Abstract
Reasoning theories can be used to specify heterogeneous reasoning systems. In this paper we present an equational version of reasoning theories, and we study their structuring and composition, and the use of annotated assertions for the control of search, as mappings between reasoning theories. We define composability and composition using the notion of faithful inclusion mapping , we define annotated reasoning theories using the notion of erasing mapping , and we lift composability and composition to consider also annotations. As an example, we give a modular specification of the top-level control (known as waterfall ) of NQTHM, the Boyer-Moore theorem prover.
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References
Armando, A., Ranise, S.: From Integrated Reasoning Specialists to “Plug-and-Play” Reasoning Components. In: Calmet, J., Plaza, J. (eds.) AISC 1998. LNCS (LNAI), vol. 1476, p. 42. Springer, Heidelberg (1998); also available as DIST Technical Report 97-0049, University of Genova, Italy
Astesiano, E., Kreowski, H.-J., Krieg-Brückner, B. (eds.): Algebraic Foundations of Systems Specifications. IFIP State-of-the-Art Reports. Springer, Hidleberg (1999)
Bertoli, P.G.: Using OMRS in Practice: A Case Study with ACL2. PhD thesis, University of Rome 3 (1997)
Bertoli, P.G., Calmet, J., Homann, K., Giunchiglia, F.: Specification and Integration of Theorem Provers and Computer Algebra Systems. In: Calmet, J., Plaza, J. (eds.) AISC 1998. LNCS (LNAI), vol. 1476, p. 94. Springer, Heidelberg (1998); also Technical Report 9804-03, IRST, Trento, Italy (April 1998)
Boyer, R.S., Moore, J.S.: A Computational Logic. Academic Press, London (1979)
Boyer, R.S., Moore, J.S.: A Computational Logic Handbook. Academic Press, London (1988)
Burstall, R.M., Goguen, J.A.: The semantics of Clear, a specification language. In: Bjørner, D. (ed.) Abstract Software Specifications. LNCS, vol. 86, pp. 292–332. Springer, Heidelberg (1980)
Clavel, M., Meseguer, J.: Reflection and strategies in rewriting logic. In: Rewriting Logic Workshop 1996. Electronic Notes in Theoretical Computer Science, vol. 4. Elsevier, Amsterdam (1996), http://www.elsevier.nl/locate/entcs/volume4.html
Coglio, A.: The control component of OMRS. Master’s thesis, University of Genova, Italy (1996)
Coglio, A.: Definizione di un formalismo per la specifica delle strategie di inferenza dei sistemi di ragionamento meccanizzato e sua applicazione ad un sistema allo stato dell’arte. Master’s thesis (1996), Master thesis, DIST - University of Genoa (Italy)
Coglio, A., Giunchiglia, F., Pecchiari, P., Talcott, C.: A logic level specification of the nqthm simplification process. Technical report, IRST, University of Genova, Stanford University (1997)
Gentzen, G.: The Collected Papers of Gerhard Gentzen. In: Szabo, M.E. (ed.) North-Holland, Amsterdam (1969)
Giunchiglia, F., Pecchiari, P., Armando, A.: Towards provably correct system synthesis and extension. Future Generation Computer Systems 12(458), 123–137 (1996)
Giunchiglia, F., Pecchiari, P., Talcott, C.: Reasoning theories: Towards an architecture for open mechanized reasoning systems. In: Workshop on Frontiers of Combining Systems FROCOS 1996 (1996)
Goguen, J., Meseguer, J.: Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theoretical Computer Science 105, 217–273 (1992)
Haxthausen, A., Nickl, F.: Pushouts of order-sorted algebraic specifications. In: Nivat, M., Wirsing, M. (eds.) AMAST 1996. LNCS, vol. 1101, pp. 132–148. Springer, Heidelberg (1996)
Martí-Oliet, N., Meseguer, J.: Inclusions and subtypes i: First-order case. J. Logic and Computation 6(3), 409–438 (1996)
Martí-Oliet, N., Meseguer, J.: Rewriting logic as a logical and semantic framework. In: Gabbay, D. (ed.) Handbook of Philosophical Logic. Kluwer Academic Publishers, Dordrecht (1997)
Martin-Löf, P.: Intuitionistic Type Theory. Bibliopolis (1984)
Meseguer, J., Talcott, C.: Reasoning theories and rewriting logic (in preparation)
Meseguer, J., Talcott, C.: Mapping OMRS to Rewriting Logic. In: Kirchner, C., Kirchner, H. (eds.) 2nd International Workshop on Rewriting Logic and its Applications, WRLA 1998. Electronic Notes in Theoretical Computer Science, vol. 15 (1998), http://www.elsevier.nl/locate/entcs/volume15.html
Meseguer, J.: Membership algebra as a semantic framework for equational specification. In: Parisi-Presicce, F. (ed.) WADT 1997. LNCS, vol. 1376, pp. 18–61. Springer, Heidelberg (1998)
Mossakowski, T.: Colimits of order-sorted specifications. In: Parisi-Presicce, F. (ed.) WADT 1997. LNCS, vol. 1376, pp. 316–322. Springer, Heidelberg (1998)
Prawitz, D.: Natural Deduction: A Proof-theoretical Study. Almquist and Wiksell (1965)
Stehr, M.-O., Meseguer, J.: The HOL-Nuprl connection from the viewpoint of general logics. In: SRI International (1999) (manuscript)
Stehr, M.-O., Meseguer, J.: Pure type systems in rewriting logic. In: Workshop on Logical Frameworks and Meta-languages (1999)
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Coglio, A., Giunchiglia, F., Meseguer, J., Talcott, C.L. (2000). Composing and Controlling Search in Reasoning Theories Using Mappings. In: Kirchner, H., Ringeissen, C. (eds) Frontiers of Combining Systems. FroCoS 2000. Lecture Notes in Computer Science(), vol 1794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10720084_14
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DOI: https://doi.org/10.1007/10720084_14
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