Linked bibliography for the SEP article "Proof-Theoretic Semantics" by Peter Schroeder-Heister |
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- Aczel, Peter (1977). “An Introduction to Inductive Definitions”. In: Handbook of Mathematical Logic. Ed. by John Barwise. Amsterdam: North-Holland, pp. 739–782. (Scholar)
- Beall, J.C. and Greg Restall (2006). Logical Pluralism. Oxford: Oxford University Press. (Scholar)
- Belnap, Nuel D. (1982). “Display Logic”. In: Journal of Philosophical Logic 11, pp. 375–417. (Scholar)
- Brandom, Robert B. (2000). Articulating Reasons: An Introduction to Inferentialism. Cambridge Mass.: Harvard University Press. (Scholar)
- de Campos Sanz, Wagner and Thomas Piecha (2009). “Inversion by Definitional Reflection and the Admissibility of Logical Rules”. In: Review of Symbolic Logic 2, pp. 550–569. (Scholar)
- de Groote, Philippe, ed. (1995). The Curry-Howard Isomorphism. Academia. (Scholar)
- Di Cosmo, Roberto and Dale Miller (2010). “Linear Logic”. In: The Stanford Encyclopedia of Philosophy. Ed. by Edward N. Zalta. Fall 2010. (Scholar)
- Došen, Kosta (1980). Logical Constants: An Essay in Proof Theory. Oxford: D.Phil. Thesis. (Scholar)
- ––– (1989). “Logical Constants as Punctuation Marks”. In: Notre Dame Journal of Formal Logic 30, pp. 362–381. (Scholar)
- Dummett, Michael (1991). The Logical Basis of Metaphysics. London: Duckworth. (Scholar)
- Francez, Nissim and Roy Dyckhoff (2010). “Proof-theoretic Semantics for a Natural Language Fragment”. In: Linguistics and Philosophy 33, pp. 447–477. (Scholar)
- Francez, Nissim, Roy Dyckhoff, and Gilad Ben-Avi (2010). “Proof-Theoretic Semantics for Subsentential Phrases”. In: Studia Logica 94, pp. 381–401. (Scholar)
- Gentzen, Gerhard (1934/35). “Untersuchungen über das logische Schließen”. In: Mathematische Zeitschrift 39, 176–210, 405–431 (English translation in: The Collected Papers of Gerhard Gentzen (ed. M. E. Szabo), Amsterdam: North Holland (1969), pp. 68–131). (Scholar)
- Girard, Jean-Yves (1987). “Linear Logic”. In: Theoretical Computer Science, pp. 1–102. (Scholar)
- Hacking, Ian (1979). “What is Logic?” In: Journal of Philosophy 76, pp. 285–319. (Scholar)
- Hallnäs, Lars (1991). “Partial Inductive Definitions”. In: Theoretical Computer Science 87, pp. 115–142. (Scholar)
- ––– (2006). “On the proof-theoretic foundation of general definition theory”. In: Synthese 148, pp. 589–602. (Scholar)
- Hallnäs, Lars and Peter Schroeder-Heister (1990/91). “A proof-theoretic approach to logic programming: I. Clauses as rules. II. Programs as definitions.” In: Journal of Logic and Computation 1, pp. 261–283, 635–660. (Scholar)
- Harper, Robert, Furio Honsell, and Gordon Plotkin (1987). “A Framework for Defining Logics”. In: Journal of the Association for Computing Machinery 40, pp. 194–204. (Scholar)
- Humberstone, Lloyd (2010). “Sentence Connectives in Formal Logic”. In: The Stanford Encyclopedia of Philosophy. Ed. by Edward N. Zalta. Summer 2010. (Scholar)
- Jäger, Gerhard and Robert F. Stärk (1998). “A Proof-Theoretic Framework for Logic Programming”. In: Handbook of Proof Theory. Ed. by Samuel R. Buss. Amsterdam: Elsevier, pp. 639–682. (Scholar)
- Kahle, Reinhard and Peter Schroeder-Heister, eds. (2006). Proof-Theoretic Semantics. Special issue of Synthese (Vol. 148). (Scholar)
