{"type":"ScholarlyArticle","title":"Interactive Theorem Proving on Hierarchically and Modularly Structured Set of Very Many Axioms","authors":[{"name":"Michio Honda","slug":"michio-honda","given":"Michio","family":"Honda","affiliation":"Dept. of Information Science Takamatsu"},{"name":"Reiji Nakajima","slug":"reiji-nakajima","given":"Reiji","family":"Nakajima","affiliation":"Kyoto University Research Institute for Mathematical Sciences Kyoto"}],"abstract":"A large number of axioms are often involved in the proof of a single theorem in many realistic applications of mechanical theorem proving such as formal verification of programs whose program domains are determined by user-defined axioms. There, fully automatic proofs are unrealistic due to the obvious constraints though a powerful machine support is highly desired. It is suggested that some meaningful structuring of theories can ease the difficulties. Several strategies are proposed to enhance efficient interactive non-resolution proofs on hierarchicall y and modularly structured theories with many axioms. Use of such strategies is illustrated in their application to verification of hierarchical programs with abstraction mechanisms.","doi":null,"url":"https://ijcai.org/proceedings/1979/86","pdf":"https://ijcai.org/proceedings/1979/0086.pdf","markdown":"https://ijcai.org/proceedings/1979/86.md","bibtex":"https://ijcai.org/proceedings/1979/bibtex/86","volume":{"slug":"1979","title":"Proceedings of the Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1979","url":"https://ijcai.org/proceedings/1979/","year":1979,"location":"Tokyo, Japan","dates":"August 20-23, 1979","editors":"Bruce G. Buchanan","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":86,"pages":{"first":null,"last":null},"keywords":[],"videos":[],"references":[{"position":1,"raw":"Bledsoe,W.W.: Non-resolution theorem proving . Artificial Intelligence 9 '77","title":"Non-resolution theorem proving","authors":"W W Bledsoe","year":null,"venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"Burstall,R., Goguen,J.: Putting theories together to make specifications. IJCAI '77","title":"Putting theories together to make specifications","authors":"R Burstall, J Goguen","year":null,"venue":"IJCAI '77","doi":null,"url":null,"internal_url":"/proceedings/1977/234"},{"position":3,"raw":"Gordon,M., Milner,R., Morris,L., Newey,M., Wadsworth,C.: A metalanguage for interactive proofs in LCF. Proc. Priciples of Prog. Lang. '78","title":"A metalanguage for interactive proofs in LCF","authors":"M Gordon, R Milner, L Morris, M Newey, C Wadsworth","year":null,"venue":"Proc. Priciples of Prog. Lang","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"Honda,M., Nakajima,R.: An interactive theorem proving system for large axiom bases. Res. Inst. for Hath. Sci., Kyoto Univ. '79","title":"An interactive theorem proving system for large axiom bases","authors":"M Honda, R Nakajima","year":null,"venue":"Res. Inst. for Hath. Sci","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"Nakajima,R., Honda,M., Nakahara,H.: Describ- ing and verifying programs with abstract data types. Formal description of Programming Con- cepts. (ed. Neuhold) North-Holland '77","title":"Describing and verifying programs with abstract data types","authors":"R Nakajima, M Honda, H Nakahara","year":null,"venue":"Formal description of Programming Concepts","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"Nakajima,R., Nakahara,H., Honda,M.: Hierar- chical program verification -a many sorted logi- cal approach-. Res. Inst. for Math. Sci., Kyoto Univ. '78","title":"Hierarchical program verification -a many sorted logical approach","authors":"R Nakajima, H Nakahara, M Honda","year":null,"venue":"Res. Inst. for Math. Sci","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"Nelson,C., Oppen,D.C.: Simplification by cooperating decision procedures. AIM-311, Stan- ford A.I. Labo '78","title":"Simplification by cooperating decision procedures. AIM-311","authors":"C Nelson, D C Oppen","year":null,"venue":"Stanford A.I. Labo","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}