Completeness and herbrand theorems for nominal logic

Journal of Symbolic Logic

Volumn 71, Issue 1, 2006, Pages 299-320

  Cheney, James ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645333675     PISSN: 00224812     EISSN: None     Source Type: Journal    
DOI: 10.2178/jsl/1140641176     Document Type: Article

References (46)

1. SERGE ABITEBOUL, RICHARD HULL, and VICTOR VIANU, Foundations of Databases, Addison-Wesley, 1995.
2. H. P. BARENDREGT, The Lambda Calculus, North-Holland, 1984.
3. N. G. DE BRUIJN, Lambda-calculus notation with nameless dummies, a tool for automatic formula manipulation, Indagationes Mathematicae, vol. 34 (1972), no. 5, pp. 381-392.
4. NORBERT BRUNNER, The Fraenkel-Mostowski method, revisited, Notre Dame Journal of Formal Logic, vol. 31 (1990), no. 1, pp. 64-75.
5. st International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science, vol. 3142, Springer-Verlag, 2004, pp. 332-344.
6. _, Nominal logic programming, Ph.D. thesis, Cornell University, Ithaca, NY, August 2004.
7. _, Equivariant unification, Proceedings of the Conference on Rewriting Techniques and Applications (RTA), Lecture Notes in Computer Science, vol. 3467, Springer-Verlag, 2005, pp. 74-89.
8. _, A simpler proof theory for nominal logic, Proceedings of the Conference on Foundations of Software Science and Computation Structures (FOSSACS), Lecture Notes in Computer Science, vol. 3441, Springer-Verlag, 2005, pp. 379-394.
9. th International Conference on Logic Programming (ICLP), Lecture Notes in Computer Science, vol. 3132, Springer-Verlag, 2004, pp. 269-283.
10. ALONZO CHURCH, A formulation of the simple theory of types, this JOURNAL, vol. 5 (1940), pp. 56-68.
11. H. B. CURRY and R. FEYS, Combinatory Logic, North-Holland, 1958.
12. ULRICH FELGNER, Models of ZF-Set Theory, Lecture Notes in Mathematics, vol. 223, Springer-Verlag, 1970.
13. A. FRAENKEL, The concept "definite" and the indepedence of the Auswahlsaxiom, From Frege to Gödel (J. van Heijenoort, editor), Harvard University Press, 1967, pp. 284-289.
14. G. FREGE, Begriffsschrift: A formula language, modeled upon that of arithmetic, for pure thought, From Frege to Gödel (J. van Heijenoort, editor), Harvard University Press, 1967, pp. 1-82.
15. MURDOCH GABBAY, A theory of inductive definitions with alpha-equivalence, Ph.D. thesis, University of Cambridge, 2001.
16. _, FM-HOL, a higher-order theory of names, Workshop on Thirty Five Years of Automath (Heriot Watt, UK) (F. Kamareddine, editor), April 2002.
17. _, Fresh logic: A logic of FM, 2003, preprint.
18. _, A general mathematics of names in syntax, preprint, March 2004.
19. MURDOCH GABBAY and JAMES CHENEY, A sequent calculus for nominal logic, Proceedings of the Annual IEEE Symposium on Logic in Computer Science (LICS) (Turku, Finland), 2004, pp. 139-148.
20. MURDOCH GABBAY and ANDREW PITTS, A new approach to abstract syntax with variable binding, Formal Aspects of Computing, vol. 13 (2002), pp. 341-363.
21. C. A. Gunter and J. C. Mitchell (editors), Theoretical Aspects of Object-Oriented Programming: Types, Semantics, and Language Design, The MIT Press, 1994.
22. ROBERT HARPER, FURIO HONSELL, and GORDON PLOTKIN, A framework for defining logics, Journal of the ACM, vol. 40 (1993), no. 1, pp. 143-184.
23. LEON HENKIN, The completeness of the first-order functional calculus, this JOURNAL, vol. 14 (1949), no. 3, pp. 159-166.
