Abstract We discuss the notion of bisimulation in various model-changing modal logics and provide an algorithmic study of the same. We provide a general algorithm which gives an overall procedure to check whether two models are bisimilar in all these logics. Through our algorithmic analyses we provide a PSPACE upper bound of the bisimulation/model comparison problem of all these modal logics. We also provide some insight into the higher complexity of the model comparison problem for these logics compared to that for the basic modal logic.
{"title":"Bisimulation in model-changing modal logics: An algorithmic study","authors":"Sujata Ghosh, Shreyas Gupta, Lei Li","doi":"10.1093/logcom/exad018","DOIUrl":"https://doi.org/10.1093/logcom/exad018","url":null,"abstract":"Abstract We discuss the notion of bisimulation in various model-changing modal logics and provide an algorithmic study of the same. We provide a general algorithm which gives an overall procedure to check whether two models are bisimilar in all these logics. Through our algorithmic analyses we provide a PSPACE upper bound of the bisimulation/model comparison problem of all these modal logics. We also provide some insight into the higher complexity of the model comparison problem for these logics compared to that for the basic modal logic.","PeriodicalId":50162,"journal":{"name":"Journal of Logic and Computation","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135465587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The article proposes de dicto and de re versions of ‘knowing-who’ modalities as well as studies the interplay between them and modalities ‘knows’ and ‘for all agents’. It shows that neither of these four modalities is definable through a combination of the three others. In addition, a sound and complete logical system describing the properties of de dicto ‘knows who’, ‘knows’ and ‘for all agents’ modalities is presented.
摘要:本文提出了“知道谁”模式的德见式和反见式，并研究了它们与“知道”和“对所有主体”模式之间的相互作用。它表明，这四种模式都不能通过其他三种模式的组合来定义。此外，还提出了一个完善的逻辑系统，描述了de dicto“know who”、“know”和“for all agents”模态的属性。
{"title":"An egocentric logic of de dicto and de re knowing who","authors":"Sophia Epstein, Pavel Naumov, Jia Tao","doi":"10.1093/logcom/exad053","DOIUrl":"https://doi.org/10.1093/logcom/exad053","url":null,"abstract":"Abstract The article proposes de dicto and de re versions of ‘knowing-who’ modalities as well as studies the interplay between them and modalities ‘knows’ and ‘for all agents’. It shows that neither of these four modalities is definable through a combination of the three others. In addition, a sound and complete logical system describing the properties of de dicto ‘knows who’, ‘knows’ and ‘for all agents’ modalities is presented.","PeriodicalId":50162,"journal":{"name":"Journal of Logic and Computation","volume":"24 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135571279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Editorial: Special issue from the 3rd International Workshop on Dynamic Logic: New Trends and Applications (DaLí 2020)","authors":"M. Martins, Igor Sedlár","doi":"10.1093/logcom/exad054","DOIUrl":"https://doi.org/10.1093/logcom/exad054","url":null,"abstract":"","PeriodicalId":50162,"journal":{"name":"Journal of Logic and Computation","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49293374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sequent-style refutation calculi with non-invertible rules are challenging to design because multiple proof-search strategies need to be simultaneously verified. In this paper, we present a refutation calculus for the multiplicative–additive fragment of linear logic ($textsf{MALL}$) whose binary rule for the multiplicative conjunction $(otimes )$ and the unary rule for the additive disjunction $(oplus )$ fail invertibility. Specifically, we design a cut-free hypersequent calculus $textsf{HMALL}$, which is equivalent to $textsf{MALL}$, and obtained by transforming the usual tree-like shape of derivations into a parallel and linear structure. Next, we develop a refutation calculus $overline{textsf{HMALL}}$ based on the calculus $textsf{HMALL}$. As far as we know, this is also the first refutation calculus for a substructural logic. Finally, we offer a fractional semantics for $textsf{MALL}$—whereby its formulas are interpreted by a rational number in the closed interval [0, 1] —thus extending to the substructural landscape the project of fractional semantics already pursued for classical and modal logics.
