined, developed, and put into the context of other well-known many-valued logics. We also deal with several extensions of this propositional logic. A predicate version of PŁ logic is introduced and developed too.
Fuzzy Logic in Logic and Philosophy of Logic
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Aristotle's Syllogistic From the Standpoint of Modern Formal Logic.Jan Łukasiewicz - 1951 - Oxford, England: Garland.details
Aristotle in Ancient Greek and Roman Philosophy
Aristotle: Logic and Philosophy of Language in Ancient Greek and Roman Philosophy
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Selected Works.Jan Łukasiewicz - 1970 - Amsterdam: North-Holland Pub. Co..details
Logic and Philosophy of Logic, Miscellaneous in Logic and Philosophy of Logic
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Peter Van Inwagen, The Problem of Evil by Dariusz Łukasiewicz.Dariusz Łukasiewicz - 2007 - Forum Philosophicum: International Journal for Philosophy 12 (2):447-454.details
The Argument from Evil in Philosophy of Religion
Łukasiewicz, Supervaluations and the Future.Greg Restall - 2005 - Logic and Philosophy of Science 3:1-10.details
A B S T R AC T: In this paper I consider an interpretation of future contingents which motivates a unification of a Łukasiewicz-style logic with the more classical supervaluational semantics. This in turn motivates a new non-classical logic modelling what is "made true by history up until now. " I give a simple Hilbert-style proof theory, and a soundness and completeness argument for the proof theory with respect to the intended models.
Truthmakers in Metaphysics
On the Principle of the Excluded Middle.Jan Łukasiewicz, Jan Woleński & Peter Simons - 1987 - History and Philosophy of Logic 8 (1):67-69.details
The brief article of 1910 which is translated here is, as the prefatory note explains, significant for understanding both the way in which ?ukasiewicz came to many-valued logic and the influences under which he stood at the time.
On Ł Ukasiewicz's ${\rm \l}$-Modal System.Timothy Smiley - 1961 - Notre Dame Journal of Formal Logic 2 (3):149-153.details
On Axiomatization of Łukasiewicz's Four-Valued Modal Logic.Marcin Tkaczyk - 2011 - Logic and Logical Philosophy 20 (3):215-232.details
Formal aspects of various ways of description of Jan Łukasiewicz's four-valued modal logic £ are discussed. The original Łukasiewicz's description by means of the accepted and rejected theorems, together with the four-valued matrix, is presented. Then the improved E.J. Lemmon's description based upon three specific axioms, together with the relational semantics, is presented as well. It is proved that Lemmon's axiomatic is not independent: one axiom is derivable on the base of the remanent two. Several axiomatizations, based on three, two (...) or one single axiom are provided and discussed, including S. Kripke's axiomatics. It is claimed that (a) all substitutions of classical theorems, (b) the rule of modus ponens, (c) the definition of "◊" and (d) the single specific axiom schema: ⬜A ∧ B → A ∧ ⬜B, called the jumping necessity axiom, constitute an elegant axiomatics of the system £. (shrink)
Łukasiewicz Logic and the Foundations of Measurement.Michael Katz - 1981 - Studia Logica 40 (3):209 - 225.details
The logic of inexactness, presented in this paper, is a version of the Łukasiewicz logic with predicates valued in [0, ∞). We axiomatize multi-valued models of equality and ordering in this logic guaranteeing their imbeddibility in the real line. Our axioms of equality and ordering, when interpreted as axioms of proximity and dominance, can be applied to the foundations of measurement (especially in the social sciences). In two-valued logic they provide theories of ratio scale measurement. In multivalued logic they enable (...) us to treat formally errors arising in nominal and ordinal measurements. (shrink)
On the Infinite-Valued Łukasiewicz Logic That Preserves Degrees of Truth.Josep Maria Font, Àngel J. Gil, Antoni Torrens & Ventura Verdú - 2006 - Archive for Mathematical Logic 45 (7):839-868.details
Łukasiewicz's infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a "truth-preserving" scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate (...) for it. Another presentation of the same deductive system can be obtained from a substructural Gentzen calculus. In this paper we use the framework of abstract algebraic logic to study a different deductive system which uses the aforementioned algebra under a scheme of "preservation of degrees of truth". We characterize the resulting deductive system in a natural way by using the lattice filters of Wajsberg algebras, and also by using a structural Gentzen calculus, which is shown to be fully adequate for it. This logic is an interesting example for the general theory: it is selfextensional, non-protoalgebraic, and satisfies a "graded" deduction theorem. Moreover, the Gentzen system is algebraizable. The first deductive system mentioned turns out to be the extension of the second by the rule of Modus Ponens. (shrink)
