Abstract
Recent deductive approaches to reasoning about action and chance allow us to model objects and methods in a deductive framework. In these approaches, inheritance of methods comes for free, whereas overriding of methods is unsupported. In this paper, we present an equational logic framework for objects, methods, inheritance and overriding of methods. Overriding is achieved via the concept of specificity, which states that more specific methods are preferred to less specific ones. Specificity is computed with the help of negation as failure. We specify equational logic programs and show that their completed versions behave as intended. Furthermore, we prove that SLDENF-resolution is complete if the equational theory is finitary, the completed programs are consistent and no derivation flounders or is infinite. Moreover, we give syntactic conditions which guarantee that no derivation flounders or is infinite. Finally, we discuss how the approach can be extended to reasoning about the past in the context of incompletely specified objects or situations. It will turn out that constructive negation is needed to solve these problems.
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J-M. Andreoli and R. Pareschi, Linear objects: Logical processes with built-in inheritance, New Generation Comp. 9(3,4) (1991).
K.R. Apt, H.A. Blair and A. Walker, Towards a theory of declarative knowledge, in:Foundations of Deductive Databases and Logic Programming, chap. 2, ed. J. Minker (Kaufmann, 1987) pp. 89–148.
F. Baader and J.H. Siekmann, Unification theory, in:Handbook of Logic in Artificial Intelligence and Logic Programming, eds. D.M. Gabbey, C.J. Hogger and J.A. Robinson (Oxford University Press, 1993).
A.B. Baker, A simple solution to the Yale shooting problem,Proc. Int. Conf. on Knowledge Representation and Reasoning, 1989, pp. 11–20.
A.B. Baker, Nonmonotonic reasoning in the framework of situation calculus, Artificial Intelligence Journal 49(1991)5–23.
W. Bibel, A deductive solution for plan generation, New Generation Comp. 4(1986)115–132.
W. Bibel, Intellectics, in:Encyclopedia of Artificial Intelligence, ed. S.C. Shapiro (Wiley, New York, 1992) pp. 705–706.
D. Chan, Constructive negation based on the completed database,Proc. Int. Joint Conf. and Symp. on Logic Programming (IJCSLP), 1988, pp. 111–125.
K.L. Clark, Negation as failure, in:Workshop Logic and Data Bases, eds. H. Gallaire and J. Minker (Plenum Press, 1978) pp. 293–322.
J.P. Delgrande, A semantically-based account of nonmonotonic reasoning in Horn-clause and logic programming (1992), submitted J. Logic. Progr.
M. Denecker and D. de Schreye, Representing incomplete knowledge in abductive logic programming,Proc. Int. Logic Programming Symposium (ILPS), Vancouver, 1993, ed. D. Miller (MIT Press) pp. 147–163.
P.M. Dung, Representing actions in logic programming and its applications in database updates,Proc. Int. Conf. on Logic Programming (ICLP), Budapest, 1993, ed. D.S. Warren (MIT Press) pp. 222–238.
L. Brownston et al.,Programming Expert Systems in OPS5 (Addison-Wesley, Reading, MA, 1985).
R.E. Fikes and N.J. Nilsson, STRIPS: A new approach to the application of theorem proving to problem solving, Artificial Intelligence Journal 5(1971)189–208.
J.H. Gallier and S. Raatz, Extending SLD-resolution to equational Horn clauses usingE-unification, J. Logic Progr. 6(1989)3–44.
H. Geffner and J. Pearl, Conditional entailment: Bridging two approaches to default reasoning, Artificial Intelligence 53(1992)209–244.
M. Gelfond and V. Lifschitz, Representing action and change by logic programs, J. Logic Progr. 17(1993)301–321.
J.Y. Girard, Linear logic, J. Theor. Comp. Sci. 50(1987)1–102.
G. Große, S. Hölldobler and J. Schneeberger, Linear deductive planning, J. Logic and Comput. (1995), to appear.
G. Große, S. Hölldobler, J. Schneeberger, U. Sigmund and M. Thielscher, Equational logic programming, actions, and change,Proc. Int. Joint Conf. and Symp. on Logic Programming (IJCSLP), Washington, 1992, ed. K. Apt (MIT Press) pp. 177–191.
S. Hanks and D. McDermott, Nonmonotonic logic and temporal projection, Artificial Intelligence Journal 33(1987)379–412.
P. Hoddinott and E.W. Elcock, Prolog: Subsumption of equality axioms by the homogeneous form.Proc. Symp. on Logic Programming (1986) pp. 115–126.
S. Hölldobler,Foundations of Equational Logic Programming, Lecture Notes in Artificial Intelligence 353 (Springer 1989).
S. Hölldobler, On deductive planning and the frame problem,Proc. Int. Conf. Logic Programming and Automated Reasoning (LPAR), Lecture Notes in Artificial Intellegence 624 (Springer, 1993) pp. 13–29.
