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Summary A logical connective is anything that joins smaller logical expressions into larger ones.  There are any number of logical connectives, depending on which logic one is using.  The subcategories here (with the obvious exception of the miscellaneous leaf node) are most appropriate for classical logic, and logics which depart from classical logic only modestly, where there is a widely held intuition (with the exception of the conditional) that the linguistic connectives, "and," "or," and "not," are, at least in most respects, the equivalents of the formal logical connectives, conjunction, disjunction, and negation.  However, even in classical propositional logic, there is the Sheffer stroke and the dagger, which allow the axiomatization of propositional logic with just one connective, but have no clear linguistic equivalent.   As one moves further afield from classical logic, along various dimensions, one will soon discover that the variety of logical connectives is limited only by the mathematical ingenuity of the human mind.  This might help explain why--with the exception of "conditionals"--there are (currently) far more entries in the miscellaneous category than there are in any of the more standard categories.
Key works Given the above variety, as discussed, there are separate key works for each logic, although there are a few multi-volume works which attempt to be all-inclusive and cover the enormous variety of logics, their operators, and their semantics.
Introductions See, key works, above.  Only the best-known logics have works that can fairly be called introductions.
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Related categories
Subcategories:
Negation* (108)
Conditionals* (1,367 | 357)
Disjunction* (45)
Conjunction* (19)
See also:
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  1. Le'O. Apostel (1972). The Relation Between Negation in Linguistics, Logic and Psychology, a Provisional Conclusion. Logique Et Analyse 15 (57-58):333-401.
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  2. Sidney Axinn (2002). Some Questions On Negation And Possibility. Florida Philosophical Review 2 (1):53-59.
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  3. Francisco J. Ayala (1974). Michel Delsol, "Hasard, Ordre Et Finalité En Biologie" John E. Cunningham "Négation de la Négation". [REVIEW] The Thomist 38 (2):397.
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  4. Archie J. Bahm (1958). Does Seven-Fold Predication Equal Four-Cornered Negation Reversed? Philosophy East and West 7 (3/4):127-130.
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  5. Jonathan Bennett (1993). Negation and Abstention: Two Theories of Allowing. Ethics 104 (1):75-96.
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  6. S. Bhatt (1978). The Concept of Negation. Indian Philosophical Quarterly 5 (3):473-476.
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  7. Robert Blanché (1957). Opposition et négation. Revue Philosophique de la France Et de l'Etranger 147:187 - 216.
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  8. J. M. Bochenski (1963). The Law of the Negation of Negation. In Joseph M. Bochenski (ed.), The Dogmatic Principles of Soviet Philosophy (as of 1958). Dordrecht, Holland, D. Reidel Pub. Co. 22--22.
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  9. Dominique Guy Brassart (1992). Negation, Concession and Refutation in Counter-Argumentative Composition by Pupils From 8 to 12 Years Old and Adults. Argumentation 6 (1):77-98.
    In a theoretical first part we attempt to articulate the notions of concession, refutation and negation for monological linguistic activity, on the basis among other things of Mœschler's work on conversation. We distinguish the illocutionary act of refutation and the complex intervention of refutation, concession-invention, concession-repetition and concession-quotation. In a second part we analyze the place and role of (descriptive) negation in counter-argumentative texts written by 8- to 12-year-old pupils and adults in an artificial situation. We consider phenomena observed by (...)
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  10. S. Breton (1994). Superlatif Et Négation. Comment Dire la Transcendance? Revue des Sciences Philosophiques Et Théologiques 78 (2):193-202.
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  11. G. Buchdahl (1961). The Problem of Negation. Philosophy and Phenomenological Research 22 (2):163-178.
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  12. Robert W. Burch (1976). What is Hume's Doctrine of Negation. International Logic Review 7:236-242.
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  13. James L. Calderwood (1983). To Be and Not to Be Negation and Metadrama in Hamlet. Monograph Collection (Matt - Pseudo).
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  14. Ahmet Çevik (2013). Antibasis Theorems for {\ Pi^ 0_1} Classes and the Jump Hierarchy. Archive for Mathematical Logic 52 (1-2):137-142.
    We prove two antibasis theorems for ${\Pi^0_1}$ classes. The first is a jump inversion theorem for ${\Pi^0_1}$ classes with respect to the global structure of the Turing degrees. For any ${P\subseteq 2^\omega}$ , define S(P), the degree spectrum of P, to be the set of all Turing degrees a such that there exists ${A \in P}$ of degree a. For any degree ${{\bf a \geq 0'}}$ , let ${\textrm{Jump}^{-1}({\bf a) = \{b : b' = a \}}}$ . We prove that, (...)
