Pub Date : 1995-01-01DOI: 10.1109/LICS.1995.523285
Hubert Comon-Lundh
{"title":"Sequentiality, Second Order Monadic Logic and Tree Automata","authors":"Hubert Comon-Lundh","doi":"10.1109/LICS.1995.523285","DOIUrl":"https://doi.org/10.1109/LICS.1995.523285","url":null,"abstract":"","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"508-517"},"PeriodicalIF":0.0,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83896662","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 : 1993-06-19DOI: 10.1109/LICS.1993.287594
A. Pnueli, L. Zuck
Two-way translations between various versions of temporal logic and between temporal logic over finite sequences and star-free regular expressions are presented. The main result is a translation from normal-form temporal logic formulas to formulas that use only future operators. The translation offers a new proof to a theorem claimed by D. Gabbay et al. (1980), stating that restricting temporal logic to the future operators does not impair its expressive power. The theorem is the basis of many temporal proof systems.<>
{"title":"In and out of temporal logic","authors":"A. Pnueli, L. Zuck","doi":"10.1109/LICS.1993.287594","DOIUrl":"https://doi.org/10.1109/LICS.1993.287594","url":null,"abstract":"Two-way translations between various versions of temporal logic and between temporal logic over finite sequences and star-free regular expressions are presented. The main result is a translation from normal-form temporal logic formulas to formulas that use only future operators. The translation offers a new proof to a theorem claimed by D. Gabbay et al. (1980), stating that restricting temporal logic to the future operators does not impair its expressive power. The theorem is the basis of many temporal proof systems.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"82 1","pages":"124-135"},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73668346","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 : 1993-06-19DOI: 10.1109/LICS.1993.287572
P. Narendran, M. Rusinowitch
It is shown that unifiability is decidable in theories presented by a set of ground equations with several associative-communicative symbols (ground AC theories). This result applies, for instance, to finitely presented commutative semigroups, and it extends the authors' previous work (P. Narendran and M. Rusinwithch, 1991) where they gave an algorithm for solving the uniform word problem in ground AC theories.<>
{"title":"The unifiability problem in ground AC theories","authors":"P. Narendran, M. Rusinowitch","doi":"10.1109/LICS.1993.287572","DOIUrl":"https://doi.org/10.1109/LICS.1993.287572","url":null,"abstract":"It is shown that unifiability is decidable in theories presented by a set of ground equations with several associative-communicative symbols (ground AC theories). This result applies, for instance, to finitely presented commutative semigroups, and it extends the authors' previous work (P. Narendran and M. Rusinwithch, 1991) where they gave an algorithm for solving the uniform word problem in ground AC theories.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"16 1","pages":"364-370"},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75664342","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 : 1993-06-19DOI: 10.1109/LICS.1993.287593
I. Walukiewicz
The long-standing problem of the complete axiomatization of the propositional mu -calculus introduced by D. Kozen (1983) is addressed. The approach can be roughly described as a modified tableau method in the sense that infinite trees labeled with sets of formulas are investigated. The tableau method has already been used in the original paper by Kozen. The reexamination of the general tableau method presented is due to advances in automata theory, especially S. Safra's determinization procedure (1988), connections between automata on infinite trees and games, and experience with the model checking. A finitary complete axiom system for the mu -calculus is obtained. It can be roughly described as a system for propositional modal logic with the addition of a induction rule to reason about least fixpoints.<>
{"title":"On completeness of the mu -calculus","authors":"I. Walukiewicz","doi":"10.1109/LICS.1993.287593","DOIUrl":"https://doi.org/10.1109/LICS.1993.287593","url":null,"abstract":"The long-standing problem of the complete axiomatization of the propositional mu -calculus introduced by D. Kozen (1983) is addressed. The approach can be roughly described as a modified tableau method in the sense that infinite trees labeled with sets of formulas are investigated. The tableau method has already been used in the original paper by Kozen. The reexamination of the general tableau method presented is due to advances in automata theory, especially S. Safra's determinization procedure (1988), connections between automata on infinite trees and games, and experience with the model checking. A finitary complete axiom system for the mu -calculus is obtained. It can be roughly described as a system for propositional modal logic with the addition of a induction rule to reason about least fixpoints.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"10 1","pages":"136-146"},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72967675","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 : 1993-06-19DOI: 10.1109/LICS.1993.287587
G. Fayolle, S. Grumbach, C. Tollu
