J. Log. Comput.最新文献_第3页

Arithmetical and Hyperarithmetical Worm Battles 算术和超算术蠕虫战斗

J. Log. Comput. Pub Date : 2021-12-14 DOI: 10.1093/logcom/exac067

David Fern'andez-Duque, J. Joosten, F. Pakhomov, Konstnatinos Papafilippou, A. Weiermann

引用次数: 0

Satisfiability of Constrained Horn Clauses on Algebraic Data Types: A Transformation-based Approach 代数数据类型约束角子句的可满足性:一种基于变换的方法

J. Log. Comput. Pub Date : 2021-11-23 DOI: 10.1093/logcom/exab090

E. D. Angelis, F. Fioravanti, A. Pettorossi, M. Proietti

{"title":"Satisfiability of Constrained Horn Clauses on Algebraic Data Types: A Transformation-based Approach","authors":"E. D. Angelis, F. Fioravanti, A. Pettorossi, M. Proietti","doi":"10.1093/logcom/exab090","DOIUrl":"https://doi.org/10.1093/logcom/exab090","url":null,"abstract":"We address the problem of checking the satisfiability of Constrained Horn Clauses (CHCs) defined on Algebraic Data Types (ADTs), such as lists and trees. We propose a new technique for transforming CHCs defined on ADTs into CHCs where the arguments of the predicates have only basic types, such as integers and booleans. Thus, our technique avoids, during satisfiability checking, the explicit use of proof rules based on induction over the ADTs. The main extension over previous techniques for ADT removal is a new transformation rule, called differential replacement, which allows us to introduce auxiliary predicates, whose definitions correspond to lemmas that are used when making inductive proofs. We present an algorithm that performs the automatic removal of ADTs by applying the new rule, together with the traditional folding/unfolding rules. We prove that, under suitable hypotheses, the set of the transformed clauses is satisfiable if and only if so is the set of the original clauses. By an experimental evaluation, we show that the use of the new rule significantly improves the effectiveness of ADT removal. We also show that our approach is competitive with respect to tools that extend CHC solvers with the use of inductive rules.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133139882","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}

引用次数: 3

Rely more or less, for better or for worse: Intertwining reliability and preferences 或多或少地依赖，是好是坏:将可靠性和偏好交织在一起

J. Log. Comput. Pub Date : 2021-11-12 DOI: 10.1093/LOGCOM/EXAB066

Sujata Ghosh, Katsuhiko Sano

引用次数: 0

Classifying all transducer degrees below N3 对N3以下所有换能器度数进行分类

J. Log. Comput. Pub Date : 2021-11-12 DOI: 10.1093/logcom/exac059

Noah Kaufmann

引用次数: 0

Interpolating between the Jaccard distance and an analogue of the normalized information distance 在Jaccard距离和标准化信息距离的模拟之间进行插值

