{"type":"ScholarlyArticle","title":"The Power of Beliefs or Translating Default Logic into Standard Autoepistemic Logic","authors":[{"name":"Georg Gottlob","slug":"georg-gottlob","given":"Georg","family":"Gottlob","affiliation":"Christian Doppler Lab for Expert Systems , TU Wien Paniglgasse 16 , A-1040 Vienna , Austria"}],"abstract":"Since Konolige's translation of default logic into strongly grounded autoepistemic logic, several other variants of Moore's original autoepistemic logic that embody default logic have been studied . All these logics differ significantly from Moore's autoepistemic logic (standard AEL) in that expansions are subject to additional groundedness-conditions. Hence, the question naturally arises whether default logic can be translated into standard AEL at all. We show, that a modular translation is not possible. However, we exhibit a a faithful polynomial-time translation from propositional default logic into standard AEL which is nonmodular. It follows that the expressive power of standard AEL is strictly greater than that of default logic . Our translation uses as important intermediate step an embedding of Marek's and Truszczynski's nonmonotonic logic N into standard AEL .","doi":null,"url":"https://ijcai.org/proceedings/1993/80","pdf":"https://ijcai.org/proceedings/1993/0080.pdf","markdown":"https://ijcai.org/proceedings/1993/80.md","bibtex":"https://ijcai.org/proceedings/1993/bibtex/80","volume":{"slug":"1993","title":"Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1993","url":"https://ijcai.org/proceedings/1993/","year":1993,"location":"Chambéry, France","dates":"","editors":"Ruzena Bajcsy","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Knowledge Representation","track":"Knowledge Representation","number":80,"pages":{"first":570,"last":576},"keywords":[],"videos":[],"references":[{"position":1,"raw":"J. Delgrande and W. Jackson . Default Logic Revi- sited . In Proc. KR-91","title":"Default Logic Revisited","authors":"J Delgrande, W Jackson","year":null,"venue":"Proc. KR-91","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"Th . Eiter and G . Gottlob Reasoning with Parsimo- nious and Moderately Grounded Expansions. Fun- damenta lnformaticae, 17:31-53, 1992.","title":"Reasoning with Parsimonious and Moderately Grounded Expansions","authors":"Th, G Eiter, Gottlob","year":"1992","venue":"Fundamenta lnformaticae","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"M.C. Fitting, W. Marek, and M. Truszczynski. The Pure Logic of Necessitation . The Journal of Logi c and Computation, 2(3) :349-373, 1992.","title":"The Pure Logic of Necessitation","authors":"M C Fitting, W Marek, M Truszczynski","year":"1992","venue":"The Journal of Logi c and Computation","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"G . Gottlob. The Power of Beliefs: Translating De- fault Logic Into Standard Autoepist~>mic Logic (Ex- tended Report) . Report CD-TR-92/34, TU Wien, Paniglgasse 16, A-1040 Wien, Austria, 1992.","title":"The Power of Beliefs: Translating Default Logic Into Standard Autoepist~>mic Logic (Ex-tended Report)","authors":"G Gottlob","year":"1992","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"G. Gottlob . Complexity Results for Nonmonoto- nic Logics. The Journal of Logic and Computation, 2:3:397-425 , June 1992.","title":"Complexity Results for Nonmonotonic Logics","authors":"G Gottlob","year":"1992","venue":"The Journal of Logic and Computation","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"T . Imielinski . Results on Translating Defaults to Circumscription . In Proc. IJCAI-1985, 1985.","title":"Results on Translating Defaults to Circumscription","authors":"T Imielinski","year":"1985","venue":"Proc. IJCAI-1985","doi":null,"url":null,"internal_url":"/proceedings/1985/21"},{"position":7,"raw":"M. Kaminski . Embedding a Default System into Nonmonotonic Logic . Fundamenta Informaticae, 14:345-354, 1991.","title":"Embedding a Default System into Nonmonotonic Logic","authors":"M Kaminski","year":"1991","venue":"Fundamenta Informaticae","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"K. Konolige. On the Relationship between Default and Autoepistemic Logic . AIJ, 35:343-382, 1988. (+Errata, vol41(1989/90), p .l15 ,1989) .","title":"On the Relationship between Default and Autoepistemic Logic","authors":"K Konolige","year":"1988","venue":"+Errata","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"F. Lin and Y. Shoham . Epistemic Semantics for Fixed-Point Non-Monotonic Logics. In Proc. TARK-90, pp . 