24. JOHN E. HOPCROFT and JEFFREY D. ULLMANN, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 1979.
25. THOMAS J. JECH, About the axiom of choice, Handbook of Mathematical Logic (J. Barwise, editor), North-Holland, 1977, pp. 345-370.
26. FAIROUZ KAMARREDINE, TWAN LAAN, and ROB NEDERPELT, Types in logic and mathematics before 1940, The Bulletin of Symbolic Logic, vol. 8 (2002), no. 2, pp. 185-245.
27. J. R. KENNAWAY, J. W. KLOP, M. R. SLEEP, and F. J. DE VRIES, Infinitary lambda calculus, Theoretical Computer Science, vol. 175 (1997), no. 1, pp. 93-125.
28. GAVIN LOWE, An attack on the Needham-Schroeder public-key authentication protocol. Information Processing Letters, vol. 56 (1995), no. 3, pp. 131-133.
29. SAUNDERS MAC LANE and IEKE MOERDIJK, Sheaves in Geometry and Logic: A First Introduction to Topos Theory, Springer-Verlag, 1992.
30. th Symposium on Logic in Computer Science (LICS), IEEE Press, 2003, pp. 118-127.
31. ROBIN MILNER, JOACHIM PARROW, and DAVID WALKER, A calculus of mobile processes, I-II. Information and Computation, vol. 100 (1992), no. 1, pp. 1-77.
32. ROBIN MILNER, MADS TOFTE, ROBERT HARPER, and DAVID MACQUEEN, The Definition of Standard ML - Revised, MIT Press, 1997.
33. G. MORRISETT and R. HARPER, Semantics of memory management for polymorphic languages, Higher Order Operational Techniques in Semantics, Publications of the Newton Institute. Cambridge University Press, 1997.
34. ROGER M. NEEDHAM and MICHAEL D. SCHROEDER, Using encryption for authentication in large networks of computers, Communications of the ACM, vol. 21 (1978), no. 12, pp. 993-999.
35. FLEMMING NIELSON, HANNE RIIS NIELSON, and CHRIS HANKIN, Principles of Program Analysis, 2nd ed., Springer, 2005.
36. P. O'HEARN and D. J. PYM, The logic of bunched implications, The Bulletin of Symbolic Logic. vol. 5 (1999), no. 2, pp. 215-244.
37. FRANK PFENNING and CONAL ELLIOTT, Higher-order abstract syntax, Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI), ACM Press. 1989, pp. 199-208.
38. A. M. PITTS, Nominal logic, A first order theory of names and binding, Information and Computation, vol. 183 (2003), pp. 165-193.
39. DAG PRAWITZ, Natural Deduction: A Proof-Theoretical Study, Almquist and Wiksell, 1965.
40. GRAHAM PRIEST, An Introduction to Non-Classical Logic, Cambridge University Press, 2001.
41. M. SCHÖNFINKEL, On the building blocks of mathematical logic, From Frege to Gödel (J. van Heijenoort, editor), Harvard University Press, 1967, pp. 355-366.
42. ULRICH SCHÖPP and IAN STARK, A dependent type theory with names and binding, Proceedings of the Computer Science Logic Conference (Karpacz, Poland), Lecture Notes in Computer Science, vol. 3210, Springer-Verlag, 2004, pp. 235-249.
43. JOSEPH E. STOY, Denotational Semantics: The Scott-Strachey Aapproach to Programming Language Ttheory, Series in Computer Systems, vol. 1, MIT Press, 1981.
44. J. K. TRUSS, Permutations and the axiom of choice, Automorphisms of First-Order Structures (Richard Kaye and Dugald Macpherson, editors), Oxford, 1994, pp. 131-152.
45. RENÉ VESTERGAARD and JAMES BROTHERSTON, A formalised first-order confluence proof for the λ-calculus using one-sorted variable names, Information and Computation, vol. 183 (2003), pp. 212-244.
46. LUCA VIGANÓ, Labelled Non-Classical Logics, Kluwer Academic Publishers, 2000.