J. Log. Comput. Pub Date : 2021-11-03 DOI: 10.1093/logcom/exac069

B. Kjos-Hanssen

引用次数: 1

An ASP-based solver for parametrized-difference revision 基于asp的参数化差分修正求解器

J. Log. Comput. Pub Date : 2021-10-01 DOI: 10.1093/logcom/exab061

T. Aravanis

引用次数: 1

Densely computable structures 密集计算结构

J. Log. Comput. Pub Date : 2021-09-24 DOI: 10.1093/logcom/exab057

W. Calvert, D. Cenzer, V. Harizanov

{"title":"Densely computable structures","authors":"W. Calvert, D. Cenzer, V. Harizanov","doi":"10.1093/logcom/exab057","DOIUrl":"https://doi.org/10.1093/logcom/exab057","url":null,"abstract":"\u0000 In recent years, computability theorists have extensively studied generically and coarsely computable sets. This study of approximate computability was originally motivated by asymptotic density problems in combinatorial group theory. We generalize the notions of generic and coarse computability of sets, introduced by Jockusch and Schupp, to arbitrary structures by defining generically and coarsely computable and computably enumerable structures. There are two directions in which these notions could potentially trivialize: either all structures could have a densely computable copy or only those having a computable (or computably enumerable) copy. We show that some particular classes of structures realize each of these extremal conditions, while other classes realize neither of them. To further explore these concepts, we introduce a graded family of elementarity conditions for substructures, in which we require that the dense sets under consideration be ‘strong’ substructures of the original structure. Here, again, for a given class, the notion could trivialize in the same two directions and we show that both are possible. For each class that we investigate, there is some natural number $n$ such that requiring $varSigma _{n}$ elementarity of substructures is enough to trivialize the class of generically or densely computable structures, witnessing the essentially structural character of these notions.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"634 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132927504","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}

引用次数: 3

Geometry of super-Łukasiewicz logics 超级几何-Łukasiewicz逻辑

J. Log. Comput. Pub Date : 2021-09-20 DOI: 10.1093/logcom/exab060

A. Nola, G. Lenzi, Gaetano Vitale

引用次数: 0

Limitations of the Invertible-Map Equivalences 可逆映射等价的限制

J. Log. Comput. Pub Date : 2021-09-15 DOI: 10.1093/logcom/exac058

A. Dawar, E. Grädel, Moritz Lichter

{"title":"Limitations of the Invertible-Map Equivalences","authors":"A. Dawar, E. Grädel, Moritz Lichter","doi":"10.1093/logcom/exac058","DOIUrl":"https://doi.org/10.1093/logcom/exac058","url":null,"abstract":"\u0000 This note draws conclusions that arise by combining two recent papers, by Anuj Dawar, Erich Grädel and Wied Pakusa, published at ICALP 2019, and by Moritz Lichter, published at LICS 2021. In both papers, the main technical results rely on the combinatorial and algebraic analysis of the invertible-map equivalences ${equiv ^{text {IM}}_{k, Q}}$ on certain variants of Cai–Fürer–Immerman structures (CFI-structures for short). These ${equiv ^{text {IM}}_{k, Q}}$-equivalences, for a natural number $k$ and a set of primes $Q$, refine the well-known Weisfeiler–Leman equivalences used in algorithms for graph isomorphism. The intuition is that two graphs $G{equiv ^{text {IM}}_{k, Q}}H$ cannot be distinguished by iterative refinements of equivalences on $k$-tuples defined via linear operators on vector spaces over fields of characteristic $p in Q$. In the first paper it has been shown, using considerable algebraic machinery, that for a prime $q notin Q$, the ${equiv ^{text {IM}}_{k, Q}}$ equivalences are not strong enough to distinguish between non-isomorphic CFI-structures over the field $mathbb {F}_q$. In the second paper, a similar but not identical construction for CFI-structures over the rings $mathbb {Z}_{2^i}$ has, again by rather involved combinatorial and algebraic arguments, been shown to be indistinguishable with respect to ${equiv ^{text {IM}}_{k, {2}}}$. Together with an earlier work on rank logic, this second result suffices to separate rank logic from polynomial time. We show here that the two approaches can be unified to prove that CFI-structures over the rings $mathbb {Z}_{2^i}$ are in fact indistinguishable with respect to ${equiv ^{text {IM}}_{k, {mathbb {P}}}}$, for the set ${mathbb {P}}$ of all primes. In particular, this implies the following two results. First, there is no fixed $k$ such that the invertible-map equivalence ${equiv ^{text {IM}}_{k, {mathbb {P}}}}$ coincides with isomorphism on all finite graphs. Second, no extension of fixed-point logic by linear-algebraic operators over fields can capture polynomial time.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"6 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116794181","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}

引用次数: 7

Internal proof calculi for modal logics with separating conjunction 分离连接模态逻辑的内部证明演算

J. Log. Comput. Pub Date : 2021-05-19 DOI: 10.1093/LOGCOM/EXAB016

Stephane Demri, Raul Fervari, Alessio Mansutti

引用次数: 1