111-120. 1990.","title":"Epistemic Semantics for Fixed-Point Non-Monotonic Logics","authors":"F Lin, Y Shoham","year":"1990","venue":"Proc. TARK-90","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"W. Marek, G.F . Schwartz, and M. Truszczynski. Modal Nonmonotonic Logics: Ranges, Characteri- zation, Computation . Proc. KR-91.","title":"Modal Nonmonotonic Logics: Ranges, Characterization","authors":"W Marek, G F Schwartz, M Truszczynski","year":null,"venue":"Computation . Proc. KR-91","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"W. Marek and M. Truszczynski. Relating Autoepi- stemic and Default Logics . In Proc . KR-89.","title":"Relating Autoepistemic and Default Logics","authors":"W Marek, M Truszczynski","year":null,"venue":"Proc . KR-89","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"W. Marek and M. Truszczynski. Modal logic for default reasoning. Annals of Mathematics and Ar- tificial Intelligence, 1:275-302, 1990.","title":"Modal logic for default reasoning","authors":"W Marek, M Truszczynski","year":"1990","venue":"Annals of Mathematics and Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"D. McDermott . Non-Monotoni c Logic II : Nonmo- notonic Modal Theories. JACM, 29:33-57, 1982.","title":"Non-Monotoni c Logic II : Nonmonotonic Modal Theories","authors":"D Mcdermott","year":"1982","venue":"JACM","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"R.C . Moore. Semantical Considerations on Nonmo- notonic Logic. AIJ, 25:75-94, 1985.","title":"Semantical Considerations on Nonmonotonic Logic","authors":"R C Moore","year":"1985","venue":"AIJ","doi":null,"url":null,"internal_url":"/proceedings/1983/67"},{"position":15,"raw":"I. Niemela. Constructive Tightly Grounded Auto- epistemic Reasoning. In Proc. IJCAI-1991, 1991.","title":"Constructive Tightly Grounded Autoepistemic Reasoning","authors":"I Niemela","year":"1991","venue":"Proc. IJCAI-1991","doi":null,"url":null,"internal_url":"/proceedings/1991/60"},{"position":16,"raw":"R. Reiter. A Logic for Default Reasoning. AIJ, 13:81-132, 1980.","title":"A Logic for Default Reasoning","authors":"R Reiter","year":"1980","venue":"AIJ","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"G. Shvarts. Autoepistemic Modal Logics. In Proc. TARK-90, pp. 97-109. 1990.","title":"Autoepistemic Modal Logics","authors":"G Shvarts","year":"1990","venue":"Proc. TARK-90","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"P. Siegel. A Modal Language for Nonmonotonic Lo- gic . In Proc. Workshop DRUMS/'CEE, Mars eille , Fran ce, 1990, 1990.","title":"A Modal Language for Nonmonotonic Logic","authors":"P Siegel","year":"1990","venue":"Proc. Workshop DRUMS/'CEE, Mars eille","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"M. Truszczynski . Modal Interpretations of Default Logic . In Proc. IJCAI-1991 , 1991.","title":"Modal Interpretations of Default Logic","authors":"M Truszczynski","year":"1991","venue":"Proc. IJCAI-1991","doi":null,"url":null,"internal_url":"/proceedings/1991/59"},{"position":20,"raw":"M. Truszczynski . Embedding Default Logic into Modal Nonmonotonic Logics. Proc . Workshop on Nonmon . Reas . and LP, Washington, July 1991 .","title":"Embedding Default Logic into Modal Nonmonotonic Logics","authors":"M Truszczynski","year":"1991","venue":"Proc . Workshop on Nonmon . Reas . and LP","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"Gottlob","title":null,"authors":"Gottlob","year":null,"venue":null,"doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}