Linked bibliography for the SEP article "Many-Sorted Logic" by María Manzano and Víctor Aranda

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Abadi, Aharon, Alexander Rabinovich, and Mooly Sagiv, 2007, “Decidable Fragments of Many-Sorted Logic”, in Logic for Programming, Artificial Intelligence, and Reasoning, Nachum Dershowitz and Andrei Voronkov (eds.), (Lecture Notes in Computer Science 4790), Berlin, Heidelberg: Springer Berlin Heidelberg, 17–31. doi:10.1007/978-3-540-75560-9_4 (Scholar)
Andréka, Hajnal, István Németi, and Johan van Benthem, 1998, “Modal Languages and Bounded Fragments of Predicate Logic”, Journal of Philosophical Logic, 27(3): 217–274. doi:10.1023/a:1004275029985 (Scholar)
Andréka, Hajnal, Johan van Benthem, Nick Bezhanishvili, and István Németi, 2014, “Changing a Semantics: Opportunism or Courage?”, in Manzano, Sain, and Alonso 2014: 307–337. doi:10.1007/978-3-319-09719-0_20">10.1007/978-3-319-09719-0_20 (Scholar)
Aranda, Víctor, 2022, “Completeness: From Husserl to Carnap”, Logica Universalis, 16(1–2): 57–83. doi:10.1007/s11787-021-00283-4 (Scholar)
Barrett, Thomas William and Hans Halvorson, 2016, “Morita Equivalence”, The Review of Symbolic Logic, 9(3): 556–582. doi:10.1017/s1755020316000186 (Scholar)
–––, 2017, “Quine’s Conjecture on Many-Sorted Logic”, Synthese, 194(9): 3563–3582. doi:10.1007/s11229-016-1107-z (Scholar)
Blackburn, Patrick and Johan van Benthem, 2007, “Modal Logic: A Semantic Perspective”, in Blackburn, van Benthem, and Wolter 2007: 1–84. doi:10.1016/s1570-2464(07)80004-8 (Scholar)
Blackburn, Patrick, Johan van Benthem, and Frank Wolter (eds.), 2007, Handbook of Modal Logic, (Studies in Logic and Practical Reasoning 3), Amsterdam/Boston: Elsevier. [Blackburn, van Benthem, and Wolter 2007 available online] (Scholar)
van Benthem, Johan, 1983, Modal Logic and Classical Logic, (Indices 3), Napoli: Bibliopolis. (Scholar)
–––, 1984a, “Correspondence Theory”, in Handbook of Philosophical Logic, D. Gabbay and F. Guenthner (eds.), Dordrecht: Springer Netherlands, 167–247. doi:10.1007/978-94-009-6259-0_4 (Scholar)
–––, 1984b, “Review: B. J. Copeland. On When a Semantics Is Not a Semantics: Some Reasons for Disliking the Routley–Semantics for Relevance Logic. Journal of Philosophical Logic, Vol. 8 (1979), pp. 399–413”, Journal of Symbolic Logic, 49(3): 994–995. doi:10.2307/2274161 (Scholar)
–––, 2010, Modal Logic for Open Minds, (CSLI Lecture Notes 199), Stanford, CA: CSLI Publications. (Scholar)
Carnielli, Walter A., Marcelo E. Coniglio, and Itala M. L. D’Ottaviano, 2009, “New Dimensions on Translations Between Logics”, Logica Universalis, 3(1): 1–18. doi:10.1007/s11787-009-0002-5 (Scholar)
Church, Alonzo, 1956, Introduction to Mathematical Logic, Volume 1, (Princeton Mathematical Series 17), Princeton, NJ: Princeton University Press. [Note: this was a new revised edition from a 1944 edition published as an Annals of Mathematics Studies volume (no. 13).] (Scholar)
Craig, William, 1957a, “Linear Reasoning. A New Form of the Herbrand-Gentzen Theorem”, Journal of Symbolic Logic, 22(3): 250–268. doi:10.2307/2963593 (Scholar)
–––, 1957b, “Three Uses of the Herbrand-Gentzen Theorem in Relating Model Theory and Proof Theory”, Journal of Symbolic Logic, 22(3): 269–285. doi:10.2307/2963594 (Scholar)
