Pub Date : 2022-10-01DOI: 10.1017/S0960129522000366
Bruno Xavier, C. Olarte, Elaine Pimentel
Abstract One of the most fundamental properties of a proof system is analyticity, expressing the fact that a proof of a given formula F only uses subformulas of F. In sequent calculus, this property is usually proved by showing that the $mathsf{cut}$ rule is admissible, i.e., the introduction of the auxiliary lemma H in the reasoning “if H follows from G and F follows from H, then F follows from G” can be eliminated. The proof of cut admissibility is usually a tedious, error-prone process through several proof transformations, thus requiring the assistance of (semi-)automatic procedures. In a previous work by Miller and Pimentel, linear logic ( $mathsf{LL}$ ) was used as a logical framework for establishing sufficient conditions for cut admissibility of object logical systems (OL). The OL’s inference rules are specified as an $mathsf{LL}$ theory and an easy-to-verify criterion sufficed to establish the cut-admissibility theorem for the OL at hand. However, there are many logical systems that cannot be adequately encoded in $mathsf{LL}$ , the most symptomatic cases being sequent systems for modal logics. In this paper, we use a linear-nested sequent ( $mathsf{LNS}$ ) presentation of $mathsf{MMLL}$ (a variant of LL with subexponentials), and show that it is possible to establish a cut-admissibility criterion for $mathsf{LNS}$ systems for (classical or substructural) multimodal logics. We show that the same approach is suitable for handling the $mathsf{LNS}$ system for intuitionistic logic.
{"title":"A linear logic framework for multimodal logics","authors":"Bruno Xavier, C. Olarte, Elaine Pimentel","doi":"10.1017/S0960129522000366","DOIUrl":"https://doi.org/10.1017/S0960129522000366","url":null,"abstract":"Abstract One of the most fundamental properties of a proof system is analyticity, expressing the fact that a proof of a given formula F only uses subformulas of F. In sequent calculus, this property is usually proved by showing that the \u0000$mathsf{cut}$\u0000 rule is admissible, i.e., the introduction of the auxiliary lemma H in the reasoning “if H follows from G and F follows from H, then F follows from G” can be eliminated. The proof of cut admissibility is usually a tedious, error-prone process through several proof transformations, thus requiring the assistance of (semi-)automatic procedures. In a previous work by Miller and Pimentel, linear logic ( \u0000$mathsf{LL}$\u0000 ) was used as a logical framework for establishing sufficient conditions for cut admissibility of object logical systems (OL). The OL’s inference rules are specified as an \u0000$mathsf{LL}$\u0000 theory and an easy-to-verify criterion sufficed to establish the cut-admissibility theorem for the OL at hand. However, there are many logical systems that cannot be adequately encoded in \u0000$mathsf{LL}$\u0000 , the most symptomatic cases being sequent systems for modal logics. In this paper, we use a linear-nested sequent ( \u0000$mathsf{LNS}$\u0000 ) presentation of \u0000$mathsf{MMLL}$\u0000 (a variant of LL with subexponentials), and show that it is possible to establish a cut-admissibility criterion for \u0000$mathsf{LNS}$\u0000 systems for (classical or substructural) multimodal logics. We show that the same approach is suitable for handling the \u0000$mathsf{LNS}$\u0000 system for intuitionistic logic.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"1176 - 1204"},"PeriodicalIF":0.5,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41931400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-01DOI: 10.1017/S0960129522000421
Leandro Gomes, A. Madeira, L. Barbosa
Abstract This paper introduces a class of automata and associated languages, suitable to model a computational paradigm of fuzzy systems, in which both vagueness and simultaneity are taken as first-class citizens. This requires a weighted semantics for transitions and a precise notion of a synchronous product to enforce the simultaneous occurrence of actions. The usual relationships between automata and languages are revisited in this setting, including a specific Kleene theorem.
