We associate an elementary cellular automaton with a set of self-referential sentences, whose revision process is exactly the evolution process of that automaton. A simple but useful result of this connection is that a set of self-referential sentences is paradoxical, iff (the evolution process for) the cellular automaton in question has no fixed points. We sort out several distinct kinds of paradoxes by the existence and features of the fixed points of their corresponding automata. They are finite homogeneous paradoxes and infinite homogeneous paradoxes. In some weaker sense, we will also introduce no-no-sort paradoxes and virtual paradoxes. The introduction of these paradoxes, in turn, leads to a new classification of the cellular automata.
{"title":"Elementary cellular automata and self-referential paradoxes","authors":"Ming Hsiung","doi":"10.1093/logcom/exaa022","DOIUrl":"https://doi.org/10.1093/logcom/exaa022","url":null,"abstract":"We associate an elementary cellular automaton with a set of self-referential sentences, whose revision process is exactly the evolution process of that automaton. A simple but useful result of this connection is that a set of self-referential sentences is paradoxical, iff (the evolution process for) the cellular automaton in question has no fixed points. We sort out several distinct kinds of paradoxes by the existence and features of the fixed points of their corresponding automata. They are finite homogeneous paradoxes and infinite homogeneous paradoxes. In some weaker sense, we will also introduce no-no-sort paradoxes and virtual paradoxes. The introduction of these paradoxes, in turn, leads to a new classification of the cellular automata.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130794647","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}
We present formula equations—first-order formulas with unknowns standing for predicates—as a general formalism for treating certain questions in logic and computer science, like the Auflösungsproblem and loop invariant generation. In the case of the language of affine terms over $mathbb{Q}$, we translate a quantifier-free formula equation into an equivalent statement about affine spaces over $mathbb{Q}$, which can then be decided by an iteration procedure.
{"title":"Decidability of affine solution problems","authors":"Stefan Hetzl, Sebastian Zivota","doi":"10.1093/logcom/exz033","DOIUrl":"https://doi.org/10.1093/logcom/exz033","url":null,"abstract":"\u0000 We present formula equations—first-order formulas with unknowns standing for predicates—as a general formalism for treating certain questions in logic and computer science, like the Auflösungsproblem and loop invariant generation. In the case of the language of affine terms over $mathbb{Q}$, we translate a quantifier-free formula equation into an equivalent statement about affine spaces over $mathbb{Q}$, which can then be decided by an iteration procedure.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114579446","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 : 2020-04-06DOI: 10.1007/978-3-030-44638-3_3
Michael Baur, T. Studer
{"title":"Semirings of Evidence","authors":"Michael Baur, T. Studer","doi":"10.1007/978-3-030-44638-3_3","DOIUrl":"https://doi.org/10.1007/978-3-030-44638-3_3","url":null,"abstract":"","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"152 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127309546","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}
Presburger Arithmetic is the true theory of natural numbers with addition. We study interpretations of Presburger Arithmetic in itself. The main result of this paper is that all self-interpretations are definably isomorphic to the trivial one. Here we consider interpretations that might be multi-dimensional. We note that this resolves a conjecture by A. Visser. In order to prove the result we show that all linear orderings that are interpretable in $(mathbb{N};+)$ are scattered orderings with the finite Hausdorff rank and that the ranks are bounded in the terms of the dimensions of the respective interpretations.
{"title":"Multi-dimensional Interpretations of Presburger Arithmetic in Itself","authors":"F. Pakhomov, A. Zapryagaev","doi":"10.1093/logcom/exaa050","DOIUrl":"https://doi.org/10.1093/logcom/exaa050","url":null,"abstract":"Presburger Arithmetic is the true theory of natural numbers with addition. We study interpretations of Presburger Arithmetic in itself. The main result of this paper is that all self-interpretations are definably isomorphic to the trivial one. Here we consider interpretations that might be multi-dimensional. We note that this resolves a conjecture by A. Visser. In order to prove the result we show that all linear orderings that are interpretable in $(mathbb{N};+)$ are scattered orderings with the finite Hausdorff rank and that the ranks are bounded in the terms of the dimensions of the respective interpretations.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131347165","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}
We introduce labelled sequent calculi for quantified modal logics with definite descriptions. We prove that these calculi have the good structural properties of G3-style calculi. In particular, all rules are height-preserving invertible, weakening and contraction are height-preserving admissible and cut is syntactically admissible. Finally, we show that each calculus gives a proof-theoretic characterization of validity in the corresponding class of models.
