Pub Date : 1992-06-22DOI: 10.1109/LICS.1992.185530
J. Talpin, P. Jouvelot
The type and effect discipline, a framework for reconstructing the principal type and the minimal effect of expressions in implicitly typed polymorphic functional languages that support imperative constructs, is introduced. The type and effect discipline outperforms other polymorphic type systems. Just as types abstract collections of concrete values, effects denote imperative operations on regions. Regions abstract sets of possibly aliased memory locations. Effects are used to control type generalization in the presence of imperative constructs while regions delimit observable side effects. The observable effects of an expression range over the regions that are free in its type environment and its type; effects related to local data structures can be discarded during type reconstruction. The type of an expression can be generalized with respect to the variables that are not free in the type environment or in the observable effect.<>
{"title":"The type and effect discipline","authors":"J. Talpin, P. Jouvelot","doi":"10.1109/LICS.1992.185530","DOIUrl":"https://doi.org/10.1109/LICS.1992.185530","url":null,"abstract":"The type and effect discipline, a framework for reconstructing the principal type and the minimal effect of expressions in implicitly typed polymorphic functional languages that support imperative constructs, is introduced. The type and effect discipline outperforms other polymorphic type systems. Just as types abstract collections of concrete values, effects denote imperative operations on regions. Regions abstract sets of possibly aliased memory locations. Effects are used to control type generalization in the presence of imperative constructs while regions delimit observable side effects. The observable effects of an expression range over the regions that are free in its type environment and its type; effects related to local data structures can be discarded during type reconstruction. The type of an expression can be generalized with respect to the variables that are not free in the type environment or in the observable effect.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"18 1","pages":"162-173"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74934165","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 : 1992-06-22DOI: 10.1109/LICS.1992.185518
Phokion G. Kolaitis, Moshe Y. Vardi
The relationship between fixpoint logic and the infinitary logic L/sub infinity omega //sup omega / with a finite number of variables is studied. It is observed that the equivalence of two finite structures with respect to L/sub infinity omega //sup omega / is expressible in fixpoint logic. As a first application of this, a normal-form theorem for L infinity /sub omega //sup omega / on finite structures is obtained. The relative expressive power of first-order logic, fixpoint logic, and L/sub infinity omega //sup omega / on arbitrary classes of finite structures is examined. A characterization of when L/sub infinity omega //sup omega / collapses to first-order logic on an arbitrary class of finite structures is given.<>
{"title":"Fixpoint logic vs. infinitary logic in finite-model theory","authors":"Phokion G. Kolaitis, Moshe Y. Vardi","doi":"10.1109/LICS.1992.185518","DOIUrl":"https://doi.org/10.1109/LICS.1992.185518","url":null,"abstract":"The relationship between fixpoint logic and the infinitary logic L/sub infinity omega //sup omega / with a finite number of variables is studied. It is observed that the equivalence of two finite structures with respect to L/sub infinity omega //sup omega / is expressible in fixpoint logic. As a first application of this, a normal-form theorem for L infinity /sub omega //sup omega / on finite structures is obtained. The relative expressive power of first-order logic, fixpoint logic, and L/sub infinity omega //sup omega / on arbitrary classes of finite structures is examined. A characterization of when L/sub infinity omega //sup omega / collapses to first-order logic on an arbitrary class of finite structures is given.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"57 1","pages":"46-57"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85587875","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 : 1992-06-22DOI: 10.1109/LICS.1992.185540
Y. Toyama
G. Huet and J.J. Levy (INRIA Rep. 359, 1979) showed that for every strongly sequential orthogonal (i.e., left-linear and non-overlapping) term rewriting system, index reduction strategy is normalizing. Their result is extended to overlapping term rewriting systems. It is shown that index reduction is normalizing for the class of strongly sequential left-linear term rewriting systems in which every critical pair can be joined with root balanced reductions. This class includes all weakly orthogonal left-normal systems, for which a leftmost-outermost reduction strategy is normalizing.<>
G. Huet和J.J. Levy (INRIA Rep. 359, 1979)表明，对于每一个强序列正交(即左线性和非重叠)项重写系统，索引约简策略都是归一化的。将其结果推广到重叠项重写系统。证明了一类强序列左线性项重写系统的索引约简是规范化的，其中每个关键对都可以用根平衡约简连接。该类包括所有弱正交左正规系统，其中最左最外约简策略是归一化。
{"title":"Strong sequentiality of left-linear overlapping term rewriting systems","authors":"Y. Toyama","doi":"10.1109/LICS.1992.185540","DOIUrl":"https://doi.org/10.1109/LICS.1992.185540","url":null,"abstract":"G. Huet and J.J. Levy (INRIA Rep. 359, 1979) showed that for every strongly sequential orthogonal (i.e., left-linear and non-overlapping) term rewriting system, index reduction strategy is normalizing. Their result is extended to overlapping term rewriting systems. It is shown that index reduction is normalizing for the class of strongly sequential left-linear term rewriting systems in which every critical pair can be joined with root balanced reductions. This class includes all weakly orthogonal left-normal systems, for which a leftmost-outermost reduction strategy is normalizing.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"30 1","pages":"274-284"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85957305","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 : 1992-06-22DOI: 10.1109/LICS.1992.185517
G. Schwarz