{"title":"Weighted synchronous automata","authors":"Leandro Gomes, A. Madeira, L. Barbosa","doi":"10.1017/S0960129522000421","DOIUrl":"https://doi.org/10.1017/S0960129522000421","url":null,"abstract":"Abstract This paper introduces a class of automata and associated languages, suitable to model a computational paradigm of fuzzy systems, in which both vagueness and simultaneity are taken as first-class citizens. This requires a weighted semantics for transitions and a precise notion of a synchronous product to enforce the simultaneous occurrence of actions. The usual relationships between automata and languages are revisited in this setting, including a specific Kleene theorem.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"1234 - 1253"},"PeriodicalIF":0.5,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43931608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-01DOI: 10.1017/S0960129523000075
A. Felty, Giselle Reis
This special issue collects selected articles from the 14th and 15th editions of the Workshop on Logical and Semantic Frameworks, with Applications (LSFA 2019 and 2020). LSFA 2019 was held on 25–26 August 2019 in Natal as a satellite event of the 27th International Conference on Automated Deduction (CADE 2019). LSFA 2020 was held on 27–28 August as an online workshop, with organizers from Salvador.
{"title":"Preface to Special Issue: LSFA 2019 and 2020","authors":"A. Felty, Giselle Reis","doi":"10.1017/S0960129523000075","DOIUrl":"https://doi.org/10.1017/S0960129523000075","url":null,"abstract":"This special issue collects selected articles from the 14th and 15th editions of the Workshop on Logical and Semantic Frameworks, with Applications (LSFA 2019 and 2020). LSFA 2019 was held on 25–26 August 2019 in Natal as a satellite event of the 27th International Conference on Automated Deduction (CADE 2019). LSFA 2020 was held on 27–28 August as an online workshop, with organizers from Salvador.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"1117 - 1118"},"PeriodicalIF":0.5,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45725339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-01DOI: 10.1017/S0960129522000378
F. E. Miranda-Perea, Lourdes del Carmen González Huesca, Pilar Selene Linares Arévalo
Abstract The proof theory of the constructive modal logic S4 (hereafter $mathsf{CS4}$ ) has been settled since the beginning of this century by means of either standard natural deduction and sequent calculi or by the reconstruction of modal logic through hypothetical and categorical judgments à la Martin-Löf, an approach carried out by using a special kind of sequents, which keeps two separated contexts representing ordinary and enhanced hypotheses, intuitively interpreted as true and valid assumptions. These so-called dual-context sequents, originated in linear logic, are used to define a natural deduction system handling judgments of validity, truth, and possibility, resulting in a formalism equivalent to an axiomatic system for $mathsf{CS4}$ . However, this proof-theoretical study of $mathsf{CS4}$ lacks, to the best of our knowledge, its third fundamental constituent, namely a sequent calculus. In this paper, we define such a dual-context formalism, called ${bf DG_{CS4}}$ , and provide detailed proofs of the admissibility for the ordinary cut rule as well as the elimination of a second cut rule, which manipulates enhanced hypotheses. Furthermore, we make available a formal verification of the equivalence of this proposal with the previously defined axiomatic and dual-context natural deduction systems for $mathsf{CS4}$ , using the Coq proof-assistant.
{"title":"A dual-context sequent calculus for the constructive modal logic S4","authors":"F. E. Miranda-Perea, Lourdes del Carmen González Huesca, Pilar Selene Linares Arévalo","doi":"10.1017/S0960129522000378","DOIUrl":"https://doi.org/10.1017/S0960129522000378","url":null,"abstract":"Abstract The proof theory of the constructive modal logic S4 (hereafter \u0000$mathsf{CS4}$\u0000 ) has been settled since the beginning of this century by means of either standard natural deduction and sequent calculi or by the reconstruction of modal logic through hypothetical and categorical judgments à la Martin-Löf, an approach carried out by using a special kind of sequents, which keeps two separated contexts representing ordinary and enhanced hypotheses, intuitively interpreted as true and valid assumptions. These so-called dual-context sequents, originated in linear logic, are used to define a natural deduction system handling judgments of validity, truth, and possibility, resulting in a formalism equivalent to an axiomatic system for \u0000$mathsf{CS4}$\u0000 . However, this proof-theoretical study of \u0000$mathsf{CS4}$\u0000 lacks, to the best of our knowledge, its third fundamental constituent, namely a sequent calculus. In this paper, we define such a dual-context formalism, called \u0000${bf DG_{CS4}}$\u0000 , and provide detailed proofs of the admissibility for the ordinary cut rule as well as the elimination of a second cut rule, which manipulates enhanced hypotheses. Furthermore, we make available a formal verification of the equivalence of this proposal with the previously defined axiomatic and dual-context natural deduction systems for \u0000$mathsf{CS4}$\u0000 , using the Coq proof-assistant.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"1205 - 1233"},"PeriodicalIF":0.5,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45348018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-19DOI: 10.1017/S0960129522000275
Uwe Wolter, A. Martini, E. Haeusler
Abstract Hoare Logic has a long tradition in formal verification and has been continuously developed and used to verify a broad class of programs, including sequential, object-oriented, and concurrent programs. Here we focus on partial and total correctness assertions within the framework of Hoare logic and show that a comprehensive categorical analysis of its axiomatic semantics needs the languages of indexed and fibered category theory. We consider Hoare formulas with local, finite contexts, of program and logical variables. The structural features of Hoare assertions are presented in an indexed setting, while the logical features of deduction are modeled in the fibered one.
