A relevant analysis of natural deduction

Journal of Logic and Computation

Volumn 8, Issue 6, 1998, Pages 809-838

  Ishtiaq, S S ^a   Pym, D J ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Linear logic; Logical frameworks; Natural deduction; Relevant logic; Type theory

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER PROGRAMMING LANGUAGES; FUNCTIONS; KNOWLEDGE REPRESENTATION;

LINEAR LOGIC; NATURAL DEDUCTION; RELEVANT ANALYSIS; RELEVANT LOGIC; TYPE THEORY;

FORMAL LOGIC;

EID: 0032284273     PISSN: 0955792X     EISSN: None     Source Type: Journal    
DOI: 10.1093/logcom/8.6.809     Document Type: Article

References (41)

1. S. Abramsky. Computational interpretations of linear logic. Theoretical Computer Science, 111, 3-57, 1993.
2. G. Allwein and J. Michael Dunn. Kripke models for linear logic. Journal of Symbolic Logic, 58, 514-545, 1993.
3. A. R. Anderson and J. D. Belnap. Entailment: The Logic of Relevance and Necessity. Princeton University Press, 1975.
4. A. Avron. The semantics and proof theory of linear logic. Theoretical Computer Science, 57, 161-184, 1988.
5. A. Avron, F. Honsell, I. A. Mason and R. Pollack. Using typed lambda calculus to implement formal systems on a machine. Journal of Automated Reasoning, 9, 309-354, 1992.
6. A. Avron, F. Honsell, M. Miculan and C. Paravano. Encoding modal logics in logical frameworks, 1997. Manuscript.
7. H. P. Barendregt. The Lambda Calculus: Its Syntax and Semantics. North-Holland, 1984.
8. H. P. Barendregt. Lambda calculi with types. In Handbook of Logic in Computer Science, Vol. 2, S. Abramsky, D. Gabbay and T. S. E. Maibaum, eds. pp. 118-310. Oxford Science Publications, 1992.
9. P. N. Benton. A mixed linear and non-linear logic: Proofs, terms and models (preliminary report). Technical Report 352, Computer Laboratory, University of Cambridge, 1994.
10. G. M. Bierman. On intuitionistic linear logic. Technical Report 346, University of Cambridge Computer Laboratory, August 1994.
11. I. Cervesato. A Linear Logical Framework. PhD thesis, Università di Torino, 1996.
12. I. Cervesato and F. Pfenning. A linear logical framework. In 11th LICS, New Brunswick, NJ, E Clarke, ed. pp. 264-275. IEEE Computer Society Press, 1996.
13. T. Coquand. An algorithm for testing conversion in type theory. In Logical Frameworks, G. Huet and G. Plotkin, eds. pp. 255-279. Cambridge University Press, 1991.
14. J. M. Dunn. Relevance logic and entailment. In Handbook of Philosophical Logic, Vol. III, D. Gabbay and F. Guenthner, eds. pp. 117-224. D. Reidel, Dordrecht, 1986.
15. R. O. Gandy. Proofs of strong normalization. In To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, J. P. Seldin and J. R. Hindley, eds. pp. 457-478. Academic Press, 1980.
16. J.-Y. Girard. Linear logic. Theoretical Computer Science, 50, 1-102, 1987.
17. J. A. Harland, D. J. Pym and J. Winikoff. Programming in Lygon: An overview. In Algebraic Methodology and Software Technology, M. Wirsing and M. Nivat, eds. pp. 391-405. Vol. 1101 of LNCS, Springer-Verlag, 1996.
18. R. Harper, F. Honsell and G. Plotkin. A framework for defining logics. Journal of the Association for Computing Machinery, 40, 143-184, 1993.
19. R. Harper, D. Sannella and A. Tarlecki. Structured theory representations and logic representations. Annals of Pure and Applied Logic, 67, 113-160, 1994.
20. J. S. Hodas and D. Miller. Logic programming in a fragment of intuitionistic linear logic. Information and Computation, 110, 327-365, 1994.
21. G. Huet and G. Plotkin, eds. Logical Frameworks. Cambridge University Press, 1991.
22. I. Kant. Immanuel Kants Logik (Edited by G. B. Jäsche). Friedrich Nicolovius, Königsberg, 1800. In translation: R. S. Hartman and W. Schwarz, Dover Publications, Inc., 1988.