{"title":"Labelled calculi for quantified modal logics with definite descriptions","authors":"E. Orlandelli","doi":"10.1093/LOGCOM/EXAB018","DOIUrl":"https://doi.org/10.1093/LOGCOM/EXAB018","url":null,"abstract":"\u0000 We introduce labelled sequent calculi for quantified modal logics with definite descriptions. We prove that these calculi have the good structural properties of G3-style calculi. In particular, all rules are height-preserving invertible, weakening and contraction are height-preserving admissible and cut is syntactically admissible. Finally, we show that each calculus gives a proof-theoretic characterization of validity in the corresponding class of models.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"13 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128859813","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 preferential conditional logic $ mathbb{PCL} $, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalizes Lewis’ sphere models for counterfactual logics, is proposed. Soundness and completeness of $ mathbb{PCL} $ and its extensions with respect to this class of models are proved directly. Labelled sequent calculi for all logics of the family are then introduced. The calculi are modular and have standard proof-theoretical properties, the most important of which is admissibility of cut that entails a syntactic proof of completeness of the calculi. By adopting a general strategy, root-first proof search terminates, thereby providing a decision procedure for $ mathbb{PCL} $ and its extensions. Finally, semantic completeness of the calculi is established: from a finite branch in a failed proof attempt it is possible to extract a finite countermodel of the root sequent. The latter result gives a constructive proof of the finite model property of all the logics considered.
{"title":"Uniform labelled calculi for preferential conditional logics based on neighbourhood semantics","authors":"Marianna Girlando, Sara Negri, N. Olivetti","doi":"10.1093/LOGCOM/EXAB019","DOIUrl":"https://doi.org/10.1093/LOGCOM/EXAB019","url":null,"abstract":"\u0000 The preferential conditional logic $ mathbb{PCL} $, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalizes Lewis’ sphere models for counterfactual logics, is proposed. Soundness and completeness of $ mathbb{PCL} $ and its extensions with respect to this class of models are proved directly. Labelled sequent calculi for all logics of the family are then introduced. The calculi are modular and have standard proof-theoretical properties, the most important of which is admissibility of cut that entails a syntactic proof of completeness of the calculi. By adopting a general strategy, root-first proof search terminates, thereby providing a decision procedure for $ mathbb{PCL} $ and its extensions. Finally, semantic completeness of the calculi is established: from a finite branch in a failed proof attempt it is possible to extract a finite countermodel of the root sequent. The latter result gives a constructive proof of the finite model property of all the logics considered.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129857116","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}
Tristan Charrier, S. Pinchinat, François Schwarzentruber
We study the symbolic model checking problem against public announcement protocol logic (PAPL), featuring protocols with public announcements, arbitrary public announcements and group announcements. Technically, symbolic models are Kripke models whose accessibility relations are presented as programs described in a dynamic logic style with propositional assignments. We highlight the relevance of such symbolic models and show that the symbolic model checking problem against PAPL is A$_{textrm{pol}}$Exptime-complete as soon as announcement protocols allow for either arbitrary announcements or iteration of public announcements. However, when both options are discarded, the complexity drops to Pspace-complete.