{"title":"Indexed and fibered structures for partial and total correctness assertions","authors":"Uwe Wolter, A. Martini, E. Haeusler","doi":"10.1017/S0960129522000275","DOIUrl":"https://doi.org/10.1017/S0960129522000275","url":null,"abstract":"Abstract Hoare Logic has a long tradition in formal verification and has been continuously developed and used to verify a broad class of programs, including sequential, object-oriented, and concurrent programs. Here we focus on partial and total correctness assertions within the framework of Hoare logic and show that a comprehensive categorical analysis of its axiomatic semantics needs the languages of indexed and fibered category theory. We consider Hoare formulas with local, finite contexts, of program and logical variables. The structural features of Hoare assertions are presented in an indexed setting, while the logical features of deduction are modeled in the fibered one.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"1145 - 1175"},"PeriodicalIF":0.5,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48868244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-06DOI: 10.1017/S0960129522000251
Vivek Nigam, Minyoung Kim, Ian Mason, C. Talcott
Abstract Given the complexity of cyber-physical systems (CPS), such as swarms of drones, often deviations, from a planned mission or protocol, occur which may in some cases lead to harm and losses. To increase the robustness of such systems, it is necessary to detect when deviations happen and diagnose the cause(s) for a deviation. We build on our previous work on soft agents, a formal framework based on using rewriting logic for specifying and reasoning about distributed CPS, to develop methods for diagnosis of CPS at design time. We accomplish this by (1) extending the soft agents framework with Fault Models; (2) proposing a protocol specification language and the definition of protocol deviations; and (3) development of workflows/algorithms for detection and diagnosis of protocol deviations. Our approach is partially inspired by existing work using counterfactual reasoning for fault ascription. We demonstrate our machinery with a collection of experiments.
{"title":"Detection and diagnosis of deviations in distributed systems of autonomous agents","authors":"Vivek Nigam, Minyoung Kim, Ian Mason, C. Talcott","doi":"10.1017/S0960129522000251","DOIUrl":"https://doi.org/10.1017/S0960129522000251","url":null,"abstract":"Abstract Given the complexity of cyber-physical systems (CPS), such as swarms of drones, often deviations, from a planned mission or protocol, occur which may in some cases lead to harm and losses. To increase the robustness of such systems, it is necessary to detect when deviations happen and diagnose the cause(s) for a deviation. We build on our previous work on soft agents, a formal framework based on using rewriting logic for specifying and reasoning about distributed CPS, to develop methods for diagnosis of CPS at design time. We accomplish this by (1) extending the soft agents framework with Fault Models; (2) proposing a protocol specification language and the definition of protocol deviations; and (3) development of workflows/algorithms for detection and diagnosis of protocol deviations. Our approach is partially inspired by existing work using counterfactual reasoning for fault ascription. We demonstrate our machinery with a collection of experiments.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"1254 - 1282"},"PeriodicalIF":0.5,"publicationDate":"2022-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46024878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-01DOI: 10.1017/S0960129523000014
Xiaoquan Xu, Meng Bao, Xiaoyuan Zhang
Abstract In this paper, we mainly study the function spaces related to H-sober spaces. For an irreducible subset system H and $T_{0}$ spaces X and Y, it is proved that the following three conditions are equivalent: (1) the Scott space $Sigma mathcal O(X)$ of the lattice of all open sets of X is H-sober; (2) for every H-sober space Y, the function space $mathbb{C}(X, Y)$ of all continuous mappings from X to Y equipped with the Isbell topology is H-sober; (3) for every H-sober space Y, the Isbell topology on $mathbb{C}(X, Y)$ has property S with respect to H. One immediate corollary is that for a $T_{0}$ space X, Y is a d-space (resp., well-filtered space) iff the function space $mathbb{C}(X, Y)$ equipped with the Isbell topology is a d-space (resp., well-filtered space). It is shown that for any $T_0$ space X for which the Scott space $Sigma mathcal O(X)$ is non-sober, the function space $mathbb{C}(X, Sigma 2)$ equipped with the Isbell topology is not sober. The function spaces $mathbb{C}(X, Y)$ equipped with the Scott topology, the compact-open topology and the pointwise convergence topology are also discussed. Our study also leads to a number of questions, whose answers will deepen our understanding of the function spaces related to H-sober spaces.