The impact of adding certain families of generalized quantifiers to first-order logic (FO) on the asymptotic behavior of sentences is studied. All the results are stated and proved for languages disallowing free variables in the scope of generalized quantifiers. For a class K of finite structures closed under isomorphism, the quantifier Q/sub K/ is said to be strongly monotonic, sm, if membership in the class is preserved under a loose form of extensions. The first theorem (O/1 law for FO with any set of sm quantifiers) subsumes a previous criterion for proving that almost no graphs satisfy a given property. A O/1 law for FO with Hartig quantifiers (equicardinality quantifiers) and a limit law for a fragment of FO with Rescher quantifiers (expressing inequalities of cardinalities) are also established. It is also proved that the O/1 law fails for the extension of FO with Hartig quantifiers if the above syntactic restriction is relaxed, giving the best upper bound for the existence of a O/1 law for FO with Hartig quantifiers.<>
{"title":"Asymptotic probabilities of languages with generalized quantifiers","authors":"G. Fayolle, S. Grumbach, C. Tollu","doi":"10.1109/LICS.1993.287587","DOIUrl":"https://doi.org/10.1109/LICS.1993.287587","url":null,"abstract":"The impact of adding certain families of generalized quantifiers to first-order logic (FO) on the asymptotic behavior of sentences is studied. All the results are stated and proved for languages disallowing free variables in the scope of generalized quantifiers. For a class K of finite structures closed under isomorphism, the quantifier Q/sub K/ is said to be strongly monotonic, sm, if membership in the class is preserved under a loose form of extensions. The first theorem (O/1 law for FO with any set of sm quantifiers) subsumes a previous criterion for proving that almost no graphs satisfy a given property. A O/1 law for FO with Hartig quantifiers (equicardinality quantifiers) and a limit law for a fragment of FO with Rescher quantifiers (expressing inequalities of cardinalities) are also established. It is also proved that the O/1 law fails for the extension of FO with Hartig quantifiers if the above syntactic restriction is relaxed, giving the best upper bound for the existence of a O/1 law for FO with Hartig quantifiers.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"199-207"},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76140573","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 : 1993-06-19DOI: 10.1109/LICS.1993.287585
P. Schroeder-Heister
The author discusses two rules of definitional reflection: the logical version of definitional reflection, as used in the extended logic programming language GCLA, and the omega version of definitional reflection. The logical version is a left-introduction rule completely analogous to the left-introduction rules for logical operators in Gentzen-style sequent systems, whereas the omega version extends the logical version by a principle related to the omega rule in arithmetic. Correspondingly, the interpretation of free variables differs between the two approaches, resulting in different principles of closure of inference rules under substitution. This difference is crucial for the computational interpretation of definitional reflection.<>
{"title":"Rules of definitional reflection","authors":"P. Schroeder-Heister","doi":"10.1109/LICS.1993.287585","DOIUrl":"https://doi.org/10.1109/LICS.1993.287585","url":null,"abstract":"The author discusses two rules of definitional reflection: the logical version of definitional reflection, as used in the extended logic programming language GCLA, and the omega version of definitional reflection. The logical version is a left-introduction rule completely analogous to the left-introduction rules for logical operators in Gentzen-style sequent systems, whereas the omega version extends the logical version by a principle related to the omega rule in arithmetic. Correspondingly, the interpretation of free variables differs between the two approaches, resulting in different principles of closure of inference rules under substitution. This difference is crucial for the computational interpretation of definitional reflection.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"4 1","pages":"222-232"},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79467833","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 : 1993-06-19DOI: 10.1109/LICS.1993.287583
J. Lambek
The question of what is an effective process or algorithm arose form the statement of Hilbert's tenth problem. It was soon seen to be related to the question of which numerical functions N/sup n/ to N are computable. Among the early answers to this question the author singles out three. A numerical function is computable if and only if it is recursive, it is computable on a Turing machine, or it is definable in the untyped lambda -calculus. Some aspects of the relevance of these three notions of computability to linguistics and logic, in particular, categorial logic, are discussed.<>
什么是有效的过程或算法的问题产生于希尔伯特第十问题的陈述。它很快就被看作是关于哪个数值函数N/sup N/ to N是可计算的问题。在对这个问题的早期回答中，作者挑出了三个。一个数值函数是可计算的当且仅当它是递归的，它在图灵机上是可计算的，或者它在未类型化的λ -微积分中是可定义的。本文讨论了这三个可计算性概念与语言学和逻辑学，特别是范畴逻辑之间的关系。
{"title":"Programs, grammars and arguments: a personal view of some connections between computation, language and logic","authors":"J. Lambek","doi":"10.1109/LICS.1993.287583","DOIUrl":"https://doi.org/10.1109/LICS.1993.287583","url":null,"abstract":"The question of what is an effective process or algorithm arose form the statement of Hilbert's tenth problem. It was soon seen to be related to the question of which numerical functions N/sup n/ to N are computable. Among the early answers to this question the author singles out three. A numerical function is computable if and only if it is recursive, it is computable on a Turing machine, or it is definable in the untyped lambda -calculus. Some aspects of the relevance of these three notions of computability to linguistics and logic, in particular, categorial logic, are discussed.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"44 1","pages":"246-249"},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79296071","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}