S. Hölldobler and J. Schneeberger, Deductive approach to planning, New Generation Comp. 8(1990)225–244.
S. Hölldobler and M. Thielscher, Actions and specificity,Proc. Int. Logic Programming Symposium (ILPS), Vancouver, 1993 (MIT Press) pp. 164–180.
S. Hölldobler and M. Thielscher, Properties vs. resources — solving simple frame problems, Technical Report AIDA-94-15, Intellektik, Informatik, TH Darmstadt (1994).
J. Jaffar, J.-L. Lassez and J. Lloyd, Completeness of the negation as failure rule,Proc. Int. Joint. Conf. on Artificial Intelligence (IJCAI), 1983, pp. 500–506.
J. Jaffar, J.-L. Lassez and M.J. Maher, A theory of complete logic programs with equality, J. Logic Progr. 1(1984)211–223.
G. Jäger and R.F. Stärk, The defining powers of stratified and hierarchical logic programs, J. Logic Progr. 15(1993)55–77.
G.N. Kartha, Soundness and completeness theorems for three formalizations of actions,Proc. Int. Joint Conf. on Artificial Intelligence (IJCAI), Chambéry, France, 1993 (Kaufmann) pp. 724–729.
R. Kowalski,Logic for Problem solving, Vol. 7 of Artificial Intelligence Series (Elsevier, 1979).
V. Lifschitz, On the semantics of STRIPS,Proc. Workshop on Reasoning about Actions and Plans, eds. M.P. Georgeff and A.L. Lansky (Kaufmann, 1986).
J.W. Lloyd,Foundations of Logic Programming, Symbolic Computation Series, 2nd extended ed. (Springer, 1987).
M. Masseron, C. Tollu and J. Vauzielles, Generating plans in linear logic, in:Foundations of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science 472 (Springer, 1990) pp. 63–75.
J. McCarthy, Situations and actions and causal laws, Memo 2, Stanford Artificial Intelligence Project (1963).
J. McCarthy, Circumscription — A form of non-monotonic reasoning, Artificial Intelligence Journal 13(1980)27–39.
J. McCarthy, Applications of circumscription to formalizing common-sense knowledge, Artificial Intelligence Journal 28(1986)89–116.
J. McCarthy and P.J. Hayes, Some philosophical problems from the standpoint of artificial intelligence, Machine Intelligence 4(1969)463–502.
E. Pednault, ADL: Exploring the middle ground between STRIPS and the situation calculus,Proc. Int. Conf. on Principles of Knowledge Representation and Reasoning (KR), 1989, eds. R. Brachman, H. Levesque and R. Reiter, pp. 324–332.
R. Reiter, The frame problem in the situation calculus: A simple solution (sometimes) and a completeness result for goal regression, in:Artificial Intelligence and Mathematical Theory of Computation, ed. V. Lifschitz (Academic Press, 1991) pp. 359–380.
R. Reiter, Formalizing database evolution in the situation calculus,Proc. Int. Conf. on Fifth Generation Computer Systems, 1992.
E. Sandewall, Features and fluents, Technical Report LiTH-IDA-R-92-30, Institutionen för datavetenskap, Univeritetet och Tekniska högskolan i Linköping, Schweden (1992).
E. Sandewall, The range of applicability of nonmonotonic logics for the inertia problem,Proc. Int. Joint Conf. on Artificial Intelligence (IJCAI), Chambéry, France, 1993 (Kaufmann) pp. 738–743.
T. Sato, Completed logic programs and their consistency, J. Logic Progr. 9(1990)33–44.
J. Schneeberger, Plan generation by linear deduction, Ph.D. Thesis, FG Intellektik, TH Darmstadt (1992).
J.C. Shepherdson, Negation in logic programming for general logic programs, in:Foundations of Deductive Databases and Logic Programming, chap. 1, ed. J. Minker (Kaufmann, 1987) pp. 19–88.
J.C. Shepherdson, SLDNF-resolution with equality, J. Autom. Reasoning 8(1992)297–306.
J.H. Siekmann, Unification theory, J. Symb. Comput. 7(1989)207–274. Special issue on unification.
K. Stroetmann, A completeness result for SLDNF-resolution, J. Logic Progr. 15(1993)337–355.
M. Thielscher, An analysis of systematic approaches to reasoning about actions and change,Int. Conf. on Artificial Intelligence: Methodology, Systems, Applications (AIMSA), Sofia, Bulgaria, 1994, ed. P. Jorrand (World Scientific, Singapore). Available by anonymous ftp from 130.83.26.1 in /pub/AIDA/Tech-Reports/OTHER.
M. Thielscher, Representing actions in equational logic programming,Proc. Int. Conf. on Logic Programming (ICLP), Santa Margherita Ligure, Italy, 1994, ed. P. Van Hentenryck (MIT Press) pp. 207–225.
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Hölldobler, S., Thielscher, M. Computing change and specificity with equational logic programs. Ann Math Artif Intell 14, 99–133 (1995). https://doi.org/10.1007/BF01530895
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DOI: https://doi.org/10.1007/BF01530895