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  1. Hierarchical Incompleteness Results for Arithmetically Definable Extensions of Fragments of Arithmetic.Rasmus Blanck - 2021 - Review of Symbolic Logic 14 (3):624-644.
    There has been a recent interest in hierarchical generalizations of classic incompleteness results. This paper provides evidence that such generalizations are readily obtainable from suitably formulated hierarchical versions of the principles used in the original proofs. By collecting such principles, we prove hierarchical versions of Mostowski’s theorem on independent formulae, Kripke’s theorem on flexible formulae, Woodin’s theorem on the universal algorithm, and a few related results. As a corollary, we obtain the expected result that the formula expressing “ $\mathrm {T}$ (...)
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  2. One Modal Logic to Rule Them All?Wesley H. Holliday & Tadeusz Litak - 2018 - In Guram Bezhanishvili, Giovanna D'Agostino, George Metcalfe & Thomas Studer (eds.), Advances in Modal Logic, Vol. 12. London: College Publications. pp. 367-386.
    In this paper, we introduce an extension of the modal language with what we call the global quantificational modality [∀p]. In essence, this modality combines the propositional quantifier ∀p with the global modality A: [∀p] plays the same role as the compound modality ∀pA. Unlike the propositional quantifier by itself, the global quantificational modality can be straightforwardly interpreted in any Boolean Algebra Expansion (BAE). We present a logic GQM for this language and prove that it is complete with respect to (...)
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  3. Containment Logics: Algebraic Completeness and Axiomatization.Stefano Bonzio & Michele Pra Baldi - 2021 - Studia Logica 109 (5):969-994.
    The paper studies the containment companion of a logic \. This consists of the consequence relation \ which satisfies all the inferences of \, where the variables of the conclusion are contained into those of the set of premises, in case this is not inconsistent. In accordance with the work started in [10], we show that a different generalization of the Płonka sum construction, adapted from algebras to logical matrices, allows to provide a matrix-based semantics for containment logics. In particular, (...)
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  4. Unification in Pretabular Extensions of S4.Stepan I. Bashmakov - 2021 - Logica Universalis 15 (3):381-397.
    L.L. Maksimova and L. Esakia, V. Meskhi showed that the modal logic \ has exactly 5 pretabular extensions PM1–PM5. In this paper, we study the problem of unification for all given logics. We showed that PM2 and PM3 have finitary, and PM1, PM4, PM5 have unitary types of unification. Complete sets of unifiers in logics are described.
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  5. Copy and Remove as Dynamic Operators.Carlos Areces, Hans van Ditmarsch, Raul Fervari, Bastien Maubert & François Schwarzentruber - forthcoming - Tandf: Journal of Applied Non-Classical Logics:1-40.
  6. $$\mathrm {ZF}$$ ZF Between Classicality and Non-classicality.Sourav Tarafder & Giorgio Venturi - forthcoming - Studia Logica:1-30.
    We present a generalization of the algebra-valued models of \ where the axioms of set theory are not necessarily mapped to the top element of an algebra, but may get intermediate values, in a set of designated values. Under this generalization there are many algebras which are neither Boolean, nor Heyting, but that still validate \.
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  7. Derivability and Metainferential Validity.Bruno Da Ré, Damian Szmuc & Paula Teijeiro - forthcoming - Journal of Philosophical Logic:1-27.
    The aim of this article is to study the notion of derivability and its semantic counterpart in the context of non-transitive and non-reflexive substructural logics. For this purpose we focus on the study cases of the logics ST and TS. In this respect, we show that this notion doesn’t coincide, in general, with a nowadays broadly used semantic approach towards metainferential validity: the notion of local validity. Following this, and building on some previous work by Humberstone, we prove that in (...)
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  8. Ns Saturated and -Definable.Stefan Hoffelner - 2021 - Journal of Symbolic Logic 86 (1):25-59.
    We show that under the assumption of the existence of the canonical inner model with one Woodin cardinal $M_1$, there is a model of $\mathsf {ZFC}$ in which $\mbox {NS}_{\omega _{1}}$ is $\aleph _2$ -saturated and ${\Delta }_{1}$ -definable with $\omega _1$ as a parameter which answers a question of S. D. Friedman and L. Wu. We also show that starting from an arbitrary universe with a Woodin cardinal, there is a model with $\mbox {NS}_{\omega _{1}}$ saturated and ${\Delta }_{1}$ (...)
