hitzler.bbl
\begin{thebibliography}{10}

\bibitem{ABW88}
Krzysztof~R. Apt, Howard~A. Blair, and Adrian Walker.
\newblock Towards a theory of declarative knowledge.
\newblock In Jack Minker, editor, {\em Foundations of Deductive Databases and
  Logic Programming}, pages 89--148. Morgan Kaufmann, Los Altos, CA, 1988.

\bibitem{BH0xjal}
Sebastian Bader and Pascal Hitzler.
\newblock Logic programs, iterated function systems, and recurrent radial basis
  function networks.
\newblock {\em Journal of Applied Logic}, 200x.
\newblock To appear.

\bibitem{BS89b}
Aida Batarekh and V.S. Subrahmanian.
\newblock The query topology in logic programming.
\newblock In {\em Proceedings of the 1989 Symposium on Theoretical Aspects of
  Computer Science}, volume 349 of {\em Lecture Notes in Computer Science},
  pages 375--387. Springer, Berlin, 1989.

\bibitem{BS89a}
Aida Batarekh and V.S. Subrahmanian.
\newblock Topological model set deformations in logic programming.
\newblock {\em Fundamenta Informaticae}, 12:357--400, 1989.

\bibitem{Blaetal97}
Howard~A. Blair, Jagan Chidella, Fred Dushin, Audrey Ferry, and Polar Humenn.
\newblock A continuum of discrete systems.
\newblock {\em Annals of Mathematics and Artificial Intelligence}, pages
  153--186, 1997.

\bibitem{BNN91}
Stefan Bonnier, Ulf Nilsson, and Torbj\"orn N\"aslund.
\newblock A simple fixed point characterization of three-valued stable model
  semantics.
\newblock {\em Information Processing Letters}, 40(2):73--78, 1991.

\bibitem{BDFZ01}
Stefan Brass, J\"{u}rgen Dix, Burkhardt Freitag, and Ulrich Zukowski.
\newblock Transformation-based bottom-up computation of the well-founded model.
\newblock {\em Theory and Practice of Logic Programming}, 1(5):497--538, 2001.

\bibitem{BS01}
Anthony Browne and Ron Sun.
\newblock Connectionist inference models.
\newblock {\em Neural Networks}, 14(10):1331--1355, 2001.

\bibitem{Bry90}
Fran{\c{c}}ois Bry.
\newblock Negation in logic programming: A formalization in constructive logic.
\newblock In Dimitris Karagiannis, editor, {\em Information Systems and
  Artificial Intelligence: Integration Aspects, First Workshop, Ulm, FRG, March
  19-21, 1990, Proceedings}, volume 474 of {\em Lecture Notes in Computer
  Science}, pages 30--46. Springer, 1991.

\bibitem{Cav91}
Lawrence Cavedon.
\newblock Acyclic programs and the completeness of {SLDNF}-resolution.
\newblock {\em Theoretical Computer Science}, 86:81--92, 1991.

\bibitem{Cla78}
Keith~L. Clark.
\newblock Negation as failure.
\newblock In Herv{\'e} Gallaire and Jack Minker, editors, {\em Logic and Data
  Bases}, pages 293--322. Plenum Press, New York, 1978.

\bibitem{ABG01}
Artur~S. d'Avila Garcez, Krysia Broda, and Dov~M. Gabbay.
\newblock Symbolic knowledge extraction from trained neural networks: {A} sound
  approach.
\newblock {\em Artificial Intelligence}, 125:155--207, 2001.

\bibitem{ABG02}
Artur~S. d'Avila Garcez, Krysia~B. Broda, and Dov~M. Gabbay.
\newblock {\em Neural-Symbolic Learning Systems --- Foundations and
  Applications}.
\newblock Perspectives in Neural Computing. Springer, Berlin, 2002.

\bibitem{AZ99}
Artur~S. d'Avila Garcez and Gerson Zaverucha.
\newblock The connectionist inductive lerarning and logic programming system.
\newblock {\em Applied Intelligence, Special Issue on Neural networks and
  Structured Knowledge}, 11(1):59--77, 1999.