{"title":"On function spaces equipped with Isbell topology and Scott topology","authors":"Xiaoquan Xu, Meng Bao, Xiaoyuan Zhang","doi":"10.1017/S0960129523000014","DOIUrl":"https://doi.org/10.1017/S0960129523000014","url":null,"abstract":"Abstract In this paper, we mainly study the function spaces related to H-sober spaces. For an irreducible subset system H and \u0000$T_{0}$\u0000 spaces X and Y, it is proved that the following three conditions are equivalent: (1) the Scott space \u0000$Sigma mathcal O(X)$\u0000 of the lattice of all open sets of X is H-sober; (2) for every H-sober space Y, the function space \u0000$mathbb{C}(X, Y)$\u0000 of all continuous mappings from X to Y equipped with the Isbell topology is H-sober; (3) for every H-sober space Y, the Isbell topology on \u0000$mathbb{C}(X, Y)$\u0000 has property S with respect to H. One immediate corollary is that for a \u0000$T_{0}$\u0000 space X, Y is a d-space (resp., well-filtered space) iff the function space \u0000$mathbb{C}(X, Y)$\u0000 equipped with the Isbell topology is a d-space (resp., well-filtered space). It is shown that for any \u0000$T_0$\u0000 space X for which the Scott space \u0000$Sigma mathcal O(X)$\u0000 is non-sober, the function space \u0000$mathbb{C}(X, Sigma 2)$\u0000 equipped with the Isbell topology is not sober. The function spaces \u0000$mathbb{C}(X, Y)$\u0000 equipped with the Scott topology, the compact-open topology and the pointwise convergence topology are also discussed. Our study also leads to a number of questions, whose answers will deepen our understanding of the function spaces related to H-sober spaces.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"1099 - 1116"},"PeriodicalIF":0.5,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44228012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-11eCollection Date: 2022-01-01DOI: 10.1155/2022/5636903
A Alradaddi, A Al Twaim, A Abu-Aliat, K Al-Atass, L Alogayell, M Aldayil, S AlBreiki, S Abed, M Fatani, O Alsharif, B Darwesh, Levent M Gunay, S Al-Khenaizan
Atopic dermatitis (AD) is a chronic skin disease with increasing prevalence worldwide. It is characterized by pruritic eczematous lesions, affecting up to 20% of the children and negatively impacting their quality of life. Guidelines for AD management are available worldwide, but specific guidelines for pediatric AD in Saudi Arabia are lacking. This consensus document aims to identify the needs for the diagnosis and management of pediatric AD in Saudi Arabia by gathering the opinions and recommendations of key experts. We conducted a three-step modified Delphi method to develop the present consensus. The experts agreed that pediatricians and dermatologists commonly encounter AD; however, it is still under-recognized in its early stage in Saudi Arabia. The family physicians should be involved in assessing suspected children with a family history of atopy, particularly in patients with isolated lesions. Further, the experts confirmed that AD diagnosis should be documented, showing assessment criteria used, key morphological characteristics, and features used to ascertain the severity of the disease. There is still a need for simple validated diagnostic criteria suitable for daily practice for pediatric AD. The experts highlighted several medical conditions that pertain to the diagnosis and management of AD in Saudi Arabia.