Intuitively clear Kripke-style semantics for nonmonotonic modal logic are provided. Minimal model semantics is defined, and soundness and completeness of the semantics for nonmonotonic modal logics are proved. It is shown how the semantics looks for some most popular or most interesting modal logics. Applications to finding expansions and comparing nonmonotonic logics based on different monotonic modal logics are presented. A few examples of using the semantics for obtaining intuitively clear proofs of some results of nonmonotonic modal logics are given.<>
{"title":"Minimal model semantics for nonmonotonic modal logics","authors":"G. Schwarz","doi":"10.1109/LICS.1992.185517","DOIUrl":"https://doi.org/10.1109/LICS.1992.185517","url":null,"abstract":"Intuitively clear Kripke-style semantics for nonmonotonic modal logic are provided. Minimal model semantics is defined, and soundness and completeness of the semantics for nonmonotonic modal logics are proved. It is shown how the semantics looks for some most popular or most interesting modal logics. Applications to finding expansions and comparing nonmonotonic logics based on different monotonic modal logics are presented. A few examples of using the semantics for obtaining intuitively clear proofs of some results of nonmonotonic modal logics are given.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"57 1","pages":"34-43"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90853769","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 : 1992-06-22DOI: 10.1109/LICS.1992.185529
I. Ulidowski
The finest observable and implementable equivalence on concurrent processes is sought as part of a larger program to develop a theory of observable processes where semantics of processes are based on locally and finitely observable process behavior and all process constructs are allowed, provided their operational meaning is defined by realistically implementable transition rules. The structure of transition rules is examined, and several conditions that all realistically implementable rules should satisfy are proposed. It is shown that the ISOS contexts capture exactly the observable behavior of processes. This leads to the result that copy plus refusal equivalence is the finest implementable equivalence.<>
{"title":"Equivalences on observable processes","authors":"I. Ulidowski","doi":"10.1109/LICS.1992.185529","DOIUrl":"https://doi.org/10.1109/LICS.1992.185529","url":null,"abstract":"The finest observable and implementable equivalence on concurrent processes is sought as part of a larger program to develop a theory of observable processes where semantics of processes are based on locally and finitely observable process behavior and all process constructs are allowed, provided their operational meaning is defined by realistically implementable transition rules. The structure of transition rules is examined, and several conditions that all realistically implementable rules should satisfy are proposed. It is shown that the ISOS contexts capture exactly the observable behavior of processes. This leads to the result that copy plus refusal equivalence is the finest implementable equivalence.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"25 1","pages":"148-159"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79355821","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 : 1992-06-22DOI: 10.1109/LICS.1992.185548
L. Hella
A generalized quantifier is n-ary if it binds any finite number of formulas, but at most n variables in each formula. It is proved that for each integer n, there is a property of finite models which is expressible in fixpoint logic, or even in DATALOG, but not in the extension of first-order logic by any set of n-ary quantifiers. It follows that no extension of first-order logic by a finite set of quantifiers captures all DATALOG-definable properties. Furthermore, it is proved that for each integer n, there is a LOGSPACE-computable property of finite models which is not definable in any extension of fixpoint logic by n-ary quantifiers. Hence, the expressive power of LOGSPACE, and a fortiori, that of PTIME, cannot be captured by adding to fixpoint logic any set of quantifiers of bounded arity.<>
{"title":"Logical hierarchies in PTIME","authors":"L. Hella","doi":"10.1109/LICS.1992.185548","DOIUrl":"https://doi.org/10.1109/LICS.1992.185548","url":null,"abstract":"A generalized quantifier is n-ary if it binds any finite number of formulas, but at most n variables in each formula. It is proved that for each integer n, there is a property of finite models which is expressible in fixpoint logic, or even in DATALOG, but not in the extension of first-order logic by any set of n-ary quantifiers. It follows that no extension of first-order logic by a finite set of quantifiers captures all DATALOG-definable properties. Furthermore, it is proved that for each integer n, there is a LOGSPACE-computable property of finite models which is not definable in any extension of fixpoint logic by n-ary quantifiers. Hence, the expressive power of LOGSPACE, and a fortiori, that of PTIME, cannot be captured by adding to fixpoint logic any set of quantifiers of bounded arity.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"124 21 1","pages":"360-368"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80143716","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 : 1992-06-22DOI: 10.1109/LICS.1992.185553
L. Fribourg
A procedure that constructs mechanically the appropriate lemmas for proving assertions about programs with arrays is described. A certain subclass of formulas for which the procedure is guaranteed to terminate and thus constitutes a decision procedure is exhibited. This subclass allows for ordering over integers but not for incrementation. A more general subclass that allows for incrementation, but without the termination property, is considered. It is also indicated how to apply the method to a still more general subclass that allows for full arithmetic. These results are extended to the case in which predicates have more than one list argument.<>