{"title":"Linear logic in a refutational setting","authors":"M. Piazza, G. Pulcini, Matteo Tesi","doi":"10.1093/logcom/exad048","DOIUrl":"https://doi.org/10.1093/logcom/exad048","url":null,"abstract":"\u0000 Sequent-style refutation calculi with non-invertible rules are challenging to design because multiple proof-search strategies need to be simultaneously verified. In this paper, we present a refutation calculus for the multiplicative–additive fragment of linear logic ($textsf{MALL}$) whose binary rule for the multiplicative conjunction $(otimes )$ and the unary rule for the additive disjunction $(oplus )$ fail invertibility. Specifically, we design a cut-free hypersequent calculus $textsf{HMALL}$, which is equivalent to $textsf{MALL}$, and obtained by transforming the usual tree-like shape of derivations into a parallel and linear structure. Next, we develop a refutation calculus $overline{textsf{HMALL}}$ based on the calculus $textsf{HMALL}$. As far as we know, this is also the first refutation calculus for a substructural logic. Finally, we offer a fractional semantics for $textsf{MALL}$—whereby its formulas are interpreted by a rational number in the closed interval [0, 1] —thus extending to the substructural landscape the project of fractional semantics already pursued for classical and modal logics.","PeriodicalId":50162,"journal":{"name":"Journal of Logic and Computation","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42126463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alongside the traditional Kripke semantics, modal logic also enjoys a topological interpretation, which is becoming increasingly influential. In this paper, we present various developments related to the topological derivational semantics, based on the Cantor derivative operator. We provide several characterizations of the validity of the axioms of bounded depth. We also elucidate the topological interpretation of the axioms of directedness and connectedness—which come in different forms, all of which we examine. We then prove results of soundness and completeness for all of these logics, using a range of old and new techniques.
{"title":"Some completeness results in derivational modal logic","authors":"Quentin Gougeon","doi":"10.1093/logcom/exad047","DOIUrl":"https://doi.org/10.1093/logcom/exad047","url":null,"abstract":"\u0000 Alongside the traditional Kripke semantics, modal logic also enjoys a topological interpretation, which is becoming increasingly influential. In this paper, we present various developments related to the topological derivational semantics, based on the Cantor derivative operator. We provide several characterizations of the validity of the axioms of bounded depth. We also elucidate the topological interpretation of the axioms of directedness and connectedness—which come in different forms, all of which we examine. We then prove results of soundness and completeness for all of these logics, using a range of old and new techniques.","PeriodicalId":50162,"journal":{"name":"Journal of Logic and Computation","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43498083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract By limiting the range of the predicate variables in a second-order language, one may obtain restricted versions of second-order logic such as weak second-order logic or definable subset logic. In this note, we provide an infinitary strongly complete axiomatization for several systems of this kind having the range of the predicate variables as a parameter. The completeness argument uses simple techniques from the theory of Boolean algebras. This article is dedicated to our friend John N. Crossley on the occasion of his 86th birthday.