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  9. Arthur N. Prior on ‘Unquestionably the Best Logical Symbolism for Most Purposes’.Jeremiah Joven B. Joaquin - forthcoming - History and Philosophy of Logic:1-17.
    In his Formal Logic, Arthur N. Prior declared that Jan Łukasiewicz's logical notation is ‘unquestionably the best logical symbolism for most purposes’. Whether he had a substantive, and...
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  10. Idempotent Variations on the Theme of Exclusive Disjunction.L. Humberstone - forthcoming - Studia Logica:1-43.
    An exclusive disjunction is true when exactly one of the disjuncts is true. In the case of the familiar binary exclusive disjunction, we have a formula occurring as the first disjunct and a formula occurring as the second disjunct, so, if what we have is two formula-tokens of the same formula-type—one formula occurring twice over, that is—the question arises as to whether, when that formula is true, to count the case as one in which exactly one of the disjuncts is (...)
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  11. The Structure and Extension of (Proto)Type Concepts: Husserl’s Correlationist Approach.Hamid Taieb - forthcoming - History and Philosophy of Logic:1-14.
    This paper aims to reassess a notion in the works of the later Husserl that is both historically important and philosophically insightful, but remains understudied, namely, that of type. In opposition to a standard reading which treats Husserl’s type presentations as pre-conceptual habits, this paper argues that these representations are a specific kind of concept. More precisely, it shows that Husserl’s account of type presentations is akin to the contemporary prototype theory of concepts. This is historically important, since the predecessor (...)
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  12. Closed Structure.Peter Fritz, Harvey Lederman & Gabriel Uzquiano - 2021 - Journal of Philosophical Logic 50 (6):1249-1291.
    According to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, which involves restricting the scope of the claim that (...)
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  13. Prolog Detects Pathological Self Reference in the Gödel Sentence.P. Olcott - manuscript
    This sentence G ↔ ¬(F ⊢ G) and its negation G ↔ ~(F ⊢ ¬G) are shown to meet the conventional definition of incompleteness: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)). They meet conventional definition of incompleteness because neither the sentence nor its negation is provable in F (or any other formal system). -- .
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  14. Peano on Symbolization, Design Principles for Notations, and the Dot Notation.Dirk Schlimm - 2021 - Philosophia Scientae 25:95-126.
    Peano was one of the driving forces behind the development of the current mathematical formalism. In this paper, we study his particular approach to notational design and present some original features of his notations. To explain the motivations underlying Peano's approach, we first present his view of logic as a method of analysis and his desire for a rigorous and concise symbolism to represent mathematical ideas. On the basis of both his practice and his explicit reflections on notations, we discuss (...)
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  15. J. M. Bocheński's Understanding of the World and Logical Albebraic Structures.Wybraniec-Skardowska Urszula - 2020 - Edukacja Filozoficzna 70 (5):81-92.
    This work will focus on Józef Maria Bocheński’s inclination towards seeing the world and its logical structure from the point of view of ontology. In section 2, we shall discuss the perception of the world deriving from Bocheński, while in the third section – issues of its logical structure will be dealt with. In section 4, we will present a formal framework of the structure of the world.
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  16. Identity and Aboutness.Benjamin Brast-McKie - 2021 - Journal of Philosophical Logic 50 (6):1471-1503.
    This paper develops a theory of propositional identity which distinguishes necessarily equivalent propositions that differ in subject-matter. Rather than forming a Boolean lattice as in extensional and intensional semantic theories, the space of propositions forms a non-interlaced bilattice. After motivating a departure from tradition by way of a number of plausible principles for subject-matter, I will provide a Finean state semantics for a novel theory of propositions, presenting arguments against the convexity and nonvacuity constraints which Fine (2016, 2017a,b) introduces. I (...)
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  17. What is a Rule of Inference?Neil Tennant - forthcoming - Review of Symbolic Logic:1-40.
    We explore the problems that confront any attempt to explain or explicate exactly what a primitive logical rule of inference is, or consists in. We arrive at a proposed solution that places a surprisingly heavy load on the prospect of being able to understand and deal with specifications of rules that are essentially self-referring. That is, any rule $\rho $ is to be understood via a specification that involves, embedded within it, reference to rule $\rho $ itself. Just how we (...)
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  18. Graded Structures of Opposition in Fuzzy Natural Logic.Petra Murinová - 2020 - Logica Universalis 14 (4):495-522.
