An error has been pointed out in the author's paper (see Proc. 2nd IEEE Symp. on Logic in Computer Science, p.37-44 (1987)). It appears that there are programs without principal type schemes in the system in that paper.<>
{"title":"Corrigendum: complete type interference for simple objects","authors":"M. Wand","doi":"10.1109/LICS.1988.5111","DOIUrl":"https://doi.org/10.1109/LICS.1988.5111","url":null,"abstract":"An error has been pointed out in the author's paper (see Proc. 2nd IEEE Symp. on Logic in Computer Science, p.37-44 (1987)). It appears that there are programs without principal type schemes in the system in that paper.<<ETX>>","PeriodicalId":425186,"journal":{"name":"[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128741742","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 operation of relativizing properties with respect to parallel environments often used in obtaining compositionality in theories for concurrency corresponds to a notion of (contraction-free) relevant deduction. The author considers program logics in which this notion of deduction is internalized by the corresponding implication. The idea is carried through for safety properties of a simple system of SCCS-type synchronous processes with an internal choice operator. They present two completeness results: first for a modal extension of positive propositional linear logic with respect to the equational class of algebras containing the safety testing quotient of the author's process system as its free member, and second for the free algebra itself.<>
{"title":"Relevance logic and concurrent composition","authors":"M. Dam","doi":"10.1109/LICS.1988.5116","DOIUrl":"https://doi.org/10.1109/LICS.1988.5116","url":null,"abstract":"The operation of relativizing properties with respect to parallel environments often used in obtaining compositionality in theories for concurrency corresponds to a notion of (contraction-free) relevant deduction. The author considers program logics in which this notion of deduction is internalized by the corresponding implication. The idea is carried through for safety properties of a simple system of SCCS-type synchronous processes with an internal choice operator. They present two completeness results: first for a modal extension of positive propositional linear logic with respect to the equational class of algebras containing the safety testing quotient of the author's process system as its free member, and second for the free algebra itself.<<ETX>>","PeriodicalId":425186,"journal":{"name":"[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121651192","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}
Parallel algorithms and computational complexity results are given for two problems; computing the relative complement of terms and antiunification. The concepts of antiunification and relative complement are useful for theorem proving, logic programming, and machine learning. The relative complement problem is shown to be NP-complete.<>
{"title":"Efficient parallel algorithms for anti-unification and relative complement","authors":"G. Kuper, K. McAloon, K. Palem, K. Perry","doi":"10.1109/LICS.1988.5109","DOIUrl":"https://doi.org/10.1109/LICS.1988.5109","url":null,"abstract":"Parallel algorithms and computational complexity results are given for two problems; computing the relative complement of terms and antiunification. The concepts of antiunification and relative complement are useful for theorem proving, logic programming, and machine learning. The relative complement problem is shown to be NP-complete.<<ETX>>","PeriodicalId":425186,"journal":{"name":"[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122602693","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 denotational, hence, compositional semantics for a subset of Concurrent Prolog is developed and related to an operational semantics. The denotational semantics makes divergence and the resultant substitutions of finite computations together with the termination mode-success, failure, or deadlock-observable. Relative to this notion of observation it is proved that the denotational semantics is fully abstract in the sense that it records the minimal amount of extra information beyond the observables to make it compositional. Full abstraction is an important property because it quantifies the information that one needs in order to reason about individual program-parts independently. This is believed to be the first such result in the area of concurrent logic programming.<>
{"title":"Fully abstract denotational semantics for flat Concurrent Prolog","authors":"R. Gerth, M. Codish, Y. Lichtenstein, E. Shapiro","doi":"10.1109/LICS.1988.5130","DOIUrl":"https://doi.org/10.1109/LICS.1988.5130","url":null,"abstract":"A denotational, hence, compositional semantics for a subset of Concurrent Prolog is developed and related to an operational semantics. The denotational semantics makes divergence and the resultant substitutions of finite computations together with the termination mode-success, failure, or deadlock-observable. Relative to this notion of observation it is proved that the denotational semantics is fully abstract in the sense that it records the minimal amount of extra information beyond the observables to make it compositional. Full abstraction is an important property because it quantifies the information that one needs in order to reason about individual program-parts independently. This is believed to be the first such result in the area of concurrent logic programming.<<ETX>>","PeriodicalId":425186,"journal":{"name":"[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129429164","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}