- Kneale, William (1956). “The Province of Logic”. In: Contemporary British Philosophy. Ed. by H. D. Lewis. London: Allen and Unwin, pp. 237–261. (Scholar)
- Koslow, Arnold (1992). A Structuralist Theory of Logic. Cambridge: Cambridge University Press. (Scholar)
- Kreisel, Georg (1971). “A Survey of Proof Theory II”. In: Proceedings of the Second Scandinavian Logic Symposium. Ed. by J. E. Renstad. Amsterdam: North-Holland, pp. 109–170. (Scholar)
- Kremer, Philip (2009). “The Revision Theory of Truth”. In: The Stanford Encyclopedia of Philosophy. Ed. by Edward N. Zalta. Spring 2009. (Scholar)
- Kreuger, Per (1994). “Axioms in Definitional Calculi”. In: Extensions of Logic Programming. 4th International Workshop, ELP'93 (St. Andrews, U.K., March/April 1993). Proceedings (Lecture Notes in Computer Science, Vol. 798). Ed. by Roy Dyckhoff. Berlin: Springer, pp. 196–205. (Scholar)
- Lambek, J. and P.J. Scott (1986). Introduction to Higher Order Categorical Logic. Cambridge: Cambridge University Press. (Scholar)
- Lorenzen, Paul (1955). Einführung in die operative Logik und Mathematik. Berlin: Springer (2nd edition 1969). (Scholar)
- Martin-Löf, Per (1971). “Hauptsatz for the intuitionistic theory of iterated inductive definitions”. In: Proceedings of the Second Scandinavian Logic Symposium. Ed. by J. E. Fenstad. Amsterdam: North-Holland, pp. 179–216. (Scholar)
- ––– (1984). Intuitionistic Type Theory. Napoli: Bibliopolis. (Scholar)
- ––– (1995). “Verificationism Then and Now”. In: The Foundational Debate: Complexity and Constructivity in Mathematics and Physics. Ed. by Werner DePauli-Schimanovich, Eckehart Köhler, and Friedrich Stadler. Dordrecht: Kluwer, pp. 187–196. (Scholar)
- ––– (1998). “Truth and Knowability: On the Principles C and K of Michael Dummett”. In: Truth in Mathematics. Ed. by Harold G. Dales and Gianluigi Oliveri. Oxford: Clarendon Press, pp. 105–114. (Scholar)
- Negri, Sara and Jan von Plato (2001). Structural Proof Theory. Cambridge University Press. (Scholar)
- Nelson, David (1949). “Constructible Falsity”. In: Journal of Symbolic Logic 14, pp. 16–26. (Scholar)
- Odintsov, Sergei P. (2008). Constructive Negations and Paraconsistency. Berlin: Springer. (Scholar)
- Popper, Karl Raimund (1947a). “Logic without Assumptions”. In: Proceedings of the Aristotelian Society 47, pp. 251–292. (Scholar)
- ––– (1947b). “New Foundations for Logic”. In: Mind 56, 193–235 (Corrections Mind 57, 1948, 69–70). (Scholar)
- Prawitz, Dag (1965). Natural Deduction: A Proof-Theoretical Study. Stockholm: Almqvist & Wiksell (Reprinted Mineola NY: Dover Publ., 2006). (Scholar)
- ––– (1971). “Ideas and Results in Proof Theory”. In: Proceedings of the Second Scandinavian Logic Symposium (Oslo 1970). Ed. by Jens E. Fenstad. Amsterdam: North-Holland, pp. 235–308. (Scholar)
- ––– (1972). “The Philosophical Position of Proof Theory”. In: Contemporary Philosophy in Scandinavia. Ed. by R. E. Olson and A. M. Paul. Baltimore, London: John Hopkins Press, pp. 123–134. (Scholar)
- ––– (1973). “Towards a Foundation of a General Proof Theory”. In: Logic, Methodology and Philosophy of Science IV . Ed. by Patrick Suppes et al. North-Holland, pp. 225–250. (Scholar)
- ––– (1974). “On the Idea of a General Proof Theory”. In: Synthese 27, pp. 63–77. (Scholar)
