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<H2>Michael Beeson </H2>
<VAR><H2>Publications in Logic and Theoretical Computer Science </H2>
<P>Numbers in the following list are not consecutive because they are the same as in the <A HREF="pubs.html"><I>List of All Publications</I></A><VAR> </P>
<P>1. Dissertation: <I>The metamathematics of constructive theories of</I> <I>effective operations</I>. Stanford, 1972. </P>
<P>2. The non-derivability in intuitionistic formal systems of theorems on the continuity of effective operations, <I>Journal of Symbolic Logic</I><B> 40</B> (1976) 321-346. </P>
<P>3. The unprovability in intuitionistic formal systems of the continuity of effective operations on the reals, <I>Journal of Symbolic Logic</I> <B>41</B> (1976) 18-24. </P>
<P>4. Derived rules of inference related to the continuity of effective operations, <I>Journal of Symbolic Logic</I> <B>41 </B>(1976) 328-336. </P>
<P>5. Continuity and comprehension in intuitionistic formal systems, <I>Pacific J. Math</I> <B>68 </B>(1977) 29-40. </P>
<P>6. Principles of continuous choice and continuity of functions in formal systems for constructive mathematics, <I>Annals of Mathematical Logic</I> <B>12 </B>(1977) 249-322. </P>
<P>9. A type-free G&ouml;del interpretation, <EM>Journal of Symbolic Logic</EM> {43} (1978) 213-227. </P>
<P>10. Some relations between classical and constructive mathematics, <I>Journal of Symbolic Logic</I> <B>43 </B>(1978) 228-246. </P>
<P>12. Goodman's theorem and beyond,<I> Pacific J. Math</I> <B>84</B> (1979) 1-16. </P>
<P>13. Continuity in intuitionistic set theories, in : Boffa, M., van Dalen, D., and McAloon, K. (eds.), <I>Logic Colloquium '78</I>, pp. 1-53. North-Holland, Amsterdam, 1979. </P>
<P>14. Extensionality and choice in constructive mathematics, <EM>Pacific J. Math</EM><B> 88</B> (1980) 1-28. </P>
<P>16. Formalizing constructive mathematics: why and how?, in Richman, F. (ed.) <I>Constructive Mathematics, Proceedings, New Mexico, 1980</I>}, Lecture Notes in Mathematics <B>873</B>, pp. 146-191, Springer, Berlin, 1981. </P>
<P>17. Problematic principles in constructive mathematics, in: van Dalen, D., Lascar, D., Smiley, J. (eds.), <I>Logic Colloquium '80</I>, pp. 11-55, North-Holland, Amsterdam, 1982. </P>
<P>18. Recursive models for constructive set theories, <I>Annals of Math. Logic</I> <B>23 </B>(1982) 127-178. </P>
<P>21. (with A. Scedrov) Church's thesis, continuity, and set theory,Journal of Symbolic Logic<B> 49</B> (1984) 630-643. </P>
<P>23. <I>Foundations of Constructive Mathematics</I>: <I>Metamathematical Studies</I>, Springer, Berlin/Heidelberg/New York, 1985. </P>
<P>24. Proving programs and programming proofs, in: Barcan, Marcus, Dorn, and Weingartner (eds.), <I>Logic, Methodology, and Philosophy of Science VII</I>, proceedings of the International Congress, Salzburg, 1983, pp. 51-81, North-Holland, Amsterdam (1986). <I>This paper has been translated into French and Russian .</I> </P>
<P>25. Some theories conservative over intuitionistic arithmetic, in:Sieg, W. (ed.) <I>Logic and Computation</I>, volume <B>106</B> in the series <I>Contemporary Mathematics�</I> American Mathematical Society, Providence, R.I. (1987). </P>
<P>26. Computerizing Mathematics: Logic and Computation, in: <I>The Universal Turing Machine: A Half-Century Survey</I>}, edited by Herken, R., Oxford University Press (1988). Second Edition, Springer-Verlag, Berlin/ Heidelberg/ New York (1994) </P>
<P>27. Towards a computation system based on set theory, <I>Theoretical Computer Science</I> <B>60</B> (1988) 297-340. </P>
		<P>35. Constructivism in the Nineties, in: Czermak, J. (ed.), <I>Proceedings of the International Wittgenstein Symposium on Philosophy of Mathematics, Aug. 16-22, 1992</I>. Wittgenstein Society, Vienna (1993). <BR>
<A
href="http://www.cs.sjsu.edu/faculty/beeson/Papers/const92.ps">const92.ps (1 mb, 15 pp.)</A> <BR>
<A
href="http://www.cs.sjsu.edu/faculty/beeson/Papers/const92.ps.gz">const92.ps.gz (300 kb)</A> <BR>
<A