{"title":"Mixing list recursion and arithmetic","authors":"L. Fribourg","doi":"10.1109/LICS.1992.185553","DOIUrl":"https://doi.org/10.1109/LICS.1992.185553","url":null,"abstract":"A procedure that constructs mechanically the appropriate lemmas for proving assertions about programs with arrays is described. A certain subclass of formulas for which the procedure is guaranteed to terminate and thus constitutes a decision procedure is exhibited. This subclass allows for ordering over integers but not for incrementation. A more general subclass that allows for incrementation, but without the termination property, is considered. It is also indicated how to apply the method to a still more general subclass that allows for full arithmetic. These results are extended to the case in which predicates have more than one list argument.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"14 1","pages":"419-429"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81045166","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 : 1992-06-22DOI: 10.1109/LICS.1992.185520
A. P. Stolboushkin
It may happen that a first order formula with two free variables over a signature defines a linear order of some finite structure of the signature. Then, naturally, this finite structure is rigid, i.e. admits the single (trivial) automorphism. Also, the class of all the finite structures such that the formula defines a linear order on any of them, is finitely axiomatizable in the class of all finite structures (of the signature). It is shown that the inverse is not true, i.e. that there exists a finitely axiomatizable class of rigid finite structures, such that no first-order formula defines a linear order on all the structures of the class. To illustrate possible applications of the result in finite model theory, it is shown that Y. Gurevich's (1984) result that E.W. Beth's (1953) definability theorem fails for finite models is an immediate corollary.<>
{"title":"Axiomatizable classes of finite models and definability of linear order","authors":"A. P. Stolboushkin","doi":"10.1109/LICS.1992.185520","DOIUrl":"https://doi.org/10.1109/LICS.1992.185520","url":null,"abstract":"It may happen that a first order formula with two free variables over a signature defines a linear order of some finite structure of the signature. Then, naturally, this finite structure is rigid, i.e. admits the single (trivial) automorphism. Also, the class of all the finite structures such that the formula defines a linear order on any of them, is finitely axiomatizable in the class of all finite structures (of the signature). It is shown that the inverse is not true, i.e. that there exists a finitely axiomatizable class of rigid finite structures, such that no first-order formula defines a linear order on all the structures of the class. To illustrate possible applications of the result in finite model theory, it is shown that Y. Gurevich's (1984) result that E.W. Beth's (1953) definability theorem fails for finite models is an immediate corollary.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"233 1","pages":"64-70"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77488010","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 : 1992-06-22DOI: 10.1109/LICS.1992.185521
Georges Gonthier, J. Lévy, Paul-André Melliès
An axiomatic version of the standardization theorem that shows the necessary basic properties between nesting of redexes and residuals is presented. This axiomatic approach provides a better understanding of standardization, and makes it applicable in other settings, such as directed acyclic graphs (dags) or interaction networks. conflicts between redexes are also treated. The axioms include stability in the sense given by G. Berry (Ph.D. thesis, Univ. of Paris, 1979), proving it to be an intrinsic notion of deterministic calculi.<>
{"title":"An abstract standardisation theorem","authors":"Georges Gonthier, J. Lévy, Paul-André Melliès","doi":"10.1109/LICS.1992.185521","DOIUrl":"https://doi.org/10.1109/LICS.1992.185521","url":null,"abstract":"An axiomatic version of the standardization theorem that shows the necessary basic properties between nesting of redexes and residuals is presented. This axiomatic approach provides a better understanding of standardization, and makes it applicable in other settings, such as directed acyclic graphs (dags) or interaction networks. conflicts between redexes are also treated. The axioms include stability in the sense given by G. Berry (Ph.D. thesis, Univ. of Paris, 1979), proving it to be an intrinsic notion of deterministic calculi.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":" 539","pages":"72-81"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91410066","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 : 1992-06-22DOI: 10.1109/LICS.1992.185538
Hubert Comon-Lundh, Marianne Haberstrau, J. Jouannaud
Results for syntactic theories are generalized to shallow theories. The main technique used is the computation by ordered completion techniques of conservative extensions of the starting shallow presentation which are, respectively, ground convergent, syntactic, and cycle-syntactic. In all cases, the property that variables occur at depth at most one appears to be crucial. shallow theories thus emerge as a fundamental nontrivial, union-closed subclass of equational theories for which all important questions are decidable.<>
{"title":"Decidable problems in shallow equational theories","authors":"Hubert Comon-Lundh, Marianne Haberstrau, J. Jouannaud","doi":"10.1109/LICS.1992.185538","DOIUrl":"https://doi.org/10.1109/LICS.1992.185538","url":null,"abstract":"Results for syntactic theories are generalized to shallow theories. The main technique used is the computation by ordered completion techniques of conservative extensions of the starting shallow presentation which are, respectively, ground convergent, syntactic, and cycle-syntactic. In all cases, the property that variables occur at depth at most one appears to be crucial. shallow theories thus emerge as a fundamental nontrivial, union-closed subclass of equational theories for which all important questions are decidable.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"3 1","pages":"255-265"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90162189","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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