Substructural Logic in Logic and Philosophy of Logic
Łukasiewicz and Leśniewski on Contradiction.A. Betti - 2004 - Reports on Philosophy 127:267-287.details
20th Century Logic in 20th Century Philosophy
Łukasiewicz Operations in Fuzzy Set and Many-Valued Representations of Quantum Logics.Jarosław Pykacz - 2000 - Foundations of Physics 30 (9):1503-1524.details
It, is shown that Birkhoff –von Neumann quantum logic (i.e., an orthomodular lattice or poset) possessing an ordering set of probability measures S can be isomorphically represented as a family of fuzzy subsets of S or, equivalently, as a family of propositional functions with arguments ranging over S and belonging to the domain of infinite-valued Łukasiewicz logic. This representation endows BvN quantum logic with a new pair of partially defined binary operations, different from the order-theoretic ones: Łukasiewicz intersection and union (...) of fuzzy sets in the first case and Łukasiewicz conjunction and disjunction in the second. Relations between old and new operations are studied and it is shown that although they coincide whenever new operations are defined, they are not identical in general. The hypothesis that quantum-logical conjunction and disjunction should be represented by Łukasiewicz operations, not by order-theoretic join and meet is formulated and some of its possible consequences are considered. (shrink)
Quantum Logic in Logic and Philosophy of Logic
Modal Definability Based on Łukasiewicz Validity Relations.Bruno Teheux - 2016 - Studia Logica 104 (2):343-363.details
We study two notions of definability for classes of relational structures based on modal extensions of Łukasiewicz finitely-valued logics. The main results of the paper are the equivalent of the Goldblatt-Thomason theorem for these notions of definability.
Ł Ukasiewicz's Twin Possibility Functors.Stanley J. Krolikoski - 1979 - Notre Dame Journal of Formal Logic 20 (2):458-460.details
Non-Commutative Łukasiewicz Propositional Logic.Ioana Leuştean - 2006 - Archive for Mathematical Logic 45 (2):191-213.details
The non-commutative counterpart of the well-known Łukasiewicz propositional logic is developed, in strong connection with the algebraic theory of psMV-algebras. An extension by a new unary logical connective is also considered and a stronger completeness result is proved for this system.
A System of Modal Logic.Jan Łukasiewicz - 1953 - Proceedings of the XIth International Congress of Philosophy 14:82-87.details
Elements of Mathematical Logic.Jan Łukasiewicz - 1963 - New York: Macmillan.details
Areas of Mathematics in Philosophy of Mathematics
Ł Ukasiewicz, Leibniz and the Arithmetization of the Syllogism.David Marshall - 1977 - Notre Dame Journal of Formal Logic 18 (2):235-242.details
An Interpretation of Łukasiewicz's 4-Valued Modal Logic.José M. Méndez, Gemma Robles & Francisco Salto - 2016 - Journal of Philosophical Logic 45 (1):73-87.details
A simple, bivalent semantics is defined for Łukasiewicz's 4-valued modal logic Łm4. It is shown that according to this semantics, the essential presupposition underlying Łm4 is the following: A is a theorem iff A is true conforming to both the reductionist and possibilist theses defined as follows: rt: the value of modal formulas is equivalent to the value of their respective argument iff A is true, etc.); pt: everything is possible. This presupposition highlights and explains all oddities arising in Łm4.
Logical Consequence and Entailment in Logic and Philosophy of Logic
Modal Logic in Logic and Philosophy of Logic
Jan Łukasiewicz's Works on the History of Logic.Tadeusz Kotarbiński - 1958 - Studia Logica 8 (1):57-62.details
O logice trójwartościowej.Jan Łukasiewicz - 1988 - Studia Filozoficzne 270 (5).details
Aristotle and Łukasiewicz on Existential Import.Stephen Read - 2015 - Journal of the American Philosophical Association 1 (3):535--544.details
Jan Lukasiewicz's treatise on Aristotle's Syllogistic, published in the 1950s, has been very influential in framing contemporary understanding of Aristotle's logical systems. However, Lukasiewicz's interpretation is based on a number of tendentious claims, not least, the claim that the syllogistic was intended to apply only to non-empty terms. I show that this interpretation is not true to Aristotle's text and that a more coherent and faithful interpretation admits empty terms while maintaining all the relations of the traditional square of opposition.
