Recently, several logics modelling evidence have been proposed in the literature. These logics often also feature beliefs. We call the process or function that maps evidence to beliefs consolidation. In this paper, we use a four-valued modal logic of evidence as a basis. In the models for this logic, agents are represented by nodes, peer connections by edges and the private evidence that each agent has by a four-valued valuation. From this basis, we propose methods of consolidating the beliefs of the agents, taking into account both their private evidence as well as their peers’ opinions. To this end, beliefs are computed iteratively. The final consolidated beliefs are the ones in the point of stabilization of the model. However, it turns out that some consolidation policies will not stabilize for certain models. Finding the conditions for stabilization is one of the main problems studied here, along with other properties of such consolidations. Our main contributions are twofold: we offer a new dynamic perspective on the process of forming evidence-based beliefs, in the context of evidence logics, and we set up and address some mathematically challenging problems, which are related to graph theory and practical subject areas such as belief/opinion diffusion and contagion in multi-agent networks.
{"title":"Iterative social consolidations: Forming beliefs from many-valued evidence and peers' opinions","authors":"Y. D. Santos, Barteld P. Kooi, R. Verbrugge","doi":"10.1093/logcom/exac030","DOIUrl":"https://doi.org/10.1093/logcom/exac030","url":null,"abstract":"\u0000 Recently, several logics modelling evidence have been proposed in the literature. These logics often also feature beliefs. We call the process or function that maps evidence to beliefs consolidation. In this paper, we use a four-valued modal logic of evidence as a basis. In the models for this logic, agents are represented by nodes, peer connections by edges and the private evidence that each agent has by a four-valued valuation. From this basis, we propose methods of consolidating the beliefs of the agents, taking into account both their private evidence as well as their peers’ opinions. To this end, beliefs are computed iteratively. The final consolidated beliefs are the ones in the point of stabilization of the model. However, it turns out that some consolidation policies will not stabilize for certain models. Finding the conditions for stabilization is one of the main problems studied here, along with other properties of such consolidations. Our main contributions are twofold: we offer a new dynamic perspective on the process of forming evidence-based beliefs, in the context of evidence logics, and we set up and address some mathematically challenging problems, which are related to graph theory and practical subject areas such as belief/opinion diffusion and contagion in multi-agent networks.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"248 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132949984","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":"Netreason: Reasoning about social networks","authors":"G. Primiero, M. Slavkovik, S. Smets","doi":"10.1093/logcom/exac050","DOIUrl":"https://doi.org/10.1093/logcom/exac050","url":null,"abstract":"","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122959509","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}
In this paper, we investigate rule semantics for deductive databases in the context of four-valued logic. In our approach, a database is a pair $varDelta =(E,R)$, where $E$ is a set of pairs, each pair associating a ground fact with a truth value (thus, allowing to store true, false or inconsistent facts) and $R$ is a set of rules generalizing standard Datalog rules in the following sense: (i) the head of a rule can be a positive or a negative atom and (ii) the body can involve any among the connectors of four-valued logic. We define the database semantics as the least fixed point of a monotonic operator and we compare this semantics with that of k-existential programs defined by Fitting and paraconsistent extended logic programs defined by Arieli. Our main contribution is to show that, if we consider rules as implications (i.e. if we view the database as a set of formulas) then the semantics of the database is the unique minimal model of the set of database formulas. Here, minimality is understood with respect to the knowledge ordering of four-valued logic satisfying a monotonicity property whereby the truth value of the head of an instantiated rule is greater than that of the body. Moreover, we characterize databases having finite semantics and then, we address the issue of database updating. We argue that our approach allows for a new kind of updates, in which the update result depends not only on the fact involved in the update but also on its current truth value in the database.