- ––– (1985). “Remarks on some Approaches to the Concept of Logical Consequence”. In: Synthese 62, pp. 152–171. (Scholar)
- ––– (2006). “Meaning Approached via Proofs”. In: Synthese 148, pp. 507–524. (Scholar)
- ––– (2007). “Pragmatist and Verificationist Theories of Meaning”. In: The Philosophy of Michael Dummett. Ed. by Randall E. Auxier and Lewis Edwin Hahn. Open Court, pp. 455–481. (Scholar)
- ––– (2013). “An Approach to General Proof Theory and a Conjecture of a Kind of Completeness of Intuitionistic Logic Revisited”. In: Advances in Natural Deduction. Ed. by Edward Hermann Haeusler, Luiz Carlos Pereira, and Valeria de Paiva. Berlin: Springer. (Scholar)
- Read, Stephen (2010). “General-Elimination Harmony and the Meaning of the Logical Constants”. In: Journal of Philosophical Logic 39, pp. 557–576. (Scholar)
- Restall, Greg (2009). “Substructural Logics”. In: The Stanford Encyclopedia of Philosophy. Ed. by Edward N. Zalta. Summer 2009. (Scholar)
- Sambin, Giovanni, Giulia Battilotti, and Claudia Faggian (2000). “Basic Logic: Reflection, Symmetry, Visibility”. In: Journal of Symbolic Logic 65, pp. 979–1013. (Scholar)
- Sandqvist, Tor (2009). “Classical Logic without Bivalence”. In: Analysis 69, pp. 211–218. (Scholar)
- Schroeder-Heister, Peter (1984). “A natural extension of natural deduction”. In: Journal of Symbolic Logic 49, pp. 1284–1300.
- ––– (1991). “Uniform Proof-Theoretic Semantics for Logical Constants (Abstract)”. In: Journal of Symbolic Logic 56, p. 1142. (Scholar)
- ––– (1992). “Cut Elimination in Logics with Definitional Reflection”. In: Nonclassical Logics and Information Processing: International Workshop, Berlin, November 1990, Proceedings (Lecture Notes in Computer Science Vol. 619). Ed. by David Pearce and Heinrich Wansing. Berlin: Springer, pp. 146–171. (Scholar)
- ––– (1993). “Rules of Definitional Reflection”. In: Proceedings of the 8th Annual IEEE Symposium on Logic in Computer Science (Montreal 1993). Los Alamitos: IEEE Press, pp. 222–232. (Scholar)
- ––– (2004). “On the notion of assumption in logical systems”. In: Selected Papers Contributed to the Sections of GAP5, Fifth International Congress of the Society for Analytical Philosophy, Bielefeld, 22-26 September 2003. Ed. by R. Bluhm and C. Nimtz. Paderborn: mentis (Online publication: http://www.gap5.de/proceedings), pp. 27–48. (Scholar)
- ––– (2005). “Popper's Structuralist Theory of Logic”. In: Karl Popper: A Centenary Assessment. Vol. III: Science. Ed. by Ian Jarvie, Karl Milford, and David Miller. Aldershot: Ashgate, pp. 17–36. (Scholar)
- ––– (2006). “Validity Concepts in Proof-Theoretic Semantics”. In: Synthese 148, pp. 525–571. (Scholar)
- ––– (2007). “Generalized Definitional Reflection and the Inversion Principle”. In: Logica Universalis 1, pp. 355–376. (Scholar)
- ––– (2008a). “Lorenzen's Operative Justification of Intuitionistic Logic”. In: One Hundred Years of Intuitionism (1907-2007): The Cerisy Conference. Ed. by Mark van Atten et al. Basel: Birkhäuser, 214–240 [References for whole volume: 391–416]. (Scholar)
- ––– (2008b). “Proof-Theoretic versus Model-Theoretic Consequence”. In: The Logica Yearbook 2007. Ed. by M. Peliš. Prague: Filosofia, pp. 187–200. (Scholar)
