Pub Date : 2000-06-26DOI: 10.1109/LICS.2000.855783
Martin Grohe, L. Segoufin
One important class of spatial database queries is the class of topological queries, i.e. queries invariant under homeomorphisms. We study topological queries expressible in the standard query language on spatial databases, first-order logic with various amounts of arithmetic. Our main technical result is a combinatorial characterization of the expressive power of topological first-order logic on regular spatial databases.
{"title":"On first-order topological queries","authors":"Martin Grohe, L. Segoufin","doi":"10.1109/LICS.2000.855783","DOIUrl":"https://doi.org/10.1109/LICS.2000.855783","url":null,"abstract":"One important class of spatial database queries is the class of topological queries, i.e. queries invariant under homeomorphisms. We study topological queries expressible in the standard query language on spatial databases, first-order logic with various amounts of arithmetic. Our main technical result is a combinatorial characterization of the expressive power of topological first-order logic on regular spatial databases.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127242808","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}
Pub Date : 2000-06-26DOI: 10.1109/LICS.2000.855759
Josée Desharnais, Vineet Gupta, R. Jagadeesan, P. Panangaden
We study approximate reasoning about continuous-state labeled Markov processes. We show how to approximate a labeled Markov process by a family of finite-state labeled Markov chains. We show that the collection of labeled Markov processes carries a Polish space structure with a countable basis given by finite state Markov chains with rational probabilities. The primary technical tools that we develop to reach these results are: a finite-model theorem for the modal logic used to characterize bisimulation; and a categorical equivalence between the category of Markov processes (with simulation morphisms) with the /spl omega/-continuous dcpo Proc, defined as the solution of the recursive domain equation Proc=/spl Pi//sub Labels/ P/sub Prob/(Proc). The correspondence between labeled Markov processes and Proc yields a logic complete for reasoning about simulation for continuous-state processes.
{"title":"Approximating labeled Markov processes","authors":"Josée Desharnais, Vineet Gupta, R. Jagadeesan, P. Panangaden","doi":"10.1109/LICS.2000.855759","DOIUrl":"https://doi.org/10.1109/LICS.2000.855759","url":null,"abstract":"We study approximate reasoning about continuous-state labeled Markov processes. We show how to approximate a labeled Markov process by a family of finite-state labeled Markov chains. We show that the collection of labeled Markov processes carries a Polish space structure with a countable basis given by finite state Markov chains with rational probabilities. The primary technical tools that we develop to reach these results are: a finite-model theorem for the modal logic used to characterize bisimulation; and a categorical equivalence between the category of Markov processes (with simulation morphisms) with the /spl omega/-continuous dcpo Proc, defined as the solution of the recursive domain equation Proc=/spl Pi//sub Labels/ P/sub Prob/(Proc). The correspondence between labeled Markov processes and Proc yields a logic complete for reasoning about simulation for continuous-state processes.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114842294","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}
Pub Date : 2000-06-26DOI: 10.1109/LICS.2000.855774
Hiroshi Nakano
We propose a modal logic that enables us to handle self-referential formulae, including ones with negative self-references, which on one hand, would introduce a logical contradiction, namely Russell's paradox, in the conventional setting, while on the other hand, are necessary to capture a certain class of programs such as fixed point combinators and objects with so-called binary methods in object oriented programming. Our logic provides a basis for axiomatic semantics of such a wider range of programs and a new framework for natural construction of recursive programs in the proofs-as-programs paradigm.
{"title":"A modality for recursion","authors":"Hiroshi Nakano","doi":"10.1109/LICS.2000.855774","DOIUrl":"https://doi.org/10.1109/LICS.2000.855774","url":null,"abstract":"We propose a modal logic that enables us to handle self-referential formulae, including ones with negative self-references, which on one hand, would introduce a logical contradiction, namely Russell's paradox, in the conventional setting, while on the other hand, are necessary to capture a certain class of programs such as fixed point combinators and objects with so-called binary methods in object oriented programming. Our logic provides a basis for axiomatic semantics of such a wider range of programs and a new framework for natural construction of recursive programs in the proofs-as-programs paradigm.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114481007","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}
Pub Date : 2000-06-26DOI: 10.1109/LICS.2000.855770
V. Danos, Russell Harmer
A category of HO/N-style games and probabilistic strategies is developed where the possible choices of a strategy are quantified so as to give a measure of the likelihood of seeing a given play. A 2-sided die is shown to be universal in this category, in the sense that any strategy breaks down into a composition between some deterministic strategy and that die. The interpretative power of the category is then demonstrated by delineating a Cartesian closed subcategory which provides a fully abstract model of a probabilistic extension of Idealized Algol.