特应性皮炎（AD）是一种慢性皮肤病，在全球的发病率越来越高。它以瘙痒性湿疹为特征，影响高达 20% 的儿童，并对他们的生活质量造成负面影响。全世界都有儿童瘙痒症治疗指南，但沙特阿拉伯却缺乏针对儿童瘙痒症的具体指南。本共识文件旨在通过收集主要专家的意见和建议，确定沙特阿拉伯儿科 AD 诊断和管理的需求。我们采用三步改良德尔菲法制定了本共识。专家们一致认为，儿科医生和皮肤科医生通常会遇到 AD，但在沙特阿拉伯，人们对 AD 的早期认识仍然不足。家庭医生应参与评估有家族过敏史的疑似儿童，尤其是有孤立皮损的患者。此外，专家们还确认，注意力缺失症的诊断应记录在案，显示所使用的评估标准、主要形态特征以及用于确定疾病严重程度的特征。目前仍需要适合儿科AD日常实践的简单有效的诊断标准。专家们强调了与沙特阿拉伯的注意力缺失症诊断和管理有关的几种医疗条件。
{"title":"Unmet Medical Needs and Early Referral of Pediatric Atopic Dermatitis: An Expert Modified Delphi Consensus from Saudi Arabia.","authors":"A Alradaddi, A Al Twaim, A Abu-Aliat, K Al-Atass, L Alogayell, M Aldayil, S AlBreiki, S Abed, M Fatani, O Alsharif, B Darwesh, Levent M Gunay, S Al-Khenaizan","doi":"10.1155/2022/5636903","DOIUrl":"10.1155/2022/5636903","url":null,"abstract":"<p><p>Atopic dermatitis (AD) is a chronic skin disease with increasing prevalence worldwide. It is characterized by pruritic eczematous lesions, affecting up to 20% of the children and negatively impacting their quality of life. Guidelines for AD management are available worldwide, but specific guidelines for pediatric AD in Saudi Arabia are lacking. This consensus document aims to identify the needs for the diagnosis and management of pediatric AD in Saudi Arabia by gathering the opinions and recommendations of key experts. We conducted a three-step modified Delphi method to develop the present consensus. The experts agreed that pediatricians and dermatologists commonly encounter AD; however, it is still under-recognized in its early stage in Saudi Arabia. The family physicians should be involved in assessing suspected children with a family history of atopy, particularly in patients with isolated lesions. Further, the experts confirmed that AD diagnosis should be documented, showing assessment criteria used, key morphological characteristics, and features used to ascertain the severity of the disease. There is still a need for simple validated diagnostic criteria suitable for daily practice for pediatric AD. The experts highlighted several medical conditions that pertain to the diagnosis and management of AD in Saudi Arabia.</p>","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"7 1","pages":"5636903"},"PeriodicalIF":1.5,"publicationDate":"2022-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11496595/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79266454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.1017/S0960129523000063
M. Ayala-Rincón, S. Mimram
The notion of confluence , which generalizes the one of determinism, is a central and ubiquitous property of computational and deductive systems. Its study is one of the main topics of rewriting theory, where it relates to other properties such as termination, modularity, commutation, and completion. It has been investigated in many formalisms of rewriting, such as conditional and unconditional first- and higher order rewriting, λ -calculi, and constraint rewriting. This special issue presents a selection of novel results and recent computational techniques related to confluence
{"title":"Introduction to the special issue: Confluence","authors":"M. Ayala-Rincón, S. Mimram","doi":"10.1017/S0960129523000063","DOIUrl":"https://doi.org/10.1017/S0960129523000063","url":null,"abstract":"The notion of confluence , which generalizes the one of determinism, is a central and ubiquitous property of computational and deductive systems. Its study is one of the main topics of rewriting theory, where it relates to other properties such as termination, modularity, commutation, and completion. It has been investigated in many formalisms of rewriting, such as conditional and unconditional first- and higher order rewriting, λ -calculi, and constraint rewriting. This special issue presents a selection of novel results and recent computational techniques related to confluence","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"827 - 828"},"PeriodicalIF":0.5,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57259233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.1017/S0960129522000408
K. Nakazawa, Ken-etsu Fujita, Yuta Imagawa
ABSTRACT This paper gives a new proof of confluence for Carraro and Guerrieri’s call-by-value lambda calculus λ v σ with permutation rules. We adapt the compositional Z theorem to λ v σ .
{"title":"Z property for the shuffling calculus","authors":"K. Nakazawa, Ken-etsu Fujita, Yuta Imagawa","doi":"10.1017/S0960129522000408","DOIUrl":"https://doi.org/10.1017/S0960129522000408","url":null,"abstract":"ABSTRACT This paper gives a new proof of confluence for Carraro and Guerrieri’s call-by-value lambda calculus λ v σ with permutation rules. We adapt the compositional Z theorem to λ v σ .","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"1015 - 1027"},"PeriodicalIF":0.5,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46648487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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