23. P. Martin-Löf. On the meanings of the logical constants and the justifications of the logical laws. Nordic Journal of Philosophical Logic, 1, 11-60, 1996. (Also: Technical Report 2, Scuola di Specializiazzione in Logica Matematica, Dipartimento di Matematica, Università di Siena, 1982.).
24. P. Martin-Löf. On the meanings of the logical constants and the justifications of the logical laws. Nordic Journal of Philosophical Logic, 1, 11-60, 1996. (Also: Technical Report 2, Scuola di Specializiazzione in Logica Matematica, Dipartimento di Matematica, Università di Siena, 1982.).
25. M. Masseron, C. Tollu and J. Vauzeilles. Generating plans in linear logic. Theoretical Computer Science, 113, 349-370 and 371-375, 1993.
26. R. K. Meyer. Relevant arithmetic. Polish Academy of Sciences, Institute of Philosophy and Bulletin of the Section of logic, 5, 133-137, 1976.
27. J. C. Mitchell and E. Moggi. Kripke-style models for typed lambda calculus. Annals of Pure and Applied Logic, 51, 99-124, 1991.
28. D. Prawitz. Proofs and the meaning and completeness of the logical constants. In Essays on Mathematical and Philosophical Logic, J. Hintikka, J. Nuniluoto and E. Saarinen, eds. pp. 25-40. D. Reidel, Dordrecht, 1978.
29. D. J. Pym. Proofs, Search and Computation in General Logic. PhD thesis, University of Edinburgh, 1990. Available as Edinburgh University Computer Science Department Technical Report ECS-LFCS-90-125.
30. D. J. Pym. A relevant analysis of natural deduction. Lecture at Workshop, EU Espirit Basic Research Action 3245, Logical Frameworks: Design, Implementation and Experiment, Bastad, Sweden, May 1992. (Joint work with D. Miller and G. Plotkin.)
31. D. J. Pym. A note on representation and semantics in logical frameworks. In Proceedings of CADE-13 Workshop on Proof-search in Type-theoretic Languages, Rutgers University, New Brunswick, NJ, D. Galmiche, ed., 1996. (Also: Technical Report 725, Department of Computer Science, Queen Mary & Westfield College, University of London.).
32. D. J. Pym. A note on representation and semantics in logical frameworks. In Proceedings of CADE-13 Workshop on Proof-search in Type-theoretic Languages, Rutgers University, New Brunswick, NJ, D. Galmiche, ed., 1996. (Also: Technical Report 725, Department of Computer Science, Queen Mary & Westfield College, University of London.).
33. D. J. Pym. Functorial Kripke models of the λΠ-calculus, 1997. Lecture at Isaac Newton Institute for Mathematical Sciences, Semantics Programme, Workshop on Categories and Logic Programming, Cambridge, 1995. Paper(s) in preparation.
34. D. J. Pym and J. A. Harland. A uniform proof-theoretic investigation of linear logic programming. Journal of Logic and Computation, 4, 175-207, 1994.
35. S. Read. Relevant Logic: A Philosophical Examination of Inference. Basil Blackwell, 1988.
36. A. Salvesen. A proof of the Church-Rosser property for the Edinburgh LF with η-conversion. Lecture given at the First Workshop on Logical Frameworks, Sophia-Antipolis, France, May 1990.
37. P. Schroeder-Heister. Generalized rules for quantifiers and the completeness of the intuitionistic operators &,∨,⊃,curly logical and sign,∀,∃. In Computation and Proof Theory, Logic Colloquim Aachen, M. M. Richter et al., eds. pp. 399-426. Vol. 1104 of LNM, Springer-Verlag, 1983.
38. P. Schroeder-Heister. Structural frameworks, substructural logics, and the role of elimination inferences. In Logical Frameworks, G. Huet and G. Plotkin, eds. pp. 385-403. Cambridge Univeristy Press, 1991.
39. N. Tennant. Autologic. Edinburgh University Press, 1992.
40. A. S. Troelstra. Lectures on Linear Logic. CSLI, 1992.
41. L. A. Wallen. Automated Deduction in Non-Classical Logics. The MIT Press, Cambridge, MA, 1990.