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  15. Xu Chang-fu (2002). Negation of “Old-Fashioned Person” and the Fonnation of “New Talent”. Modern Philosophy 4:001.
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  16. O. Chateaubriand (2004). Negation and Negative Properties: Reply to Richard Vallée. Manuscrito 27 (1):235-242.
    I argue in §1 that there is a clear distinction between predicate negation and sentential negation and that sentential negation is a special case of predicate negation operating on the predicate ‘is true’. In §2 I reply to Richard’s objections to negative properties on the basis of the conception of properties as identity conditions presented in Chapter 12 of Logical Forms.
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  17. Hsueh-Li Cheng (1986). Negation, Affirmation and Zen Logic. International Philosophical Quarterly 26 (3):241-251.
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  18. S. B. Cooper (1972). Jump Equivalence of the ? 0/2 Hyperhyperimmune Sets. Journal of Symbolic Logic 37 (3):598-600.
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  19. Francis Corblin (1996). Multiple Negation Processing in Natural Language. Theoria 62 (3):214-259.
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  20. Monique David-Ménard (2001). La négation comme sortie de l'ontologie. Revue de Métaphysique et de Morale 2 (2):59-67.
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  21. Devra Lee Davis (1974). Watergate: Government by Negation. [REVIEW] Theory and Society 1 (1):111-115.
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  22. H. C. M. de Swart, L. J. M. Bergman & Johan J. de Iongh (1995). Perspectives on Negation Essays in Honour of Johan J. De Iongh on His 80th Birthday = Perspectives Sur la Négation : Hommage À Johan J. De Iongh Pour Son 80e Anniversaire. [REVIEW] Monograph Collection (Matt - Pseudo).
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  23. J. Michael Dunn (1996). Generalized Onrno Negation. In H. Wansing (ed.), Negation: A Notion in Focus. W. De Gruyter 7--3.
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  24. J. Michael Dunn (1993). Star and Perp: Two Treatments of Negation. Philosophical Perspectives 7:331-357.
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  25. G. -L. Duprat (1903). La négation: Étude de psychologie pathologique. Revue Philosophique de la France Et de l'Etranger 55:498 - 507.
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  26. G. L. Duprat (1903). La Negation: Etude de Psychologie Pathologique. Philosophical Review 12:675.
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  27. Mortimer Lamson Earle (1892). The Subjunctive of Purpose in Relative Clauses in Greek. The Classical Review 6 (03):93-95.
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  28. George Englebretsen (1969). Knowledge, Negation, and Incompatibility. Journal of Philosophy 66 (18):580-585.
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  29. Frederic B. Fitch (1984). Correction to a Definition of Negation. Journal of Symbolic Logic 49 (1):47-50.
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  30. Melvin Fitting, Negation As Refutation.
    A refutation mechanism is introduced into logic programming, dual to the usual proof mechanism; then negation is treated via refutation. A four-valued logic is appropriate for the semantics: true, false, neither, both. Inconsistent programs are allowed, but inconsistencies remain localized. The four-valued logic is a well-known one, due to Belnap, and is the simplest example of Ginsberg’s bilattice notion. An efficient implementation based on semantic tableaux is sketched; it reduces to SLD resolution when negations are not involved. The resulting system (...)
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  31. J. E. Fowler (1998). Suzanne at Ste Eutrope: Negation and Narration in "La Religieuse". Diderot Studies 27:83 - 96.
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  32. Richard T. Garner (1971). Some Doubts About Illocutionary Negation. Analysis 31 (3):106 - 112.
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  33. P. T. Geach (1959). Is It Right to Say 'Or' is a Conjunction? Analysis 19 (6):143 - 144.
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  34. Anastasia Giannakidou, Metalinguistic Contrast in Greek: Para Comparatives and Metalinguistic Negation.
    In preparation. With Melita Stavrou, Aristole University of Thessaloniki.
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  35. Brendan Gillon (1990). Laurence R. Horn, A Natural History of Negation. [REVIEW] Philosophy in Review 10:181-184.
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  36. Brendan S. Gillon (1990). Laurence R. Horn, A Natural History of Negation Reviewed By. Philosophy in Review 10 (5):181-184.
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  37. Modechai Gilula (1972). The Negation of the Adverb in Demotic. Journal of the American Oriental Society 92 (3):460-465.