    The main objective of this paper is devoted to two main parts. First, the paper introduces logical interpretations of classical structures of opposition that are constructed as extensions of the square of opposition. Blanché’s hexagon as well as two cubes of opposition proposed by Morreti and pairs Keynes–Johnson will be introduced. The second part of this paper is dedicated to a graded extension of the Aristotle’s square and Peterson’s square of opposition with intermediate quantifiers. These quantifiers are linguistic expressions such (...)
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  19. Logics of Variable Inclusion and the Lattice of Consequence Relations.Michele Pra Baldi - 2020 - Journal of Applied Non-Classical Logics 30 (4):367-381.
    In this paper, first, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic ⊢ with a composition term. Then, we investigate their position into the lattice of co...
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  20. Humble Connexivity.Andreas Kapsner - 2019 - Logic and Logical Philosophy 28.
    In this paper, I review the motivation of connexive and strongly connexive logics, and I investigate the question why it is so hard to achieve those properties in a logic with a well motivated semantic theory. My answer is that strong connexivity, and even just weak connexivity, is too stringent a requirement. I introduce the notion of humble connexivity, which in essence is the idea to restrict the connexive requirements to possible antecedents. I show that this restriction can be well (...)
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  21. Rejection in Łukasiewicz's and Słupecki's Sense.Wybraniec-Skardowska Urszula - 2018 - In The Lvov-Warsaw School, Past and Present. Cham: pp. 575-597.
    The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz and developed by (...)
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  22. On the Eliminability of Ideal Linguistic Entities.Wybranie-Skardowska Urszula - 1989 - Studia Logica (4):587-615.
    With reference to Polish logical-philosophical tradition two formal theories of language syntax have been sketched and then compared with each other. The first theory is based on the assumption that the basic linguistic stratum is constituted by object-tokens (concrete objects perceived through the senses) and that the types of such objects (ideal objects) are derivative constructs. The other is founded on an opposite philosophical orientation. The two theories are equivalent. The main conclusion is that in syntactic researches it is redundant (...)
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  23. Complexity of the Infinitary Lambek Calculus with Kleene Star.Stepan Kuznetsov - forthcoming - Review of Symbolic Logic:1-27.
    We consider the Lambek calculus, or noncommutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an $\omega $ -rule, and prove that the derivability problem in this calculus is $\Pi _1^0$ -hard. This solves a problem left open by Buszkowski, who obtained the same complexity bound for infinitary action logic, which additionally includes additive conjunction and disjunction. As a by-product, we prove that any context-free language without the empty word can be generated by a (...)
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  24. Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic.Nils Kürbis - 2019 - Bulletin of the Section of Logic 48 (4):299-317.
    Sentences containing definite descriptions, expressions of the form ‘The F’, can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ιx[F, G] is read as ‘The F is G’. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INFι of intuitionist negative free logic extended by such a quantifier, which was presented in (...)
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  25. Horst Wessel: Contributions to the Theory of Logical Consequence, Non-Traditional Theory of Predication and Logical Theory of Terms.Klaus Wuttich - 2020 - History and Philosophy of Logic 41 (3):291-300.
    The present work takes the decease of Horst Wessel as an opportunity to present and honour his work (and that of his group), which has not received the attention it deserves. The focus will be on works which might not be sufficiently well-known. Wessel was, as we aim to show, familiar with the international debate concerning logical and philosophical issues and strived to solve them by considering theories of logical consequence, a non-traditional theory of predication and the theory of logical (...)
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  26. É a Identidade Fundamental?Kherian Gracher - 2016 - Dissertation, Federal University of Santa Catarina
    (Abstract - Inglês) Identity is traditionally taken to be a fundamental notion of our conceptual framework as well as a fundamental metaphysical component of entities. But as far as we make this claim we face ourselves with two problems: what is identity? And why would it be fundamental? These questions will guide us towards a discussion put forward by Bueno (2014), Krause and Arenhart (2015). Bueno holds that there are four aspects that make identity being fundamental: (1) identity is assumed (...)
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  27. Extended Contact Algebras and Internal Connectedness.Tatyana Ivanova - 2020 - Studia Logica 108 (2):239-254.
    The notion of contact algebra is one of the main tools in the region-based theory of space. It is an extension of Boolean algebra with an additional relation C, called contact. Standard models of contact algebras are topological and are the contact algebras of regular closed sets in a given topological space. In such a contact algebra we add the predicate of internal connectedness with the following meaning—a regular closed set is internally connected if and only if its interior is (...)
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  28. When is a Schema Not a Schema? On a Remark by Suszko.Lloyd Humberstone & Allen Hazen - 2020 - Studia Logica 108 (2):199-220.