Unquantified Presburger arithmetic is proved to be nonaxiomatizable by a canonical (i.e. Noetherian and confluent) term-rewriting system, if Boolean connectives are not allowed in the left-hand sides of the rewrite rules. It is conjectured that the same is true if the number of Boolean connectives in left-hand sides of the rules is uniformly bounded by an arbitrary natural number.<>
{"title":"On the arithmetic inexpressiveness of term rewriting systems","authors":"S. Vorobyov","doi":"10.1109/LICS.1988.5120","DOIUrl":"https://doi.org/10.1109/LICS.1988.5120","url":null,"abstract":"Unquantified Presburger arithmetic is proved to be nonaxiomatizable by a canonical (i.e. Noetherian and confluent) term-rewriting system, if Boolean connectives are not allowed in the left-hand sides of the rewrite rules. It is conjectured that the same is true if the number of Boolean connectives in left-hand sides of the rules is uniformly bounded by an arbitrary natural number.<<ETX>>","PeriodicalId":425186,"journal":{"name":"[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127801137","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 possibility of extending some of the logical methods that have been recommended for the design of software to the design of hardware, in particular, of synchronous switching circuits implemented in CMOS, is explored. The objective is to design networks that are known by construction. Things that can go wrong with circuits designed in this way are examined. The application of the techniques is discussed.<>
{"title":"Partial correctness of C-MOS switching circuits: an exercise in applied logic","authors":"C. Hoare, M. Gordon","doi":"10.1109/LICS.1988.5098","DOIUrl":"https://doi.org/10.1109/LICS.1988.5098","url":null,"abstract":"The possibility of extending some of the logical methods that have been recommended for the design of software to the design of hardware, in particular, of synchronous switching circuits implemented in CMOS, is explored. The objective is to design networks that are known by construction. Things that can go wrong with circuits designed in this way are examined. The application of the techniques is discussed.<<ETX>>","PeriodicalId":425186,"journal":{"name":"[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126627617","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 authors give a very simple uniform explanation of the persistence of exponential decidability. They follow M. Vardi and P. Wolper's theory (1986) that given a formula gamma of a temporal or dynamic logic, it is important to construct an equivalent automation M/sub gamma /. They characterize the weak monadic theory of the tree; it turns out that weak alternating automata greatly simplify design procedures.<>
{"title":"Weak alternating automata give a simple explanation of why most temporal and dynamic logics are decidable in exponential time","authors":"D. E. Muller, A. Saoudi, P. Schupp","doi":"10.1109/LICS.1988.5139","DOIUrl":"https://doi.org/10.1109/LICS.1988.5139","url":null,"abstract":"The authors give a very simple uniform explanation of the persistence of exponential decidability. They follow M. Vardi and P. Wolper's theory (1986) that given a formula gamma of a temporal or dynamic logic, it is important to construct an equivalent automation M/sub gamma /. They characterize the weak monadic theory of the tree; it turns out that weak alternating automata greatly simplify design procedures.<<ETX>>","PeriodicalId":425186,"journal":{"name":"[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127223859","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 author characterizes Rabin definability (see M.O. Rabin, 1969) of properties of infinite trees of fixed-point definitions based on the basic operations of a standard powerset algebra of trees and involving the least and greatest fixed-point operators as well as the finite union operator and functional composition. A strict connection is established between a hierarchy resulting from alternating the least and greatest fixed-point operators and the hierarchy induced by Rabin indices of automata. The characterization result is actually proved on a more general level, namely, for arbitrary powerset algebra, where the concept of Rabin automaton is replaced by the more general concept of infinite grammar.<>