{"title":"Probabilistic game semantics","authors":"V. Danos, Russell Harmer","doi":"10.1109/LICS.2000.855770","DOIUrl":"https://doi.org/10.1109/LICS.2000.855770","url":null,"abstract":"A category of HO/N-style games and probabilistic strategies is developed where the possible choices of a strategy are quantified so as to give a measure of the likelihood of seeing a given play. A 2-sided die is shown to be universal in this category, in the sense that any strategy breaks down into a composition between some deterministic strategy and that die. The interpretative power of the category is then demonstrated by delineating a Cartesian closed subcategory which provides a fully abstract model of a probabilistic extension of Idealized Algol.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115836806","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}
Pub Date : 2000-06-26DOI: 10.1109/LICS.2000.855760
B. Bloom, W. Fokkink, R. V. Glabbeek
This paper explores the connection between semantic equivalences and preorders for concrete sequential processes, represented by means of labelled transition systems, and formats of transition system specifications using Plotkin's (1981) structural approach. For several preorders in the linear time-branching time spectrum a format is given, as general as possible, such that this preorder is a precongruence for all operators specifiable in that format. The formats are derived using the modal characterizations of the corresponding preorders.
{"title":"Precongruence formats for decorated trace preorders","authors":"B. Bloom, W. Fokkink, R. V. Glabbeek","doi":"10.1109/LICS.2000.855760","DOIUrl":"https://doi.org/10.1109/LICS.2000.855760","url":null,"abstract":"This paper explores the connection between semantic equivalences and preorders for concrete sequential processes, represented by means of labelled transition systems, and formats of transition system specifications using Plotkin's (1981) structural approach. For several preorders in the linear time-branching time spectrum a format is given, as general as possible, such that this preorder is a precongruence for all operators specifiable in that format. The formats are derived using the modal characterizations of the corresponding preorders.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131263344","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}
Pub Date : 2000-06-26DOI: 10.1109/LICS.2000.855772
Mark Reynolds
We continue in the same vein as O. Lichtenstein et al. (1985) in "The Glory of the Past", demonstrating the advantages of including past-time operators in using temporal logic in computer science. A normal form for temporal formulas, based on a simple combination of past formulas, is arrived at via syntactic rewrites and is shown to be a useful alternative to automata based temporal reasoning. The use of the normal form in providing a complete axiomatization for PCTL* (i.e. CTL* with past connectives) is sketched.
{"title":"More past glories [temporal logic]","authors":"Mark Reynolds","doi":"10.1109/LICS.2000.855772","DOIUrl":"https://doi.org/10.1109/LICS.2000.855772","url":null,"abstract":"We continue in the same vein as O. Lichtenstein et al. (1985) in \"The Glory of the Past\", demonstrating the advantages of including past-time operators in using temporal logic in computer science. A normal form for temporal formulas, based on a simple combination of past formulas, is arrived at via syntactic rewrites and is shown to be a useful alternative to automata based temporal reasoning. The use of the normal form in providing a complete axiomatization for PCTL* (i.e. CTL* with past connectives) is sketched.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126721009","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}
Pub Date : 2000-06-26DOI: 10.1109/LICS.2000.855764
Kjell Lemström, L. Hella
A sartorial query language facilitates the formulation of queries to a (string) database. One step towards an implementation of such a query language can be taken by defining a logical formalism expressing a known solution for the particular problem at hand. The simplicity of the logic is a desired property because the simpler the logic that the query language is based on, the more efficiently it can be implemented. We introduce a logical formalism for expressing approximate pattern matching. The formalism uses properties of the dynamic programming approach; a minimizing path of a dynamic programming table is expressed by using a formula in an extension of first-order logic (FO). We consider the well-known problems of k mismatches and k differences. Assuming first that k is given as a part of the input, those problems are expressed by using deterministic transitive closure logic (FO(DTC)) and transitive closure logic (FO(TC)), respectively. We believe that in the general case the k differences is not expressible in FO(DTC), and show that solving this question in the affirmative is at least as hard as separating LOGSPACE from NLOGSPACE. We show, however, that if k is fixed, the k differences problem can be expressed by an FO(DTC)formula.
{"title":"Approximate pattern matching is expressible in transitive closure logic","authors":"Kjell Lemström, L. Hella","doi":"10.1109/LICS.2000.855764","DOIUrl":"https://doi.org/10.1109/LICS.2000.855764","url":null,"abstract":"A sartorial query language facilitates the formulation of queries to a (string) database. One step towards an implementation of such a query language can be taken by defining a logical formalism expressing a known solution for the particular problem at hand. The simplicity of the logic is a desired property because the simpler the logic that the query language is based on, the more efficiently it can be implemented. We introduce a logical formalism for expressing approximate pattern matching. The formalism uses properties of the dynamic programming approach; a minimizing path of a dynamic programming table is expressed by using a formula in an extension of first-order logic (FO). We consider the well-known problems of k mismatches and k differences. Assuming first that k is given as a part of the input, those problems are expressed by using deterministic transitive closure logic (FO(DTC)) and transitive closure logic (FO(TC)), respectively. We believe that in the general case the k differences is not expressible in FO(DTC), and show that solving this question in the affirmative is at least as hard as separating LOGSPACE from NLOGSPACE. We show, however, that if k is fixed, the k differences problem can be expressed by an FO(DTC)formula.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116951904","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}
Pub Date : 2000-06-26DOI: 10.1109/LICS.2000.855775
F. Prost
Dependency analysis aims at identifying how different parts of a program depend on each other. It is the kernel of many issues in program analysis such as dead-code, binding time, strictness, program slicing etc. We address the problem of dependency analysis in the context of typed /spl lambda/-calculus. We consider all systems of the /spl lambda/-cube and extend them conservatively by the addition of new typing rules in order to determine which parts of a /spl lambda/-term may contribute to its evaluation. We show how typing information can be used to statically identify dependencies.