\bibitem{DK89}
Phan~Minh Dung and Kanchana Kanchanasut.
\newblock A fixpoint approach to declarative semantics of logic programs.
\newblock In Ewing~L. Lusk and Ross~A. Overbeek, editors, {\em Logic
  Programming, Proceedings of the North American Conference 1989, NACLP'89,
  Cleveland, Ohio}, pages 604--625. MIT Press, 1989.

\bibitem{Fit85}
Melvin Fitting.
\newblock A {K}ripke-{K}leene-semantics for general logic programs.
\newblock {\em The Journal of Logic Programming}, 2:295--312, 1985.

\bibitem{Fit94}
Melvin Fitting.
\newblock Metric methods: Three examples and a theorem.
\newblock {\em The Journal of Logic Programming}, 21(3):113--127, 1994.

\bibitem{FitTCS}
Melvin Fitting.
\newblock Fixpoint semantics for logic programming --- {A} survey.
\newblock {\em Theoretical Computer Science}, 278(1--2):25--51, 2002.

\bibitem{Fun89}
Ken-Ichi Funahashi.
\newblock On the approximate realization of continuous mappings by neural
  networks.
\newblock {\em Neural Networks}, 2:183--192, 1989.

\bibitem{GL88}
Michael Gelfond and Vladimir Lifschitz.
\newblock The stable model semantics for logic programming.
\newblock In Robert~A. Kowalski and Kenneth~A. Bowen, editors, {\em Logic
  Programming. Proceedings of the 5th International Conference and Symposium on
  Logic Programming}, pages 1070--1080. MIT Press, 1988.

\bibitem{GH92}
Hans~W. G{\"u}sgen and Steffen H{\"o}lldobler.
\newblock Connectionist inference systems.
\newblock In Bertram Fronh{\"o}fer and Graham Wrightson, editors, {\em
  Parallelization in Inference Systems}, volume 590 of {\em Lecture Notes in
  Artificial Intelligence}, pages 82--120. Springer, Berlin, 1992.

\bibitem{thesis}
Pascal Hitzler.
\newblock {\em Generalized Metrics and Topology in Logic Programming
  Semantics}.
\newblock PhD thesis, Department of Mathematics, National University of
  Ireland, University College Cork, 2001.

\bibitem{HHS0xjal}
Pascal Hitzler, Steffen H{\"o}lldobler, and Anthony~K. Seda.
\newblock Logic programs and connectionist networks.
\newblock {\em Journal of Applied Logic}, 200x.
\newblock To appear.

\bibitem{HS99d}
Pascal Hitzler and Anthony~K. Seda.
\newblock Acceptable programs revisited.
\newblock In {\em Proceedings of the Workshop on Verification in Logic
  Programming, 16th Int. Conf. on Logic Programming, ICLP'99, Las Cruces, New
  Mexico}, volume~30 of {\em Electronic Notes in Theoretical Computer Science},
  pages 1--18. Elsevier, 1999.

\bibitem{HS99b}
Pascal Hitzler and Anthony~K. Seda.
\newblock The fixed-point theorems of {P}riess-{C}rampe and {R}ibenboim in
  logic programming.
\newblock In {\em Valuation Theory and its Applications, Proceedings of the
  1999 Valuation Theory Conference, University of Saskatchewan in Saskatoon,
  Canada}, volume~32 of {\em Fields Institute Communications Series}, pages
  219--235. American Mathematical Society, 1999.

\bibitem{HS99e}
Pascal Hitzler and Anthony~K. Seda.
\newblock Some issues concerning fixed points in computational logic:
  Quasi-metrics, multivalued mappings and the {K}naster-{T}arski theorem.
\newblock In {\em Proceedings of the 14th Summer Conference on Topology and its
  Applications: Special Session on Topology in Computer Science, New York},
  volume~24 of {\em Topology Proceedings}, pages 223--250, 1999.