    A 1971 paper by Roman Suszko, ‘Identity Connective and Modality’, claimed that a certain identity-free schema expressed the condition that there are at most two objects in the domain. Section 1 here gives that schema and enough of the background to this claim to explain Suszko’s own interest in it and related conditions—via non-Fregean logic, in which the objects in question are situations and the aim is to refrain from imposing this condition. Section 3 shows that the claim is false, (...)
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  29. Hintikka on the “Kant–Frege View”: A Critical Assessment.Giovanni Mion - 2019 - Logica Universalis 13 (2):171-178.
    In “Kant on Existence, Predication, and the Ontological Argument”, Hintikka argues that the so-called “Kant–Frege view” is wrong, for its supporters erroneously assume that for Kant ‘is’ is ambiguous. In this paper, I will first critically evaluate Hintikka’s arguments against the Kant–Frege view. Then, I will attempt to prove that Kant’s claim that existence is not a real predicate and Frege’s claim that existence is a quantifier are in fact logically interdependent. Finally, I will use the Kant–Frege view in order (...)
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  30. Some Observations About Generalized Quantifiers in Logics of Imperfect Information.Fausto Barbero - 2019 - Review of Symbolic Logic 12 (3):456-486.
    We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engström, comparing them with a more general, higher order definition of team quantifier. We show that Engström’s definitions can be identified, by means of appropriate lifts, with special classes of team quantifiers. We point out that the new team quantifiers express a quantitative and a qualitative component, while Engström’s quantifiers only range over the latter. We further argue that Engström’s definitions (...)
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  31. A Critical Examination of the Historical Origins of Connexive Logic.Wolfgang Lenzen - 2019 - History and Philosophy of Logic 41 (1):16-35.
    It is often assumed that Aristotle, Boethius, Chrysippus, and other ancient logicians advocated a connexive conception of implication according to which no proposition entails, or is entailed by, its own negation. Thus Aristotle claimed that the proposition ‘if B is not great, B itself is great […] is impossible’. Similarly, Boethius maintained that two implications of the type ‘If p then r’ and ‘If p then not-r’ are incompatible. Furthermore, Chrysippus proclaimed a conditional to be ‘sound when the contradictory of (...)
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  32. End of the Square?Fabien Schang - 2018 - South American Journal of Logic 4 (2):485-505.
    It has been recently argued that the well-known square of opposition is a gathering that can be reduced to a one-dimensional figure, an ordered line segment of positive and negative integers [3]. However, one-dimensionality leads to some difficulties once the structure of opposed terms extends to more complex sets. An alternative algebraic semantics is proposed to solve the problem of dimensionality in a systematic way, namely: partition (or bitstring) semantics. Finally, an alternative geometry yields a new and unique pattern of (...)
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  33. Agglomerative Algebras.Jeremy Goodman - 2018 - Journal of Philosophical Logic 48 (4):631-648.
    This paper investigates a generalization of Boolean algebras which I call agglomerative algebras. It also outlines two conceptions of propositions according to which they form an agglomerative algebra but not a Boolean algebra with respect to conjunction and negation.
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  34. Strong Noncontingency: On the Modal Logics of an Operator Expressively Weaker Than Necessity.Jie Fan - 2019 - Notre Dame Journal of Formal Logic 60 (3):407-435.
    Operators can be compared in at least two respects: expressive strength and deductive strength. Inspired by Hintikka’s treatment of question embedding verbs, the variations of noncontingency operator, and also the various combinations of modal operators and Boolean connectives, we propose a logic with strong noncontingency operator as the only primitive modality. The novel operator is deductively but not expressively stronger than both noncontingency operator and essence operator, and expressively but not deductively weaker than the necessity operator. The frame-definability power of (...)
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  35. Explicit Conditionals in the Framework of Classical Conditional Logic.Claudio Ercole Antonio Pizzi - forthcoming - Logic and Logical Philosophy:1.
  36. A Poly-Connexive Logic.Nissim Francez - forthcoming - Logic and Logical Philosophy:1.
    The paper introduces a variant of connexive logic in which connexivity is extended from the interaction of negation with implication to the interaction of negation also with conjunction and disjunction. The logic is presented by two deductively equivalent methods: an axiomatic one and a natural-deduction one. Both are shown to be complete for a four-valued model theory.
