Model sets in a nonconstructive logic of partial terms with definite descriptions

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1847 LNAI, Issue , 2000, Pages 268-278

  Gumb, Raymond D ^a  

^a University of Massachusetts Lowell   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEFINITE DESCRIPTIONS; FREE VARIABLE; MODEL SET; MODEL SYSTEM; NATURAL DEDUCTION SYSTEMS; PROOF RULES; TABLEAUX SYSTEMS; HILBERT;

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTERS;

FORMAL LOGIC;

EID: 84886042887     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/10722086_22     Document Type: Conference Paper

References (35)

1. Michael Beeson. Foundations of Constructive Mathematics. Springer, Berlin, 1985.
2. Ermanno Bencievenga, Karel Lambert, and Bas van Fraassen. Logic, Bivalence, and Denotation. Ridgeview, Atascadero, California, second edition, 1991.
3. George S. Boolos and Richard C. Jeffrey. Computability and Logic. Cambridge University Press, Cambridge, 1974.
4. Tyler Burge. Truth and singular terms. In [18], 1991.
5. William M. Farmer. Reasoning about partial functions with the aid of a computer. Erkenntnis, 43:279-294, 1995.
6. Solomon Feferman. Definedness. Erkenntnis, 43:295-320, 1995.
7. L. M. G. Feijs and H. B. M. Jonkers. Formal Specification and Design. Cambridge University Press, Cambridge, 1992.
8. Melvin Fitting. First-Order Logic and Automated Theorem Proving. Springer, New York, second edition, 1996.
9. M. P. Fourman, C. J. Mulvey, and D. S. Scott, editors. Applications of sheaves : Proceedings of the Research Symposium on Applications of Sheaf Theory to Logic, Algebra, and Analysis, Durham, volume 753 of Lecture Notes in Mathematics. Springer, Berlin, 1979.
10. ESPRIT CoFI Working Group. Cofi: The Common Framework Initiative for algebraic specification and development (various documents). Available at http://www.briks.dk/Projects/CoFI.
11. Raymond D. Gumb. Evolving Theories. Haven, New York, 1979.
12. Raymond D. Gumb. An extended joint consistency theorem for free logic with equality. Notre Dame Journal of Formal Logic, 20:321-335, 1979.
13. Abstract in Journal of Symbolic Logic, 42:146, 1977.
14. Raymond D. Gumb. An extended joint consistency theorem for a family of free modal logics with equality. Journal of Symbolic Logic, 49:174-183, 1984.
15. Abstract in Journal of Symbolic Logic, 46:435-436, 1981.
16. Raymond D. Gumb. Programming Logics: An Introduction to Verification and Semantics. Wiley, New York, 1989.
17. Raymond D. Gumb. Free logic in program specification and verification. In E. Morsher, editor, New Directions in Free Logic. Akademia Verlag, Bonn, 1996.
18. Raymond D. Gumb and Karel Lambert. Definitions in nonstrict positive free logic. Modern Logic, 7:25-55, 1997. Corrected version available at http://www.cs.uml.edu/~gumb.
19. C. A. R. Hoare. An axiomatic basis of computer programming. Communications of the ACM, 12:576-583, 1969.
20. K. Lambert, editor. Philosophical Applications of Free Logic. Oxford University Press, Oxford, 1991.
21. Karel Lambert. On the philosophical foundations of free description theory. History and Philosophy of Logic, 8:57-66, 1987.
22. Hugues Leblanc. Truth-Value Semantics. North Holland, Amsterdam, 1976.
23. David L. Parnas. A logic for describing, not verifying, software. Erkenntnis, 43:321-338, 1995.
24. R. A. Pljuškevi?cus. A sequential variant of constructive logic calculi for normal formulas not containing structural rules. In The Calculi of Symbolic Logic, I, Proceedings of the Steklov Institute for Mathematics 98, pages 175-229. AMS Translations, Dordrecht, 1971.
25. Gordon D. Plotkin. Denotational semantics with partial functions. Lecture Notes, CSLI Summer School, Stanford University, July 1985.
26. Gordon D. Plotkin. Types and partial functions. Lecture Notes, Computer Science Department, University of Edinburgh, 1985.
27. Ronald Scales. Attribution and Existence. PhD thesis, University of California, Irvine, 1969.
28. Rolf Schock. Contributions to syntax, semantics, and the philosophy of science. Notre Dame Journal of Formal Logic, 5:241-289, 1964.
29. Rolf Schock. On definitions. Archiv für Mathematische Logik und Grundlagenforschung, 8:28-44, 1965.
30. Rolf Schock. Logics without Existence Assumptions. Almqvist and Wiksell, Stockholm, 1968.
31. Dana S. Scott. Existence and description in formal logic. In R. Schoe0nmann, editor, Bertrand Russell, Philosopher of the Century, pages 181-200. Allen and Unwin, London, 1967. Reprinted in [18].
32. Dana S. Scott. Identity and existence in intuitionistic logic. In [9], pages 660-696, 1979.
33. Neil Tennant. Natural Logic. Edinburgh University Press, Edinburgh, corrected edition, 1990.
34. A. S. Troelstra and D. van Dalen. Constructivity in Mathematics, volume I and II. North-Holland, Amsterdam, 1988.
35. Michael Unterhalt. Kripke-Semantik für Logik mit partieller Existenz. PhD thesis, Westfälische Wilhelms-Universität Münster, 1986.