\bibitem{HS00e}
Pascal Hitzler and Anthony~K. Seda.
\newblock A new fixed-point theorem for logic programming semantics.
\newblock In {\em Proceedings of the joint IIIS \& IEEE meeting of the 4th
  World Multiconference on Systemics, Cybernetics and Informatics, SCI2000, and
  the 6th International Conference on Information Systems Analysis and
  Synthesis, ISAS2000, Orlando, Florida, USA}, volume VII, Computer Science and
  Engineering Part 1, pages 418--423. International Institute of Informatics
  and Systemics: IIIS, 2000.

\bibitem{HS03}
Pascal Hitzler and Anthony~K. Seda.
\newblock Continuity of semantic operators in logic programming and their
  approximation by artificial neural networks.
\newblock In Andreas G{\"u}nter, Rudolf Krause, and Bernd Neumann, editors,
  {\em Proceedings of the 26th German Conference on Artificial Intelligence,
  KI2003}, volume 2821 of {\em Lecture Notes in Artificial Intelligence}, pages
  105--119. Springer, 2003.

\bibitem{HS03tcs}
Pascal Hitzler and Anthony~K. Seda.
\newblock Generalized metrics and uniquely determined logic programs.
\newblock {\em Theoretical Computer Science}, 305(1--3):187--219, 2003.

\bibitem{Hol93}
Steffen H{\"o}lldobler.
\newblock {\em Automated Inferencing and Connectionist Models}.
\newblock Fakult{\"a}t Informatik, Technische Hochschule Darmstadt, 1993.
\newblock Habilitationsschrift.

\bibitem{HK94}
Steffen H\"olldobler and Yvonne Kalinke.
\newblock Towards a massively parallel computational model for logic
  programming.
\newblock In {\em Proceedings ECAI94 Workshop on Combining Symbolic and
  Connectionist Processing}, pages 68--77. ECCAI, 1994.

\bibitem{HKS99}
Steffen H{\"ol}ldobler, Yvonne Kalinke, and Hans-Peter St\"orr.
\newblock Approximating the semantics of logic programs by recurrent neural
  networks.
\newblock {\em Applied Intelligence}, 11:45--58, 1999.

\bibitem{HSW89}
Kurt Hornik, Maxwell Stinchcombe, and Halbert White.
\newblock Multilayer feedforward networks are universal approximators.
\newblock {\em Neural Networks}, 2:359--366, 1989.

\bibitem{LL03}
Joohyung Lee and Vladimir Lifschitz.
\newblock Loop formulas for disjunctive logic programs.
\newblock In Catuscia Palamidessi, editor, {\em Logic Programming, 19th
  International Conference, ICLP 2003, Mumbai, India, December 2003,
  Proceedings}, volume 2916 of {\em Lecture Notes in Computer Science}, pages
  451--465. Springer, 2003.

\bibitem{LZ03}
Fangzhen Lin and Jicheng Zhao.
\newblock On tight logic programs and yet another translation from normal logic
  programs to propositional logic.
\newblock In Georg Gottlob and Toby Walsh, editors, {\em Proceedings of the
  18th International Joint Conference on Artificial Intelligence, Acapulco,
  Mexico, August 2003}, pages 853--858. Morgan Kaufmann Publishers, 2003.

\bibitem{LZ02}
Fangzhen Lin and Yiting Zhao.
\newblock {ASSAT:} {C}omputing answer sets of a logic program by {SAT} solvers.
\newblock In {\em Proceedings of the Eighteenth National Conference on
  Artificial Intelligence and Fourteenth Conference on Innovative Applications
  of Artificial Intelligence, July/August, 2002, Edmonton, Alberta, Canada},
  pages 112--118. AAAI Press, 2002.

\bibitem{Llo88}
John~W. Lloyd.
\newblock {\em Foundations of Logic Programming}.
\newblock Springer, Berlin, 1988.

\bibitem{Mah88}
Michael~J. Maher.
\newblock Equivalences of logic programs.
\newblock In Jack Minker, editor, {\em Foundations of Deductive Databases and
  Logic Programming}, pages 627--658. Morgan Kaufmann, Los Altos, CA, 1988.