da Silva, Jairo J., Itala Marı́a L. D’Ottaviano, and A. M. Sette, 1999, “Translations between Logics”, in Models, Algebras, and Proofs, Xavier Caicedo and Carlos H. Montenegro (eds.), (Lecture Notes in Pure and Applied Mathematics 203), New York: Marcel Dekker, 435–448. (Scholar)
D’Ottaviano, Itala M. Loffredo and Hércules de Araújo Feitosa, 2019, “Translations Between Logics: A Survey”, in Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium, Gabriele M. Mras, Paul Weingartner, and Bernhard Ritter (eds.), Boston/Berlin: De Gruyter, 71–90. doi:10.1515/9783110657883-005 (Scholar)
Ebbinghaus, Heinz-Dieter, Jörg Flum, and Wolfgang Thomas, 1984, Mathematical Logic, (Undergraduate Texts in Mathematics), New York: Springer-Verlag. (Scholar)
Eilenberg, Samuel and Saunders MacLane, 1942, “Group Extensions and Homology”, The Annals of Mathematics, 43(4): 757–831. doi:10.2307/1968966 (Scholar)
–––, 1945, “General Theory of Natural Equivalences”, Transactions of the American Mathematical Society, 58(2): 231–294. (Scholar)
Enderton, Herbert B., 1972, A Mathematical Introduction to Logic, New York: Academic Press. (Scholar)
Feferman, Solomon, 1968, “Lectures on Proof Theory”, in Proceedings of the Summer School in Logic Leeds, 1967, M. H. Löb (ed.), (Lecture Notes in Mathematics 70), Berlin/Heidelberg: Springer Berlin Heidelberg, 1–107. doi:10.1007/bfb0079094 (Scholar)
–––, 1974, “Applications of many-sorted interpolation theorems”, in Proceedings of the Tarski Symposium, L. Henkin, J. Addison, C. Chang, W. Craig, D. Scott and R. Vaught (eds.), (Proceedings of Symposia in Pure Mathematics, 25), Providence, RI: AMS, pp. 205–224. (Scholar)
–––, 2008, “Harmonious Logic: Craig’s Interpolation Theorem and Its Descendants”, Synthese, 164(3): 341–357. doi:10.1007/s11229-008-9354-2 (Scholar)
–––, 2016, “Many-sorted first-order model theory as a conceptual framework for biological and other complex dynamical systems”, Keynote address to the AMS/ASL session on applications of Logic, Model Theory, and Theoretical Computer Science to System Biology, Seattle, 9 January 2016. [Feferman 2016 draft available online] (Scholar)
Friedman, Harvey and Visser, Albert, 2014, “When bi-interpretability implies synonymy”, Logic Group Preprint Series, 320: 1–19. (Scholar)
Gabbay, Dov M. (ed.), 1994, What Is a Logical System?, (Studies in Logic and Computation 4), Oxford: Clarendon Press. (Scholar)
–––, 1996, Labelled Deductive Systems, Volume 1, (Oxford Logic Guides 33), Oxford: Oxford University Press. (Scholar)
Gilmore, Paul, 1958, “An addition to ‘Logic of Many-Sorted Theories’”, Compositio Mathematica, 13: 277–281. (Scholar)
Glymour, Clark, 1971, “Theoretical Realism and Theoretical Equivalence”, in PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1970, Roger C. Buck and Robert S. Cohen (eds.), (Boston Studies in the Philosophy of Science 8), Dordrecht: Springer Netherlands, 275–288. doi:10.1007/978-94-010-3142-4_19 (Scholar)
Gödel, Kurt, 1931, “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I”, Monatshefte für Mathematik und Physik, 38–38(1): 173–198. doi:10.1007/bf01700692 (Scholar)
Grzegorczyk, Andrzej, 1955, “The Systems of Leśniewski in Relation to Contemporary Logical Research”, Studia Logica, 3(1): 77–95. doi:10.1007/bf02067248 (Scholar)