{"title":"Fixed points vs. infinite generation","authors":"D. Niwinski","doi":"10.1109/LICS.1988.5137","DOIUrl":"https://doi.org/10.1109/LICS.1988.5137","url":null,"abstract":"The author characterizes Rabin definability (see M.O. Rabin, 1969) of properties of infinite trees of fixed-point definitions based on the basic operations of a standard powerset algebra of trees and involving the least and greatest fixed-point operators as well as the finite union operator and functional composition. A strict connection is established between a hierarchy resulting from alternating the least and greatest fixed-point operators and the hierarchy induced by Rabin indices of automata. The characterization result is actually proved on a more general level, namely, for arbitrary powerset algebra, where the concept of Rabin automaton is replaced by the more general concept of infinite grammar.<<ETX>>","PeriodicalId":425186,"journal":{"name":"[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131050160","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}
J. Gallier, Wayne Snyder, P. Narendran, D. Plaisted
Rigid E-unification is a restricted kind of unification modulo equational theories, or E-unification, that arises naturally in extending P. Andrews' (1981) theorem-proving method of mating to first-order languages with equality. It is shown that rigid E-unification is NP-complete and that finite complete sets of rigid E-unifiers always exist. As a consequence, deciding whether a family of mated sets is an equational mating is an NP-complete problem. Some implications of this result regarding the complexity of theorem proving in first-order logic with equality are discussed.<>
{"title":"Rigid E-unification is NP-complete","authors":"J. Gallier, Wayne Snyder, P. Narendran, D. Plaisted","doi":"10.1109/LICS.1988.5121","DOIUrl":"https://doi.org/10.1109/LICS.1988.5121","url":null,"abstract":"Rigid E-unification is a restricted kind of unification modulo equational theories, or E-unification, that arises naturally in extending P. Andrews' (1981) theorem-proving method of mating to first-order languages with equality. It is shown that rigid E-unification is NP-complete and that finite complete sets of rigid E-unifiers always exist. As a consequence, deciding whether a family of mated sets is an equational mating is an NP-complete problem. Some implications of this result regarding the complexity of theorem proving in first-order logic with equality are discussed.<<ETX>>","PeriodicalId":425186,"journal":{"name":"[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134199046","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}
Given a finite set T identical to (T/sub 1/, . . . ,T/sub t/) of terms of the lambda - beta -K-calculus and a set X/sub T/ identical to (x/sub 1/, . . ., x/sub n/) of free variables (occurring in the elements of T), X/sub T/-separability is the problem of deciding whether there exists a simultaneous substitution for the elements of X/sub T/ transforming T into the set Z identical to (Z/sub 1/, . . . Z/sub t/) of arbitrary terms. The X/sub T/-separability problem is proved to be solvable for any approximation T/sup Hash / of the set T by terms in lambda - beta - Omega -normal form. Since the characterization is constructive, if the terms T/sup , Hash //sub i/ identical to lambda x/sub 1/ . . . x/sub n/. T/sup Hash //sub i/ (i=1, . . ., t) are closed then the sequence T/sup Hash //sub 1/, . . ., T/sup Hash //sub t/ induces a family of mappings (from n to t dimensions) whose surjectivity and right-invertibility becomes decidable. The left-invertibility of this family is proved to be decidable too.<>
给定一个有限集合T等于(T/下标1/)，…，T/下标T/)项的- - k -微积分和一个集合X/下标T/等于(X/下标1/，…，X/下标n/)的自由变量(出现在T的元素中)，X/下标T/-可分性是决定是否存在一个同时替换X/下标T的元素/将T转换成等于(Z/下标1/，…)的集合Z的问题。任意项的Z/下标t/)证明了X/下标T/可分性问题对于集合T的任何近似T/sup哈希/都是可解的。由于表征是建设性的，如果项T/sup, Hash //下标i/与λ x/下标1/相同…x / an /。T/sup哈希//sub i/ (i=1，…，T)是闭合的，那么序列T/sup哈希//sub 1/，…，T/sup哈希//sub T/引出一系列映射(从n维到T维)，它们的满性和右可逆性是可决定的。这个家族的左可逆性也被证明是可决定的
{"title":"Characterizing X-separability and one-side invertibility in lambda - beta - Omega -calculus","authors":"C. Böhm, A. Piperno","doi":"10.1109/LICS.1988.5104","DOIUrl":"https://doi.org/10.1109/LICS.1988.5104","url":null,"abstract":"Given a finite set T identical to (T/sub 1/, . . . ,T/sub t/) of terms of the lambda - beta -K-calculus and a set X/sub T/ identical to (x/sub 1/, . . ., x/sub n/) of free variables (occurring in the elements of T), X/sub T/-separability is the problem of deciding whether there exists a simultaneous substitution for the elements of X/sub T/ transforming T into the set Z identical to (Z/sub 1/, . . . Z/sub t/) of arbitrary terms. The X/sub T/-separability problem is proved to be solvable for any approximation T/sup Hash / of the set T by terms in lambda - beta - Omega -normal form. Since the characterization is constructive, if the terms T/sup , Hash //sub i/ identical to lambda x/sub 1/ . . . x/sub n/. T/sup Hash //sub i/ (i=1, . . ., t) are closed then the sequence T/sup Hash //sub 1/, . . ., T/sup Hash //sub t/ induces a family of mappings (from n to t dimensions) whose surjectivity and right-invertibility becomes decidable. The left-invertibility of this family is proved to be decidable too.<<ETX>>","PeriodicalId":425186,"journal":{"name":"[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128553820","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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