The infinitary language obtained from the first-order language of graphs by closure under conjunctions and disjunctions of arbitrary sets of formulas, provided only finitely many distinct variables occur among the formulas, is considered. Let p(n) be the edge probability of the random graph on n vertices. It is shown that if p(n)<1, then the probability is either smaller than 2 raised to the power-n/sup d/ for some d>0, or it is asymptotic to the cn/sup -d/ for some c>0, d>or=0. Results on the difficulty of computing the asymptotic probability are given.<>
{"title":"Infinitary logics and very sparse random graphs","authors":"J. Lynch","doi":"10.2307/2275550","DOIUrl":"https://doi.org/10.2307/2275550","url":null,"abstract":"The infinitary language obtained from the first-order language of graphs by closure under conjunctions and disjunctions of arbitrary sets of formulas, provided only finitely many distinct variables occur among the formulas, is considered. Let p(n) be the edge probability of the random graph on n vertices. It is shown that if p(n)<<n/sup -1/, then for every sigma belonging to the infinitary language the probability that sigma holds for the random graph on n vertices converges. Further, if p(n)=n/sup -a/, alpha >1, then the probability is either smaller than 2 raised to the power-n/sup d/ for some d>0, or it is asymptotic to the cn/sup -d/ for some c>0, d>or=0. Results on the difficulty of computing the asymptotic probability are given.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"18 1","pages":"191-198"},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80725247","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 : 1993-06-19DOI: 10.1109/LICS.1993.287605
G. Longo, K. Milsted, S. Soloviev
The authors focus on how polymorphic functions, which may take types as inputs, depend on types. These functions are generally understood to have an essentially constant meaning, in all models, on input types. It is shown how the proof theory of the polymorphic lambda -calculus suggests a clear syntactic description of this phenomenon. Under a reasonable condition, it is shown that identity of two polymorphic functions on a single type implies identity of the functions (equivalently, every type is a generic input).<>
{"title":"The genericity theorem and the notion of parametricity in the polymorphic lambda -calculus","authors":"G. Longo, K. Milsted, S. Soloviev","doi":"10.1109/LICS.1993.287605","DOIUrl":"https://doi.org/10.1109/LICS.1993.287605","url":null,"abstract":"The authors focus on how polymorphic functions, which may take types as inputs, depend on types. These functions are generally understood to have an essentially constant meaning, in all models, on input types. It is shown how the proof theory of the polymorphic lambda -calculus suggests a clear syntactic description of this phenomenon. Under a reasonable condition, it is shown that identity of two polymorphic functions on a single type implies identity of the functions (equivalently, every type is a generic input).<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"59 1","pages":"6-14"},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91492563","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 : 1993-06-19DOI: 10.1109/LICS.1993.287581
D. Kesner, Laurence Puel, V. Tannen
The theory of programming with pattern-matching function definitions has been studied mainly in the framework of first-order rewrite systems. The authors present a typed functional calculus that emphasizes the strong connection between the structure of whole pattern definitions and their types. In this calculus, type-checking guarantees the absence of runtime errors caused by nonexhaustive pattern-matching definitions. Its operational semantics is deterministic in a natural way, without the imposition of ad hoc solutions such as clause order or best fit. The calculus is designed as a computational interpretation of the Gentzen sequent proofs for the intuitionistic propositional logic. The basic properties connecting typing and evaluation, subject reduction, and strong normalization are proved. The authors believe that this calculus offers a rational reconstruction of the pattern-matching features found in successful functional languages.<>
{"title":"A typed pattern calculus","authors":"D. Kesner, Laurence Puel, V. Tannen","doi":"10.1109/LICS.1993.287581","DOIUrl":"https://doi.org/10.1109/LICS.1993.287581","url":null,"abstract":"The theory of programming with pattern-matching function definitions has been studied mainly in the framework of first-order rewrite systems. The authors present a typed functional calculus that emphasizes the strong connection between the structure of whole pattern definitions and their types. In this calculus, type-checking guarantees the absence of runtime errors caused by nonexhaustive pattern-matching definitions. Its operational semantics is deterministic in a natural way, without the imposition of ad hoc solutions such as clause order or best fit. The calculus is designed as a computational interpretation of the Gentzen sequent proofs for the intuitionistic propositional logic. The basic properties connecting typing and evaluation, subject reduction, and strong normalization are proved. The authors believe that this calculus offers a rational reconstruction of the pattern-matching features found in successful functional languages.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"26 1","pages":"262-274"},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84843598","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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