Henkin, Leon, 1949, “The Completeness of the First-Order Functional Calculus”, Journal of Symbolic Logic, 14(3): 159–166. doi:10.2307/2267044 (Scholar)
–––, 1950, “Completeness in the Theory of Types”, Journal of Symbolic Logic, 15(2): 81–91. doi:10.2307/2266967 (Scholar)
–––, 1953, “Banishing the Rule of Substitution for Functional Variables”, Journal of Symbolic Logic, 18(3): 201–208. doi:10.2307/2267403 (Scholar)
–––, 1963a, “A Theory of Prepositional Types”, Fundamenta Mathematicae, 52(3): 323–344. doi:10.4064/fm-52-3-323-344 (Scholar)
–––, 1963b, “An Extension of the Craig-Lyndon Interpolation Theorem”, Journal of Symbolic Logic, 28(3): 201–216. doi:10.2307/2271066 (Scholar)
–––, 1996, “The Discovery of My Completeness Proofs”, Bulletin of Symbolic Logic, 2(2): 127–158. doi:10.2307/421107 (Scholar)
Herbrand, Jacques, 1930, Recherches sur la théorie de la démonstration, PhD thesis, University of Paris. (Scholar)
Hodges, Wilfrid, 1986, “Truth in a Structure”, Proceedings of the Aristotelian Society, 86(1): 135–152. doi:10.1093/aristotelian/86.1.135 (Scholar)
–––, 1993, Model Theory, Cambridge/New York: Cambridge University Press. doi:10.1017/cbo9780511551574 (Scholar)
–––, 1998, “The Laws of Distribution for Syllogisms”, Notre Dame Journal of Formal Logic, 39(2): 221–230. doi:10.1305/ndjfl/1039293064 (Scholar)
Hook, Julian L., 1985, “A Note on Interpretations of Many-Sorted Theories”, Journal of Symbolic Logic, 50(2): 372–374. doi:10.2307/2274223 (Scholar)
Kennedy, Juliette and Väänänen, Jouko, 2021, “Logicality and Model Classes”, The Bulletin of Symbolic Logic, 27(4): 385–414. doi:10.1017/bsl.2021.42 (Scholar)
Kreisel, Georg and J. L. Krivine, 1967, Éléments de logique mathématique, théorie des modèles (Monographies de la Société mathématique de France 3), Paris: Dunod; translated as Elements of Mathematical Logic: Model Theory (Studies in Logic and the Foundations of Mathematics), Amsterdam: North Holland, 1967.
Langford, C. H., 1939, “Review: Arnold Schmidt. ‘Über deduktive Theorien mit mehreren Sorten von Grunddingen’, Mathematische Annalen, 115. 4 (1938), pp. 485–506”, Journal of Symbolic Logic, 4(2): 98–98. doi:10.2307/2269080 (Scholar)
Liezi, (列子, El libro de la perfecta vacuidad), Barcelona: Kairos, 1982. Translated directly from Chinese by Iñaki Preciado. Example translated to English for this Entry by Ulises Tindón. (Scholar)
Lindström, Per, 1969, “On Extensions of Elementary Logic”, Theoria, 35(1): 1–11. doi:10.1111/j.1755-2567.1969.tb00356.x (Scholar)
Lyndon, Roger C., 1959, “An Interpolation Theorem in the Predicate Calculus”, Pacific Journal of Mathematics, 9(1): 129–142. (Scholar)
Manzano, María, 1989 [1999], Teoría de modelos, Madrid: Alianza Editorial. Translated as Model Theory, Ruy J. G. B. de Queiroz (trans.), (Oxford Logic Guides 37), Oxford/New York: Clarendon Press ; Oxford University Press, 1999. (Scholar)
–––, 1993, “Introduction to Many-sorted logic”, Meinke and Tucker 1993: 3–86. (Scholar)
–––, 1996, Extensions of First Order Logic, (Cambridge Tracts in Theoretical Computer Science 19), Cambridge/New York: Cambridge University Press. (Scholar)
–––, 2014a, “April the 19th”, in Manzano, Sain, and Alonso 2014: 265–278. doi:10.1007/978-3-319-09719-0_18 (Scholar)