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  37. R. Cartwright. Propositions. Analytical Philosophy, Edited by R. J. Butler, Barnes & Noble, Inc., New York1962, Pp. 81–103. [REVIEW]Alan Ross Anderson - 1964 - Journal of Symbolic Logic 29 (3):139.
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  38. Gerald E. Sacks. Recursive Enumerability and the Jump Operator. Transactions of the American Mathematical Society, Vol. 108 , Pp. 223–239. [REVIEW]Donald L. Kreider - 1964 - Journal of Symbolic Logic 29 (4):204.
  39. Leon Henkin. Are Logic and Mathematics Identical?Science, Vol. 138 , Pp. 788–794.Alfons Borgers - 1964 - Journal of Symbolic Logic 29 (3):141-142.
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  40. David Nelson. Non-Null Implication. The Journal of Symbolic Logic, Vol. 31 . Pp. 562–572.Gene F. Rose - 1968 - Journal of Symbolic Logic 33 (1):129.
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  41. Timothy Smiley. Relative Necessity. The Journal of Symbolic Logic, Vol. 28 No. 2 , Pp. 113–134. - T. J. Smiley. The Logical Basis of Ethics. Proceedings of a Colloquium on Modal and Many-Valued Logics, Helsinki, 23–26 August, 1962, Acta Philosophica Fennica, No. 16, Helsinki1963, Pp. 237–246. [REVIEW]Alan Ross Anderson - 1967 - Journal of Symbolic Logic 32 (3):401-401.
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  42. Ludwik Borkowski. On Proper Quantifiers I. English with Polish and Russian Summaries. Studia Logica, Vol. 8 , Pp. 65–130. [REVIEW]Hugues Leblanc - 1967 - Journal of Symbolic Logic 32 (2):262-263.
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  43. Ludwik Borkowski. On Proper Quantifiers II. English, with Polish and Russian Summaries. Studia Logica, Vol. 10 , Pp. 7–28. , P. 272.). [REVIEW]Hugues Leblanc - 1967 - Journal of Symbolic Logic 32 (2):263.
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  44. Robert McNaughton. Undefinability of Addition From One Unary Operator. Transactions of the American Mathematical Society, Vol. 117 , Pp. 329–337. [REVIEW]Julia Robinson - 1966 - Journal of Symbolic Logic 31 (2):270.
  45. Wolfgang Yourgrau and Donald Livingstone. On the Matter of Mathematical Constants. Methodos, Vol. 9 , Pp. 3–29.H. Arnold Schmidt - 1966 - Journal of Symbolic Logic 31 (1):115-115.
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  46. H. H. LoomsJr., and R. H. WymanJr., On Complete Sets of Logic Primitives. IEEE Transactions on Electronic Computers, Vol. EC-14 , Pp. 173–174. [REVIEW]H. B. Enderton - 1970 - Journal of Symbolic Logic 35 (1):160.
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  47. Per Lindström. On Relations Between Structures. Theoria , Vol. 32 , Pp. 172–185.G. Fuhrken - 1969 - Journal of Symbolic Logic 34 (3):515.
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  48. William T. Fontaine. Avoidability and the Contrary-to-Fact Conditional in C. L. Stevenson and C. I. Lewis. The Journal of Philosophy, Vol. 48 , Pp. 783–788. [REVIEW]B. J. Diggs - 1969 - Journal of Symbolic Logic 34 (3):500.
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  49. A. P. Éršov. Opératornyé Algorifmy. II. Problémy Kibérnétiki, Vol. 8 , Pp. 211–233. - A. P. Jerschow. Operator-Algorithmen. II. German Translation of the Preceding by Heinz D. Modrow. Probleme der Kybernetik, Vol. 8 , Pp. 208–232. [REVIEW]E. M. Fels - 1968 - Journal of Symbolic Logic 33 (3):467.
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  50. John Watling. The Problem of Contrary-to-Fact Conditionals. Analysis , Vol. 17 No. 4 , Pp. 73–80. - Alan R. White. Contrary-to-Fact Conditionals and Logical Impossibility. Analysis , Vol. 18 No. 1 , Pp. 14–16. - Sidney Gendin and Robert Hoffman. On Verifying Contrary-to-Fact Subjunctive Conditionals. The Indian Journal of Philosophy, Vol. 3 No. 10 , Pp. 282–284. - M. R. Ayers. Counterfactuals and Subjunctive Conditionals. Mind, N.S. Vol. 74 , Pp. 347–364. [REVIEW]Hans Freudenthal - 1968 - Journal of Symbolic Logic 33 (2):310-311.
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