Product Ukasiewicz Logic.Rostislav Hork & Petr Cintula - 2004 - Archive for Mathematical Logic 43 (4):477-503.details
On Arithmetic in the Cantor- Łukasiewicz Fuzzy Set Theory.Petr Hájek - 2005 - Archive for Mathematical Logic 44 (6):763-782.details
Axiomatic set theory with full comprehension is known to be consistent in Łukasiewicz fuzzy predicate logic. But we cannot assume the existence of natural numbers satisfying a simple schema of induction; this extension is shown to be inconsistent.
Selected Works.Jan Łukasiewicz & L. Borkowski - 1973 - Synthese 26 (1):165-171.details
Logical and Metaphysical Assumptions of Bernard Bolzano's Theodicy.Dariusz Łukasiewicz - 2007 - Forum Philosophicum: International Journal for Philosophy 12 (1):33-56.details
17th/18th Century Logic in 17th/18th Century Philosophy
Łukasiewicz Logic: From Proof Systems To Logic Programming.George Metcalfe, Nicola Olivetti & Dov Gabbay - 2005 - Logic Journal of the IGPL 13 (5):561-585.details
We present logic programming style "goal-directed" proof methods for Łukasiewicz logic Ł that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goal-directed calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational Pavelka logic RPL, an extension of Ł with rational constants.
Torn by Reason: Łukasiewicz on the Principle of Contradiction.Graham Priest - 2016 - In Sorin Costreie (ed.), Early Analytic Philosophy – New Perspectives on the Tradition. Springer Verlag.details
In 1910, Jan Łukasiewicz published a groundbreaking book, On the Principle of Contradiction in Aristotle. The book contained a critique of the traditional attitude to the Principle of Non-Contradiction, and a reevaluation of its significance in the light of contemporary developments in logic. In the first half of the book, Łukasiewicz produced an analysis of Aristotle's defence of the Principle in the Metaphysics, showing its deep inadequacy. In the second half of the book, Łukasiewicz, in his own terms, considers the (...) pros and cons of the principle. The present paper provides an analysis and commentary on the second half of the book. Łukasiewicz is seen to be badly torn. Though he eventually endorses the principle, he does so, not in virtue of the evidence he considers, but in despite of it. In particular, he considers arguments against the Principle, drawn from Hegel, Meinong, and the paradoxes of self-reference, but rejects them for what appear to be patently inadequate reasons. (shrink)
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On the Expressive Power of Łukasiewicz Square Operator.Marcelo E. Coniglio, Francesc Esteva, Tommaso Flaminio & Lluis Godo - forthcoming - Journal of Logic and Computation.details
The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)
Free Łukasiewicz Implication Algebras.José Patricio Díaz Varela - 2008 - Archive for Mathematical Logic 47 (1):25-33.details
Łukasiewicz implication algebras are the {→,1}-subreducts of MV- algebras. They are the algebraic counterpart of Super-Łukasiewicz Implicational Logics investigated in Komori (Nogoya Math J 72:127–133, 1978). In this paper we give a description of free Łukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Łukasiewicz implication algebra is isomorphic to ${\bigcup_{x\in X} [x_\theta)}$ for a certain congruence θ over the |X|-free MV-algebra. As corollary we describe the free algebras in all subvarieties of Łukasiewicz (...) implication algebras. (shrink)
Consequence and Interpolation in Łukasiewicz Logic.Daniele Mundici - 2011 - Studia Logica 99 (1-3):269-278.details
Building on Wójcicki's work on infinite-valued Łukasiewicz logic Ł ∞ , we give a self-contained proof of the deductive interpolation theorem for Ł ∞ . This paper aims at introducing the reader to the geometry of Łukasiewicz logic.