–––, 2014b, “Henkin on Completeness”, in Manzano, Sain, and Alonso 2014: 149–175. doi:10.1007/978-3-319-09719-0_12 (Scholar)
Manzano, Maria and Enrique Alonso, 2014, “Completeness: From Gödel to Henkin”, History and Philosophy of Logic, 35(1): 50–75. doi:10.1080/01445340.2013.816555 (Scholar)
Manzano, María, Ildikó Sain, and Enrique Alonso (eds.), 2014, The Life and Work of Leon Henkin, (Studies in Universal Logic), Cham: Springer International Publishing. doi:10.1007/978-3-319-09719-0 (Scholar)
Martí-Oliet, Narciso and José Meseguer, 1994, “General Logics and Logical Frameworks”, in What Is a Logical System?, Dov M. Gabbay (ed.), Oxford: Clarendon Press, 355–391. (Scholar)
Mceldowney, Paul Anh, 2020, “On Morita Equivalence and Interpretability”, The Review of Symbolic Logic, 13(2): 388–415. doi:10.1017/s1755020319000303 (Scholar)
Meinke, Karl and John Tucker (eds.), 1993, Many-Sorted Logic and Its Applications, (Wiley Professional Computing), Chichester/New York: Wiley. (Scholar)
Meseguer, José, 1989, “General Logics”, in Logic Colloquium’87: Proceedings of the Colloquium Held in Granada, H.-D. Ebbinghaus, J. Fernandez-Prida, M. Garrido, D. Lascar, and M. Rodriquez Artalejo (eds.), (Studies in Logic and the Foundations of Mathematics 129), Amsterdam: North-Holland, 275–329. doi:10.1016/s0049-237x(08)70132-0 (Scholar)
Otto, Martin, 2000, “An Interpolation Theorem”, Bulletin of Symbolic Logic, 6(4): 447–462. doi:10.2307/420966 (Scholar)
Quine, Willard Van Orman, 1940, Mathematical Logic, New York: W. W. Norton & Company. (Scholar)
Schmidt, Arnold, 1938, “Über deduktive Theorien mit mehreren Sorten von Grunddingen”, Mathematische Annalen, 115(4): 485–506. doi:10.1007/bf01448954 (Scholar)
Tarski, Alfred, 1933 [1983], Pojęcie prawdy w językach nauk dedukcyjnych, (Prace Towarzystwa Naukowego Warszawskiego, Wydzial III Nauk Matematyczno-Fizycznych, 34), Warsaw: Nakładem Towarzystwa Naukowego Warszawskiego. Translated as “The Concept of Truth in Formalized Languages”, J.H. Woodger (trans.), in Logic, Semantics, Metamathematics, second edition, J. Corcoran (ed.), Indianapolis, IN: Hackett, 1983, 152–278. (Scholar)
Tarski, Alfred and Robert Lawson Vaught, 1956, “Arithmetical Extensions of Relational Systems”, Compositio Mathematica, 13: 81–102. (Scholar)
Väänänen, Jouko, 1979, “Abstract Logic and Set Theory. I. Definability”, in Logic Colloquium ’78: Proceedings of the Colloquium Held in Mons, Maurice Boffa, Dirkvan Dalen, and Kenneth Mcaloon (eds.), (Studies in Logic and the Foundations of Mathematics 97), Amsterdam: Elsevier, 391–421. doi:10.1016/s0049-237x(08)71637-9 (Scholar)
–––, 1982, “Abstract Logic and Set Theory. II. Large Cardinals”, Journal of Symbolic Logic, 47(2): 335–346. doi:10.2307/2273145 (Scholar)
–––, 2014, “Sort Logic and Foundations of Mathematics”, in Infinity and Truth, by Chitat Chong, Qi Feng, Theodore A Slaman, and W Hugh Woodin, (Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore 25), Singapore: World Scientific, 171–186. doi:10.1142/9789814571043_0005 (Scholar)
Wang, Hao, 1952, “Logic of Many-Sorted Theories”, Journal of Symbolic Logic, 17(2): 105–116. doi:10.2307/2266241 (Scholar)

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