href="http://www.cs.sjsu.edu/faculty/beeson/Papers/const92.pdf">const92.pdf (442 kb)</A></P>
		<P>36. Using nonstandard analysis to verify the correctness of computations, <I>International Journal of Foundations of Computer Science</I>, Vol. 6, No. 3 (1995) 299-338. <BR>
  <A href="nsappt.dvi"> dvi (156 kb, 40 pp.)</A> <BR>
  <A href="nsappt.ps"> ps (3.2 mb, 40 pp.)</A> <BR>
  <A href="nsappt.ps.gz"> ps.gz (663 kb)</A></P>
		<P>41. Reality and Truth in Mathematics, <I>Philosophia Mathematica</I>,1998. <BR>
		    <A href="reality.dvi">ps (153 kb, 38 pp.)</A> <BR>
		    <A href="reality.ps">ps (2 mb, 38 pp.)</A> <BR>
		    <A href="reality.ps.gz">ps.gz (640 kb)</A> </P>
  <P>47. <I>with Freek Wiedijk</I>: The meaning of infinity in calculus and computer algebra systems, in: Calmet, J., <I>et. al.</I> (eds.), <I>Artificial Intelligence, Automated Reasoning, and Symbolic Computation: Joint International Conferences, AISC 2002 and Calculemus 2002, Marseille, France, July 2002, Proceedings,</I> pp. 246-248, Lecture Notes in Artificial Intelligence <B>2385</B>, Springer (2002).</P>
		<P>See paper 52 below for an expanded version. </P>
<P>50. Lambda Logic, in Basin, David; Rusinowitch, Michael (eds.) <em>Automated Reasoning: Second International Joint Conference, IJCAR 2004, Cork, Ireland, July 4-8, 2004, Proceedings. </em> <a href="http://www.springeronline.com/sgw/cda/frontpage/0,11855,4-147-69-1181004-0,00.html">Lecture Notes in Artificial Intelligence</a> <strong>3097</strong>, pp. 460-474, Springer (2004). <br>
  <BR>
  <a href="LambdaLogic.dvi">dvi(62 kb, 15 pages)</a> <BR>
<a href="LambdaLogic.pdf">pdf(131 kb, 15 pages)</a></P>
		<P>This paper gives the theoretical basis for the prover Otter-lambda. </P>
		<P>Two proofs were omitted from this paper to meet the 15-page length limit. Those proofs can be found here:<BR>
            <a href="LambdaLogicExtras.dvi">dvi(24 kb, 6 pages)</a><BR>
            <a href="LambdaLogicExtras.pdf">pdf (84 kb, 6 pages)</a></P>
<P>53. <I>with Robert Veroff and Larry Wos</I>: Double negation elimination in some propositional logics , submitted to <I>Studia Logica</I> in November, 2002. Accepted in October, 2004 for a special issue on Negation in Constructive Logic.<BR>
  <A href="dn.dvi">dvi (141 kb, 41 pages)</A>. <BR>
  <A href="dn.pdf">pdf(185 kb, 41 pages)</A></P>
		<P>This is a paper about logic, published in a logic journal, which contains many computer-generated proofs. </P>
		<P>54. Constructivity, computability, and the continuum. To appear in Sica, Giandomenico (ed.)<em>Advanced Studies in Mathematical Logic</em>, <em>volume 2, </em>Polimetrica, Milan (2005). </P>
		<P><a href="papers/ccc.dvi">dvi(115 kb, 29 pages)</a><br>
            <a href="papers/ccc.pdf">pdf(197 kb, 29 pages)</a></P>
		<P>This is a paper about the philosophy of constructive mathematics, containing some metamathematics, some physics, some philosophy, some history, and some mathematics. It was first presented as an invited talk at the Association for Symbolic Logic's spring meeting at Stanford, March 2005. </P>
		<P>55. Implicit typing in lambda logic, submitted to LPAR-12. That conference will be held in December, 2005. </P>
		<P><a href="ImplicitTyping.dvi">dvi(71 kb, 16 pages)</a><br>
            <a href="ImplicitTyping.pdf">pdf(126 kb, 16 pages)</a></P>
		<P>This theoretical paper addresses the relationship between proofs in a typed logic and proofs in lambda logic such as are found by Otter-lambda. </P>
		<P>59. Constructive geometry, to appear in Arai, T. (ed.) <em>Proceedings of the Tenth Asian Logic Colloquium, Kobe, Japan, 2008, </em>World Scientific, Singapore, 2009. </P>
		<P><a href="ConstructiveGeometry.pdf">pdf (319kb, 35 pages)</a></P>
		<!-- <P>59. Tiling a triangle with congruent triangles. </P>
<P>This draft is still being proofread and checked, and then will be submitted for publication. Comments welcome! </P>
<P><a href="TriangleTiling.pdf">pdf(338 kb, 42 pages)</a><br>
  <a href="TriangleTiling.dvi">dvi(316 kb, 42 pages)</a></P>
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