{"title":"A parametrized axiomatization for a large number of restricted second-order logics","authors":"Guillermo Badia, John L Bell","doi":"10.1093/logcom/exad050","DOIUrl":"https://doi.org/10.1093/logcom/exad050","url":null,"abstract":"Abstract By limiting the range of the predicate variables in a second-order language, one may obtain restricted versions of second-order logic such as weak second-order logic or definable subset logic. In this note, we provide an infinitary strongly complete axiomatization for several systems of this kind having the range of the predicate variables as a parameter. The completeness argument uses simple techniques from the theory of Boolean algebras. This article is dedicated to our friend John N. Crossley on the occasion of his 86th birthday.","PeriodicalId":50162,"journal":{"name":"Journal of Logic and Computation","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136082555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the minimal unsatisfiable core (MUC) problem for linear temporal logic over finite traces (LTL$_{f}$), which nowadays is a popular formal-specification language for AI-related systems. Efficient algorithms to compute such MUCs can help locate the inconsistency rapidly in the written LTL$_{f}$ specification and are very useful for the system designers to amend the flawed requirement. As far as we know, there are no available tools off-the-shelf so far that provide MUC computation for LTL$_{f}$. We present here two generic approaches NaiveMUC and BinaryMUC to compute an MUC for LTL$_{f}$. Moreover, we introduce heuristics that are based on the Boolean unsatisfiable core (UC) technique to accelerate the two approaches, which are named NaiveMUC+UC and BinaryMUC+UC, respectively. In particular, for global LTL$_{f}$ formulas, we show that the MUC computation can be reduced to the pure Boolean MUC computation, which therefore conducts the GlobalMUC approach. Our experiments show that GlobalMUC performs the best to compute an MUC for global formulas, and BinaryMUC+UC is the best for an arbitrary unsatisfiable formula.
{"title":"Computing minimal unsatisfiable core for LTL over finite traces","authors":"Tong Niu, Shengping Xiao, Xiaoyu Zhang, Jianwen Li, Yanhong Huang, Jianqi Shi","doi":"10.1093/logcom/exad049","DOIUrl":"https://doi.org/10.1093/logcom/exad049","url":null,"abstract":"\u0000 In this paper, we consider the minimal unsatisfiable core (MUC) problem for linear temporal logic over finite traces (LTL$_{f}$), which nowadays is a popular formal-specification language for AI-related systems. Efficient algorithms to compute such MUCs can help locate the inconsistency rapidly in the written LTL$_{f}$ specification and are very useful for the system designers to amend the flawed requirement. As far as we know, there are no available tools off-the-shelf so far that provide MUC computation for LTL$_{f}$. We present here two generic approaches NaiveMUC and BinaryMUC to compute an MUC for LTL$_{f}$. Moreover, we introduce heuristics that are based on the Boolean unsatisfiable core (UC) technique to accelerate the two approaches, which are named NaiveMUC+UC and BinaryMUC+UC, respectively. In particular, for global LTL$_{f}$ formulas, we show that the MUC computation can be reduced to the pure Boolean MUC computation, which therefore conducts the GlobalMUC approach. Our experiments show that GlobalMUC performs the best to compute an MUC for global formulas, and BinaryMUC+UC is the best for an arbitrary unsatisfiable formula.","PeriodicalId":50162,"journal":{"name":"Journal of Logic and Computation","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41987050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A strict graph-matching mechanism brings normativeness to graph grammar but leads to graph grammar insufficiency when processing fuzzy grammatical structures. To address this issue, the current paper proposes an improved formal framework for graph grammar that enables it to effectively specify the ambiguity of graph models while maintaining normativeness and intuition. First, the improved framework defines the connection probability for edges and classifies the edges based on the connection probability, which is used as the quantitative and qualitative description of the graph grammar structure’s ambiguity. Second, the concepts of credibility threshold, credible subgraphs and candidate subgraphs are defined, and the constraints on the redex are adjusted to increase the fault tolerance of the graph-matching process. Finally, the grammatical operation is redesigned, with a matching weight defined for each redex based on the connection probability and the credibility threshold, thereby providing a theoretical basis and practical guidance for the selection of multiple redexes.