{"title":"A static calculus of dependencies for the /spl lambda/-cube","authors":"F. Prost","doi":"10.1109/LICS.2000.855775","DOIUrl":"https://doi.org/10.1109/LICS.2000.855775","url":null,"abstract":"Dependency analysis aims at identifying how different parts of a program depend on each other. It is the kernel of many issues in program analysis such as dead-code, binding time, strictness, program slicing etc. We address the problem of dependency analysis in the context of typed /spl lambda/-calculus. We consider all systems of the /spl lambda/-cube and extend them conservatively by the addition of new typing rules in order to determine which parts of a /spl lambda/-term may contribute to its evaluation. We show how typing information can be used to statically identify dependencies.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129144310","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}
Pub Date : 2000-06-26DOI: 10.1109/LICS.2000.855753
A. Simpson, G. Plotkin
We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. We then show how iteration operators arise in axiomatic domain theory. One result derives them from the existence of sufficiently many bifree algebras (exploiting the universal property Freyd introduced in his notion of algebraic compactness). Another result shows that, in the presence of a parameterized natural numbers object and an equational lifting monad, any uniform fixed-point operator is necessarily an iteration operator.
{"title":"Complete axioms for categorical fixed-point operators","authors":"A. Simpson, G. Plotkin","doi":"10.1109/LICS.2000.855753","DOIUrl":"https://doi.org/10.1109/LICS.2000.855753","url":null,"abstract":"We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. We then show how iteration operators arise in axiomatic domain theory. One result derives them from the existence of sufficiently many bifree algebras (exploiting the universal property Freyd introduced in his notion of algebraic compactness). Another result shows that, in the presence of a parameterized natural numbers object and an equational lifting monad, any uniform fixed-point operator is necessarily an iteration operator.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115117626","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}
Pub Date : 2000-06-26DOI: 10.1109/LICS.2000.855782
N. Yoshida, M. Hennessy
In wide area distributed systems it is now common for higher-order code to be transferred from one domain to another; the receiving host may initialise parameters and then execute the code in its local environment. We propose a fine-grained typing system for a higher-order /spl pi/-calculus which can be used to control the effect of such migrating code on local environments. Processes may be assigned different types depending on their intended use. This is in contrast to most of the previous work on typing processes where all processes are typed by a unique constant type, indicating essentially that they are well-typed relative to a particular environment. Our process type takes a form of an interface limiting the resources to which it has access, and the types at which they may be used. Allowing resource names to appear both in process types and process terms, as interaction ports, complicates the typing system considerably. For the development of a coherent typing system, we use a kinding technique, similar to that used by the subtyping of the system F, and order-theoretic properties of our subtyping relation. Various examples illustrate the use of our fine-grained typing system for distributed systems. As a specific application we define a new typed behavioural equivalence for the higher-order /spl pi/-calculus. The expressiveness of our types enables us to state and prove interesting identities between typed processes.
{"title":"Assigning types to processes","authors":"N. Yoshida, M. Hennessy","doi":"10.1109/LICS.2000.855782","DOIUrl":"https://doi.org/10.1109/LICS.2000.855782","url":null,"abstract":"In wide area distributed systems it is now common for higher-order code to be transferred from one domain to another; the receiving host may initialise parameters and then execute the code in its local environment. We propose a fine-grained typing system for a higher-order /spl pi/-calculus which can be used to control the effect of such migrating code on local environments. Processes may be assigned different types depending on their intended use. This is in contrast to most of the previous work on typing processes where all processes are typed by a unique constant type, indicating essentially that they are well-typed relative to a particular environment. Our process type takes a form of an interface limiting the resources to which it has access, and the types at which they may be used. Allowing resource names to appear both in process types and process terms, as interaction ports, complicates the typing system considerably. For the development of a coherent typing system, we use a kinding technique, similar to that used by the subtyping of the system F, and order-theoretic properties of our subtyping relation. Various examples illustrate the use of our fine-grained typing system for distributed systems. As a specific application we define a new typed behavioural equivalence for the higher-order /spl pi/-calculus. The expressiveness of our types enables us to state and prove interesting identities between typed processes.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115877554","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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