Jan Łukasiewicz contre le dictum de omni et de nullo.Michel Bastit - 2011 - Philosophia Scientae 15:55-68.details
Tableaux for Łukasiewicz Infinite-Valued Logic.Nicola Olivetti - 2003 - Studia Logica 73 (1):81-111.details
In this work we propose a labelled tableau method for Łukasiewicz infinite-valued logic $\scr{L}_{\omega}$. The method is based on the Kripke semantics of this logic developed by Urquhart [25] and Scott [24]. On the one hand, our method falls under the general paradigm of labelled deduction [8] and it is rather close to the systems for substructural logics proposed in [4]. On the other hand, it provides a CoNP decision procedure for $\scr{L}_{\omega}$ validity by reducing the check of branch closure (...) to linear programming. (shrink)
Phenomeno-Semantic Complexity: A Proposal for an Alternative Notion of Complexity as a Foundation for the Management of Complexity in Human Affairs.Darek Eriksson - 2007 - Emergence: Complexity and Organization 9:1-2.details
The Deduction Theorem for Łukasiewicz Many-Valued Propositional Calculi.Witold A. Pogorzelski - 1964 - Studia Logica 15 (1):7-19.details
N-Valued Logics and Łukasiewicz–Moisil Algebras. [REVIEW]George Georgescu - 2006 - Axiomathes 16 (1-2):123-136.details
Fundamental properties of N-valued logics are compared and eleven theorems are presented for their Logic Algebras, including Łukasiewicz–Moisil Logic Algebras represented in terms of categories and functors. For example, the Fundamental Logic Adjunction Theorem allows one to transfer certain universal, or global, properties of the Category of Boolean Algebras,, to the more general category \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal L}$$\end{document}Mn of Łukasiewicz–Moisil Algebras. Furthermore, the relationships of LMn-algebras to other many-valued logical structures, such as the (...) n-valued Post, MV and Heyting logic algebras, are investigated and several pertinent theorems are derived. Applications of Łukasiewicz–Moisil Algebras to biological problems, such as nonlinear dynamics of genetic networks – that were previously reported – are also briefly noted here, and finally, probabilities are precisely defined over LMn-algebras with an eye to immediate, possible applications in biostatistics. (shrink)
On Semantic Games for Łukasiewicz Logic.Ondrej Majer & Christian Fermüller - 2018 - In Hans van Ditmarsch & Gabriel Sandu (eds.), Jaakko Hintikka on Knowledge and Game Theoretical Semantics. Springer. pp. 263-278.details
We explore different ways to generalize Hintikka's classic game theoretic semantics to a many-valued setting, where the unit interval is taken as the set of truth values. In this manner a plethora of characterizations of Łukasiewicz logic arise. Among the described semantic games is Giles's dialogue and betting game, presented in a manner that makes the relation to Hintikka's game more transparent. Moreover, we explain a so-called explicit evaluation game and a 'bargaining game' variant of it. We also describe a (...) recently introduced backtracking game as well as a game with random choices for Łukasiewicz logic. (shrink)
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The Logics Stronger Than Łukasiewicz's Three Valued Sentential Calculus-the Notion of Degree of Maximality Versus the Notion of Degree of Completeness.Ryszard Wójcicki - 1974 - Studia Logica 33 (2):201-214.details
Was Łukasiewicz Wrong? : Three-Valued Logic and Determinism.Daisuke Kachi - 1996 - In Łukasiewicz in Dublin -- An International Conference on the Work of Jan Łukasiewicz.details
Łukasiewicz has often been criticized for his motive for inventing his three-valued logic, namely the avoidance of determinism. First of all, I want to show that almost all of the critcism along this line was wrong. Second I will indicate that he made mistakes, however, in constructing his system, because he had other motives at the same time. Finally I will propose some modification of his system and its interpretation which can attain his original purpose in some sense.
Logical Semantics and Logical Truth in Logic and Philosophy of Logic
Arithmetic and Truth in Łukasiewicz's Infinitely Valued Logic.Greg Restall - 1992 - Logique Et Analyse 139 (140):303-312.details
Truth in Philosophy of Language
Kilka uwag do metaetycznych poglądów Kazimierza Twardowskiego.Dariusz Łukasiewicz - 2004 - Etyka 37:215-226.details
Agathological Rationalism and First-Order Religions.Dariusz Łukasiewicz - 2017 - European Journal for Philosophy of Religion 9 (2):223-229.details
Religious Experience in Philosophy of Religion
Religious Imagination in Philosophy of Religion
Łukasiewicz, Determinism, and the Four-Valued System of Logic.Zuzana Rybaříková - 2021 - Semiotica 2021 (240):129-143.details
Jan Łukasiewicz is known primarily as the founder of the three-valued system of logic. It is also generally renowned that his reason for introducing many-valued systems of logic was an attempt to refute determinism. When he developed the three-valued and n-valued logic, he employed these systems in his arguments against determinism. On the contrary, Łukasiewicz preferred the four-valued system of logic that is not suitable for a refutation of determinism in his latest period. It seems, however, that determinism still interested (...) Łukasiewicz, as he discussed its denial in his last work, the second edition of the book Aristotle's syllogistic from the standpoint of modern formal logic. The aim of my paper is to introduce the issue and describe the relation of these two topics primarily in the latest period of Łukasiewicz's work. There are several possible solutions to the issue. However, Łukasiewicz never addressed the issue clearly in his published works. Therefore, the solutions might be supported or contradicted by his unpublished works in the future. (shrink)
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