It is proved that in every undirected graph or, more generally, in every undirected hypergraph of bounded rank, one can specify an orientation of the edges or hyperedges by monadic second-order formulas using quantifications on sets of edges or hyperedges. The proof uses an extension to hypergraphs of the classical notion of a depth-first search spanning tree. Applications are given to the partially open problem of characterizing the classes of graphs (or hypergraphs) having decidable monadic theories, with and without quantifications on sets of edges (or hyperedges).<>
{"title":"Monadic second-order logic and hypergraph orientation","authors":"B. Courcelle","doi":"10.1109/LICS.1993.287589","DOIUrl":"https://doi.org/10.1109/LICS.1993.287589","url":null,"abstract":"It is proved that in every undirected graph or, more generally, in every undirected hypergraph of bounded rank, one can specify an orientation of the edges or hyperedges by monadic second-order formulas using quantifications on sets of edges or hyperedges. The proof uses an extension to hypergraphs of the classical notion of a depth-first search spanning tree. Applications are given to the partially open problem of characterizing the classes of graphs (or hypergraphs) having decidable monadic theories, with and without quantifications on sets of edges (or hyperedges).<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"21 1","pages":"179-190"},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86987590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is shown how to naturally embed, in the typed lambda -calculus with equality, many database query languages, including the relational calculus/algebra, inflationary Datalog, and the complex object calculus/algebra. The embeddings considered are such that a database is a lambda -term coding list of tuples and a query is a lambda -term which when applied to the input database normalizes to the output database. In addition, if the query expressed is a PTIME query, then the normal form can be computed in a number of reduction steps polynomial in the size of the input database. It is also shown that, for all PTIME queries, there is such an embedding in the order-three typed lambda -calculus with equality.<>
{"title":"Database query languages embedded in the typed lambda calculus","authors":"Gerd G. Hillebrand, P. Kanellakis, Harry G. Mairson","doi":"10.1109/LICS.1993.287575","DOIUrl":"https://doi.org/10.1109/LICS.1993.287575","url":null,"abstract":"It is shown how to naturally embed, in the typed lambda -calculus with equality, many database query languages, including the relational calculus/algebra, inflationary Datalog, and the complex object calculus/algebra. The embeddings considered are such that a database is a lambda -term coding list of tuples and a query is a lambda -term which when applied to the input database normalizes to the output database. In addition, if the query expressed is a PTIME query, then the normal form can be computed in a number of reduction steps polynomial in the size of the input database. It is also shown that, for all PTIME queries, there is such an embedding in the order-three typed lambda -calculus with equality.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"68 1","pages":"332-343"},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89331477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A compositional proof systems for a parallel language, P, with dynamic process creation is presented. It is shown how a dynamic system of processes can be described in terms of specifications of the local processes which involve a characterization of their interface with the environment. The proof system formalizes reasoning about these interfaces on an abstraction level that is at least as high as that of the programming language. The programming language P is described, and two assertion languages, the local one and the global one, are defined. The proof system is described and its soundness and completeness are discussed. >
{"title":"A Compositional Proof System for Dynamic Process Creation","authors":"F. S. Boer","doi":"10.1109/LICS.1991.151663","DOIUrl":"https://doi.org/10.1109/LICS.1991.151663","url":null,"abstract":"A compositional proof systems for a parallel language, P, with dynamic process creation is presented. It is shown how a dynamic system of processes can be described in terms of specifications of the local processes which involve a characterization of their interface with the environment. The proof system formalizes reasoning about these interfaces on an abstraction level that is at least as high as that of the programming language. The programming language P is described, and two assertion languages, the local one and the global one, are defined. The proof system is described and its soundness and completeness are discussed. >","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"15 1","pages":"399-405"},"PeriodicalIF":0.0,"publicationDate":"1991-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82662005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"0-1 Laws for Infinitary Logics (Preliminary Report)","authors":"Phokion G. Kolaitis, Moshe Y. Vardi","doi":"10.1109/LICS.1990.113742","DOIUrl":"https://doi.org/10.1109/LICS.1990.113742","url":null,"abstract":"","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"22 1","pages":"156-167"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79369676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Almost all of the categories normally used as a mathematical foundation for denotational semantics satisfy a condition known as consistent completeness. The goal of this paper is to explore the possibility of using a different condition that of coherence which has its origins in topology and logic. In particular, we concentrate on those posets whose principal ideals are algebraic lattices and whose topologies are coherent. These form a cartesian closed category which has fixed points for domain equations. It is shown that a "universal domain" exists. Since the construction of this domain seems to be of general significance, a categorical treatment is provided and its relationship to other applications discussed. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-88-20. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/616 COHERENCE AND CONSISTENCY IN DOMAINS (EXTENDED OUTLINE) Carl A. Gunter Achim Jung MS-CIS-88-20 LlNC LAB 106 Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 191 04
几乎所有通常用作指称语义数学基础的范畴都满足一个称为一致完备性的条件。本文的目的是探讨在拓扑和逻辑中使用不同的相干条件的可能性。特别地，我们集中于那些主理想是代数格且拓扑是相干的偏序集。这就形成了一个笛卡尔闭范畴，它对域方程具有不动点。证明了“普遍域”的存在。由于该领域的构建似乎具有普遍意义，因此提供了分类处理并讨论了其与其他应用的关系。评论宾夕法尼亚大学计算机与信息科学系技术报告编号摩根士丹利资本国际(msci) - 88 - 20。本技术报告可在ScholarlyCommons获取:http://repository.upenn.edu/cis_reports/616 COHERENCE AND CONSISTENCY IN DOMAINS (EXTENDED OUTLINE) Carl A. Gunter Achim Jung MS-CIS-88-20 LlNC LAB 106计算机与信息科学系宾夕法尼亚大学费城工程与应用科学学院，PA 191 2004
{"title":"Coherence and Consistency in Domains (Extended Outline)","authors":"Carl A. Gunter, A. Jung","doi":"10.1109/LICS.1988.5129","DOIUrl":"https://doi.org/10.1109/LICS.1988.5129","url":null,"abstract":"Almost all of the categories normally used as a mathematical foundation for denotational semantics satisfy a condition known as consistent completeness. The goal of this paper is to explore the possibility of using a different condition that of coherence which has its origins in topology and logic. In particular, we concentrate on those posets whose principal ideals are algebraic lattices and whose topologies are coherent. These form a cartesian closed category which has fixed points for domain equations. It is shown that a \"universal domain\" exists. Since the construction of this domain seems to be of general significance, a categorical treatment is provided and its relationship to other applications discussed. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-88-20. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/616 COHERENCE AND CONSISTENCY IN DOMAINS (EXTENDED OUTLINE) Carl A. Gunter Achim Jung MS-CIS-88-20 LlNC LAB 106 Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 191 04","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"266 1","pages":"309-317"},"PeriodicalIF":0.0,"publicationDate":"1988-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76774881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the higher-order rewrite/equational proof systems obtained by adding the simply typed lambda calculus to algebraic rewrite/equational proof systems. We show that if a many-sorted algebraic rewrite system has the Church-Rosser property, then the corresponding higher-order rewrite system which adds simply typed s-reduction has the Church-Rosser property too. This result is relevant to parallel implementations of functional programming languages. We also show that provability in the higher-order equational proof system obtained by adding the simply typed s and η axioms to some many-sorted algebraic proof system is effectively reducible to provability in that algebraic proof system. This effective reduction also establishes transformations between higher-order and algebraic equational proofs, transformations which can be useful in automated deduction. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-88-21. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/617 COMBINING ALGEBRA AND HIGHER-ORDER TYPES Val Breazu-Tannen MS-CIS-88-21 LlNC LAB 107 Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 191 04
{"title":"Combining Algebra and Higher-Order Types","authors":"V. Tannen","doi":"10.1109/LICS.1988.5103","DOIUrl":"https://doi.org/10.1109/LICS.1988.5103","url":null,"abstract":"We study the higher-order rewrite/equational proof systems obtained by adding the simply typed lambda calculus to algebraic rewrite/equational proof systems. We show that if a many-sorted algebraic rewrite system has the Church-Rosser property, then the corresponding higher-order rewrite system which adds simply typed s-reduction has the Church-Rosser property too. This result is relevant to parallel implementations of functional programming languages. We also show that provability in the higher-order equational proof system obtained by adding the simply typed s and η axioms to some many-sorted algebraic proof system is effectively reducible to provability in that algebraic proof system. This effective reduction also establishes transformations between higher-order and algebraic equational proofs, transformations which can be useful in automated deduction. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-88-21. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/617 COMBINING ALGEBRA AND HIGHER-ORDER TYPES Val Breazu-Tannen MS-CIS-88-21 LlNC LAB 107 Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 191 04","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"156 2","pages":"82-90"},"PeriodicalIF":0.0,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91450187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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