{"title":"A fuzzy structure processing mechanism for graph grammar","authors":"Yu-Feng Liu, Fan Yang, Jian Liu, Song Li","doi":"10.1093/logcom/exad046","DOIUrl":"https://doi.org/10.1093/logcom/exad046","url":null,"abstract":"\u0000 A strict graph-matching mechanism brings normativeness to graph grammar but leads to graph grammar insufficiency when processing fuzzy grammatical structures. To address this issue, the current paper proposes an improved formal framework for graph grammar that enables it to effectively specify the ambiguity of graph models while maintaining normativeness and intuition. First, the improved framework defines the connection probability for edges and classifies the edges based on the connection probability, which is used as the quantitative and qualitative description of the graph grammar structure’s ambiguity. Second, the concepts of credibility threshold, credible subgraphs and candidate subgraphs are defined, and the constraints on the redex are adjusted to increase the fault tolerance of the graph-matching process. Finally, the grammatical operation is redesigned, with a matching weight defined for each redex based on the connection probability and the credibility threshold, thereby providing a theoretical basis and practical guidance for the selection of multiple redexes.","PeriodicalId":50162,"journal":{"name":"Journal of Logic and Computation","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44336914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correction to: Arithmetical and Hyperarithmetical Worm Battles","authors":"","doi":"10.1093/logcom/exad051","DOIUrl":"https://doi.org/10.1093/logcom/exad051","url":null,"abstract":"","PeriodicalId":50162,"journal":{"name":"Journal of Logic and Computation","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42869111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The continuous interest in Artificial Intelligence (AI) has brought, among other things, the development of several scenarios where multiple artificial entities interact with each other. As for all the other autonomous settings, these multi-agent systems require orchestration. This is, generally, achieved through techniques derived from the vast field of Automated Planning. Notably, arbitration in multi-agent domains is not only tasked with regulating how the agents act, but must also consider the interactions between the agents’ information flows and must, therefore, reason on an epistemic level. This brings a substantial overhead that often diminishes the reasoning process’s usability in real-world situations. To address this problem, we present ECHO, a hierarchical framework that embeds classical and multi-agent epistemic (epistemic, for brevity) planners in a single architecture. The idea is to combine (i) classical; and(ii) epistemic solvers to model efficiently the agents’ interactions with the (i) ‘physical world’; and(ii) information flows, respectively. In particular, the presented architecture starts by planning on the ‘epistemic level’, with a high level of abstraction, focusing only on the information flows. Then it refines the planning process, due to the classical planner, to fully characterize the interactions with the ‘physical’ world. To further optimize the solving process, we introduced the concept of macros in epistemic planning and enriched the ‘classical’ part of the domain with goal-networks. Finally, we evaluated our approach in an actual robotic environment showing that our architecture indeed reduces the overall computational time.
{"title":"ECHO: A hierarchical combination of classical and multi-agent epistemic planning problems","authors":"Davide Soldà, F. Fabiano, A. Dovier","doi":"10.1093/logcom/exad036","DOIUrl":"https://doi.org/10.1093/logcom/exad036","url":null,"abstract":"The continuous interest in Artificial Intelligence (AI) has brought, among other things, the development of several scenarios where multiple artificial entities interact with each other. As for all the other autonomous settings, these multi-agent systems require orchestration. This is, generally, achieved through techniques derived from the vast field of Automated Planning. Notably, arbitration in multi-agent domains is not only tasked with regulating how the agents act, but must also consider the interactions between the agents’ information flows and must, therefore, reason on an epistemic level. This brings a substantial overhead that often diminishes the reasoning process’s usability in real-world situations. To address this problem, we present ECHO, a hierarchical framework that embeds classical and multi-agent epistemic (epistemic, for brevity) planners in a single architecture. The idea is to combine (i) classical; and(ii) epistemic solvers to model efficiently the agents’ interactions with the (i) ‘physical world’; and(ii) information flows, respectively. In particular, the presented architecture starts by planning on the ‘epistemic level’, with a high level of abstraction, focusing only on the information flows. Then it refines the planning process, due to the classical planner, to fully characterize the interactions with the ‘physical’ world. To further optimize the solving process, we introduced the concept of macros in epistemic planning and enriched the ‘classical’ part of the domain with goal-networks.\u0000 Finally, we evaluated our approach in an actual robotic environment showing that our architecture indeed reduces the overall computational time.","PeriodicalId":50162,"journal":{"name":"Journal of Logic and Computation","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61625302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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