{"title":"Symbolic model checking of public announcement protocols","authors":"Tristan Charrier, S. Pinchinat, François Schwarzentruber","doi":"10.1093/logcom/exz023","DOIUrl":"https://doi.org/10.1093/logcom/exz023","url":null,"abstract":"\u0000 We study the symbolic model checking problem against public announcement protocol logic (PAPL), featuring protocols with public announcements, arbitrary public announcements and group announcements. Technically, symbolic models are Kripke models whose accessibility relations are presented as programs described in a dynamic logic style with propositional assignments. We highlight the relevance of such symbolic models and show that the symbolic model checking problem against PAPL is A$_{textrm{pol}}$Exptime-complete as soon as announcement protocols allow for either arbitrary announcements or iteration of public announcements. However, when both options are discarded, the complexity drops to Pspace-complete.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128664262","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}
This paper introduces a logic to reason about a well-known model of opinion dynamics in socialnetworks initially developed by Morris DeGroot as well as Keith Lehrer and Carl Wagner. The proposed logic is an extension of Lukasiewicz' famous fuzzy logic with additional equational expressivity, modal operators, machinery from hybrid logic, and dynamic modalities. The model of opinion dynamics in social networks is simple enough to be easily grasped, but still complex enough to have interesting mathematical properties and applications. Thus, developing a logic to reason about this particular model serves as a paradigmatic example of how logic can be useful in social network analysis.
{"title":"Reasoning about opinion dynamics in social networks","authors":"Jens Ulrik Hansen","doi":"10.1093/LOGCOM/EXV083","DOIUrl":"https://doi.org/10.1093/LOGCOM/EXV083","url":null,"abstract":"This paper introduces a logic to reason about a well-known model of opinion dynamics in socialnetworks initially developed by Morris DeGroot as well as Keith Lehrer and Carl Wagner. The proposed logic is an extension of Lukasiewicz' famous fuzzy logic with additional equational expressivity, modal operators, machinery from hybrid logic, and dynamic modalities. The model of opinion dynamics in social networks is simple enough to be easily grasped, but still complex enough to have interesting mathematical properties and applications. Thus, developing a logic to reason about this particular model serves as a paradigmatic example of how logic can be useful in social network analysis.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"355 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123426749","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}
We develop a logic for reasoning about semi-public environments, that is, environments in which a process is executing, and where agents in the environment have partial and potentially different views of the process. Previous work on this problem illustrated that it was problematic to obtain both an adequate semantic model and a language for reasoning about semi-public environments. We here use program models for representing the changes that occur during the execution of a program. These models serve both as syntactic objects and as semantic models, and are a modification of action models in Dynamic Epistemic Logic, in the sense that they allow for ontic change (i.e., change in the world or state). We show how program models can elegantly capture a notion of observation of the environment. The use of these models resolves several difficulties identified in earlier work, and admit a much simpler treatment than was possible in previous work on semi-public environments.
{"title":"Program models and semi-public environments","authors":"Davide Grossi, W. Hoek, C. Moyzes, M. Wooldridge","doi":"10.1093/LOGCOM/EXV086","DOIUrl":"https://doi.org/10.1093/LOGCOM/EXV086","url":null,"abstract":"We develop a logic for reasoning about semi-public environments, that is, environments in which a process is executing, and where agents in the environment have partial and potentially different views of the process. Previous work on this problem illustrated that it was problematic to obtain both an adequate semantic model and a language for reasoning about semi-public environments. We here use program models for representing the changes that occur during the execution of a program. These models serve both as syntactic objects and as semantic models, and are a modification of action models in Dynamic Epistemic Logic, in the sense that they allow for ontic change (i.e., change in the world or state). We show how program models can elegantly capture a notion of observation of the environment. The use of these models resolves several difficulties identified in earlier work, and admit a much simpler treatment than was possible in previous work on semi-public environments.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117184837","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}
{"title":"Topological facets of the logic of subset spaces (with emphasis on canonical models)","authors":"B. Heinemann","doi":"10.1093/LOGCOM/EXV087","DOIUrl":"https://doi.org/10.1093/LOGCOM/EXV087","url":null,"abstract":"","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"2011 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121546104","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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