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  38. Joanna Golińska-Pilarek & Taneli Huuskonen (2012). Logic. Of Descriptions. A New Approach to the Foundations of Mathematics and Science. Studies in Logic, Grammar and Rhetoric 27:63-94.
    We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and complete- ness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems.
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  39. Caroline Jacot Grapa & Carine Trévisan (1995). Figures de la Négation. Monograph Collection (Matt - Pseudo).
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  40. Jean‐Blaise Grize (1955). L'implication Et la Négation Vues au Travers Des méthoDes de Gentzen Et de Fitch. Dialectica 9 (3‐4):363-381.
    Résumé1Le rôle prlvilégié que joue l'implication « si … alors » dans la pensée donne à sa formalisation loglque une importance capitale. Mais la formalisation classique se heurte à certaines difficultés.2On montre, par la méthode L de Gentzen, que c'est la partie positive de la logique intuitionniste qui exprime au plus près l'idée intuitive de l'implication.3L'implication est liée à la négation. On est conduit à distinguer « réfutable », «absurde» et «faux».4L'analyse de ces notions peut se faire aussi par la (...)
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  41. Joanna Grygiel (2004). Some Properties of H-Irreducible Lattices. Bulletin of the Section of Logic 33 (2):71-80.
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  42. Gopa Gupta (1982). On Substantive Negation. Indian Philosophical Quarterly 10 (1):93.
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  43. Michael Robert Hand (1985). Negation in English: An Essay in Game-Theoretical Semantics. Dissertation, The Florida State University
    This essay treats semantical negation from the standpoint of game-theoretical semantics. It consists of an exposition and critique of the one previous treatment of negation from this viewpoint, a formulation of negation-formation rules with special attention to the interaction of quantifier scopes and the scope of negation, and applications of this treatment to a number of problems: negation of sentences containing definite descriptions, sentences having contextually determined restrictions on quantifier domains, reciprocal quantification, negative polarity, negative raising, term negation of quantifier (...)
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  44. Charles M. Harris (2012). Badness and Jump Inversion in the Enumeration Degrees. Archive for Mathematical Logic 51 (3-4):373-406.
    This paper continues the investigation into the relationship between good approximations and jump inversion initiated by Griffith. Firstly it is shown that there is a ${\Pi^{0}_{2}}$ set A whose enumeration degree a is bad—i.e. such that no set ${X \in a}$ is good approximable—and whose complement ${\overline{A}}$ has lowest possible jump, in other words is low2. This also ensures that the degrees y ≤ a only contain ${\Delta^{0}_{3}}$ sets and thus yields a tight lower bound for the complexity of both (...)
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  45. Jacek Hawranek & Jan Zygmunt (1983). Some Elementary Properties of Conditionally Distributive Lattices. Bulletin of the Section of Logic 12 (3):117-120.
    The notion of a conditionally distributive lattice was introduced by B. Wolniewicz while formally investigating the ontology of situations . In several of this lectures he has appealed for a study of that class of lattices. The present abstract is a response to that request.
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  46. Uri Henig (1994). Meaning and Negation.
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  47. Keith G. Hossack (1990). A Problem About the Meaning of Intuitionist Negation. Mind 99 (394):207-219.
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  48. I. L. Humberstone (1995). Negation by Iteration. Theoria 61 (1):1-24.
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  49. Lloyd Humberstone (2008). Béziau's Translation Paradox. Theoria 71 (2):138-181.
    Jean-Yves Béziau (‘Classical Negation can be Expressed by One of its Halves’, Logic Journal of the IGPL 7 (1999), 145–151) has given an especially clear example of a phenomenon he considers a sufficiently puzzling to call the ‘paradox of translation’: the existence of pairs of logics, one logic being strictly weaker than another and yet such that the stronger logic can be embedded within it under a faithful translation. We elaborate on Béziau’s example, which concerns classical negation, as well as (...)
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  50. Lloyd Humberstone (2000). The Revival of Rejective Negation. Journal of Philosophical Logic 29 (4):331-381.
    Whether assent ("acceptance") and dissent ("rejection") are thought of as speech acts or as propositional attitudes, the leading idea of rejectivism is that a grasp of the distinction between them is prior to our understanding of negation as a sentence operator, this operator then being explicable as applying to A to yield something assent to which is tantamount to dissent from A. Widely thought to have been refuted by an argument of Frege's, rejectivism has undergone something of a revival in (...)
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