\bibitem{CP43}
Warren~S. Mc{C}ulloch and Walter Pitts.
\newblock A logical calculus of the ideas immanent in nervous activity.
\newblock {\em Bulletin of Mathematical Biophysics}, 5:115--133, 1943.

\bibitem{Pin91a}
Gadi Pinkas.
\newblock Propositional non-monotonic reasoning and inconsistency in symmetric
  neural networks.
\newblock In John Mylopoulos and Raymond Reiter, editors, {\em Proceedings of
  the 12th International Joint Conference on Artificial Intelligence}, pages
  525--530. Morgan Kaufmann, 1991.

\bibitem{Plo78}
Gordon Plotkin.
\newblock {${T}^\omega$} as a universal domain.
\newblock {\em Journal of Computer and System Sciences}, 17:209--236, 1978.

\bibitem{Pol90}
Jordan~B. Pollack.
\newblock Recursive distributed representations.
\newblock {\em Artificial Intelligence}, 46(1):77--105, 1990.

\bibitem{PR00a}
Sibylla Prie\ss{}-Crampe and Paolo Ribenboim.
\newblock Ultrametric spaces and logic programming.
\newblock {\em The Journal of Logic Programming}, 42:59--70, 2000.

\bibitem{Prz88}
Teodor~C. Przymusinski.
\newblock On the declarative semantics of deductive databases and logic
  programs.
\newblock In Jack Minker, editor, {\em Foundations of Deductive Databases and
  Logic Programming}, pages 193--216. Morgan Kaufmann, Los Altos, CA, 1988.

\bibitem{Sed95}
Anthony~K. Seda.
\newblock Topology and the semantics of logic programs.
\newblock {\em Fundamenta Informaticae}, 24(4):359--386, 1995.

\bibitem{Sed97}
Anthony~K. Seda.
\newblock Quasi-metrics and the semantics of logic programs.
\newblock {\em Fundamenta Informaticae}, 29(1):97--117, 1997.

\bibitem{SH97}
Anthony~K. Seda and Pascal Hitzler.
\newblock Topology and iterates in computational logic.
\newblock In {\em Proceedings of the 12th Summer Conference on Topology and its
  Applications: Special Session on Topology in Computer Science, Ontario,
  August 1997}, volume~22 of {\em Topology Proceedings}, pages 427--469, 1997.

\bibitem{Sha99}
Lokenda Shastri.
\newblock Advances in {S}hruti --- {A} neurally motivated model of relational
  knowledge representation and rapid inference using temporal synchrony.
\newblock {\em Applied Intelligence}, 11:78--108, 1999.

\bibitem{TS94}
Geoffrey~G. Towell and Jude~W. Shavlik.
\newblock Knowledge-based artificial neural networks.
\newblock {\em Artificial Intelligence}, 70(1--2):119--165, 1994.

\bibitem{GRS91}
Allen van Gelder, Kenneth~A. Ross, and John~S. Schlipf.
\newblock The well-founded semantics for general logic programs.
\newblock {\em Journal of the ACM}, 38(3):620--650, 1991.

\bibitem{Wen02b}
Matthias Wendt.
\newblock Unfolding the well-founded semantics.
\newblock {\em Journal of Electrical Engineering, Slovak Academy of Sciences},
  53(12/s):56--59, 2002.
\newblock (Proceedings of the 4th Slovakian Student Conference in Applied
  Mathematics, Bratislava, April 2002)\footnote{Available online as
  \cite{Wen02tr}.}.

\bibitem{Wen02tr}
Matthias Wendt.
\newblock Unfolding the well-founded semantics.
\newblock Technical Report WV--02--08, Knowledge Representation and Reasoning
  Group, Department of Computer Science, Dresden University of Technology,
  2002.
\newblock http://www.wv.inf.tu-dresden.de/Publications/2002/.

\bibitem{Wil70}
Stephen Willard.
\newblock {\em General Topology}.
\newblock Addison-Wesley, Reading, MA, 1970.

\end{thebibliography}