- ––– (2012a). “Definitional Reasoning in Proof-Theoretic Semantics and the Square of Opposition.” In: The Square of Opposition: A General Framework for Cognition. Ed. by Jean-Yves Béziau and Gillman Payette. Bern: Peter Lang, pp. 323–349. (Scholar)
- ––– (2012b). “Definitional Reflection and Basic Logic”. In: Annals of Pure and Applied Logic (Special issue, Festschrift 60th Birthday Giovanni Sambin). (Scholar)
- ––– (2012c). “Proof-Theoretic Semantics, Self-Contradiction, and the Format of Deductive Reasoning”. In: Topoi 31, pp. 77–85. (Scholar)
- Shoesmith, D. J. and Timothy J. Smiley (1978). Multiple-Conclusion Logic. Cambridge: Cambridge University Press. (Scholar)
- Sommaruga, Giovanni (2000). History and Philosophy of Constructive Type Theory. Dordrecht: Kluwer. (Scholar)
- Sørensen, Morten Heine B. and Pawel Urzyczyn (2006). Lectures on the Curry-Howard Isomorphism. Amsterdam: Elsevier. (Scholar)
- Tait, W. W: (1967). “Intensional Interpretations of Functionals of Finite Type I”. In: Journal of Symbolic Logic 32, pp. 198–212. (Scholar)
- Tennant, Neil (1978). Natural Logic. Edinburgh: Edinburgh University Press. (Scholar)
- ––– (1982). “Proof and Paradox”. In: Dialectica 36, pp. 265–296. (Scholar)
- ––– (1987). Anti-Realism and Logic: Truth as Eternal. Oxford: Clarendon Press. (Scholar)
- ––– (1997). The Taming of the True. Oxford: Clarendon Press. (Scholar)
- Tranchini, Luca (2011a). “Natural Deduction for Dual Intuitionistic Logic”. In: Studia Logica. (Scholar)
- ––– (2011b). Proof and Truth: An Anti-Realist Perspective. Milano, to appear (available as: Dissertation, Universität Tübingen). (Scholar)
- ––– (2012a). “Truth from a Proof-Theoretic Perspective”. In: Topoi 31, pp. 47–57. (Scholar)
- Troelstra, Anne S. and Dirk van Dalen (1988). Constructivism in Mathematics: An Introduction. Amsterdam: North-Holland. (Scholar)
- Troelstra, A. S. and H. Schwichtenberg (2000). Basic Proof Theory. Cambridge University Press (second edition). (Scholar)
- von Kutschera, Franz (1968). “Die Vollständigkeit des Operatorensystems {¬, ∧, ∨, ⊃} für die intuitionistische Aussagenlogik im Rahmen der Gentzensemantik”. In: Archiv für mathematische Logik und Grundlagenforschung 11, pp. 3–16. (Scholar)
- ––– (1969). “Ein verallgemeinerter Widerlegungsbegrifff für Gentzenkalküle”. In: Archiv für mathematische Logik und Grundlagenforschung 12, pp. 104–118. (Scholar)
- Wansing, Heinrich (1993a). “Functional Completeness for Subsystems of Intuitionistic Propositional Logic”. In: Journal of Philosophical Logic 22, pp. 303–321. (Scholar)
- ––– (1993b). The Logic of Information Structures. Berlin: Springer Springer Lecture Notes in Artificial Intelligence, Vol. 681. (Scholar)
- ––– (2000). “The Idea of a Proof-theoretic Semantics”. In: Studia Logica 64, pp. 3–20. (Scholar)
- ––– (2001). “Negation”. In: The Blackwell Guide to Philosophical Logic. Ed. by L. Goble. Cambridge MA: Blackwell, pp. 415–436. (Scholar)
- Wieckowski, Bartosz (2008). “Predication in Fiction”. In: The Logica Yearbook 2007. Ed. by M. Peliš. Prague: Filosofia, pp. 267–285. (Scholar)
- ––– (2011). “Rules for Subatomic Derivation”. In: Review of Symbolic Logic 4. (Scholar)
- Zeilberger, Noam (2008). “On the Unity of Duality”. In: Annals of Pure and Applied Logic 153, pp. 66–96. (Scholar)
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