{"title":"Deductive databases in four-valued logic: rule semantics and models","authors":"D. Laurent, N. Spyratos","doi":"10.1093/logcom/exac047","DOIUrl":"https://doi.org/10.1093/logcom/exac047","url":null,"abstract":"\u0000 In this paper, we investigate rule semantics for deductive databases in the context of four-valued logic. In our approach, a database is a pair $varDelta =(E,R)$, where $E$ is a set of pairs, each pair associating a ground fact with a truth value (thus, allowing to store true, false or inconsistent facts) and $R$ is a set of rules generalizing standard Datalog rules in the following sense: (i) the head of a rule can be a positive or a negative atom and (ii) the body can involve any among the connectors of four-valued logic. We define the database semantics as the least fixed point of a monotonic operator and we compare this semantics with that of k-existential programs defined by Fitting and paraconsistent extended logic programs defined by Arieli. Our main contribution is to show that, if we consider rules as implications (i.e. if we view the database as a set of formulas) then the semantics of the database is the unique minimal model of the set of database formulas. Here, minimality is understood with respect to the knowledge ordering of four-valued logic satisfying a monotonicity property whereby the truth value of the head of an instantiated rule is greater than that of the body. Moreover, we characterize databases having finite semantics and then, we address the issue of database updating. We argue that our approach allows for a new kind of updates, in which the update result depends not only on the fact involved in the update but also on its current truth value in the database.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125563650","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}
Big Data allows analysing and assessing all human production types with its 5Vs, which are Volume, Velocity, Variety, Veracity and Value. Big Data is useful to improve decision-making to adjust it better to market demand, specifically selection of supplier that is an important link to optimize the logistic chain of enterprises. In this case, leadership or decider is ahead one serious complex problem, inexact and fuzzy. Pythagorean fuzzy set (PFS) is disposing the indeterminacy data by the membership and the nonmembership functions; it is a generalization of the intuitionist fuzzy set when the last set is limited. First, some results for PFSs are displaying in this study as particular cases and generalization of some binary operations. After, an improved score function of Pythagorean fuzzy number is proposed to avoid the comparison problem in practice. In addition, an existing approach exploring the combined alternatives weight to settle Pythagorean fuzzy issue by multi-parametric similarity measure is applied with the new proposed score function to selection of supplier issue with five serious criteria as a Big Data industry decision-making problem in economic environment. Finally, a comparison of the presented method with some existing approaches has been executed in the light of counterintuitive phenomena for validating its advantages.
{"title":"Contribution to decision-making in the big data industry based on the multiparametric similarity measure for Pythagorean fuzzy sets","authors":"Bechar Ibrahim, A. Benyettou","doi":"10.1093/logcom/exac046","DOIUrl":"https://doi.org/10.1093/logcom/exac046","url":null,"abstract":"\u0000 Big Data allows analysing and assessing all human production types with its 5Vs, which are Volume, Velocity, Variety, Veracity and Value. Big Data is useful to improve decision-making to adjust it better to market demand, specifically selection of supplier that is an important link to optimize the logistic chain of enterprises. In this case, leadership or decider is ahead one serious complex problem, inexact and fuzzy. Pythagorean fuzzy set (PFS) is disposing the indeterminacy data by the membership and the nonmembership functions; it is a generalization of the intuitionist fuzzy set when the last set is limited. First, some results for PFSs are displaying in this study as particular cases and generalization of some binary operations. After, an improved score function of Pythagorean fuzzy number is proposed to avoid the comparison problem in practice. In addition, an existing approach exploring the combined alternatives weight to settle Pythagorean fuzzy issue by multi-parametric similarity measure is applied with the new proposed score function to selection of supplier issue with five serious criteria as a Big Data industry decision-making problem in economic environment. Finally, a comparison of the presented method with some existing approaches has been executed in the light of counterintuitive phenomena for validating its advantages.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129446984","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 distributed temporal logic (DTL) is a logic for reasoning about temporal properties of distributed systems from the local point of view of the system’s agents, which are assumed to execute sequentially and to interact by means of synchronous event sharing. Different versions of DTL have been proposed over the years for a number of different applications, reflecting different perspectives on how non-local information can be accessed by each agent. In a recent paper, an automata-theoretic approach to model check DTL was proposed Subtil et al. (2020, Technical Report). Herein, we follow a different approach and adapt the bounded model-checking (BMC) algorithm for linear temporal logic to the case of DTL (see Biere et al. (2003, Adv. Comput., 58, 117–148) and Biere et al. (1999, TACAS 1999, 193–207)). For that purpose, a new notion of bounded semantics for DTL is proposed. In the BMC approach, the witness problem is translated to the satisfiability of a propositional formula that can be addressed (efficiently) by SAT solvers. An important application for this approach is verification of security protocols (Basin et al. (2011, Theoret. Comput. Sci., 412, 4007–4043); Caleiro et al. (2005, Electron. Notes Theor. Comput. Sci., 125, 67–89)).
分布式时间逻辑(DTL)是从系统代理的本地角度对分布式系统的时间属性进行推理的逻辑，这些代理被假定为顺序执行并通过同步事件共享进行交互。多年来，针对许多不同的应用程序提出了不同版本的DTL，反映了每个代理如何访问非本地信息的不同观点。在最近的一篇论文中，Subtil等人(2020,technology Report)提出了一种模型检查DTL的自动机理论方法。在这里，我们采用了一种不同的方法，并将线性时间逻辑的有界模型检查(BMC)算法适应于DTL的情况(见Biere等人(2003年，adp . Comput)。Biere et . (1999, TACAS 1999, 193-207))。为此，提出了DTL有界语义的新概念。在BMC方法中，证人问题被转化为命题公式的可满足性，可以被SAT求解器(有效地)解决。该方法的一个重要应用是安全协议的验证(Basin et al. (2011, theory .))。第一版。科学。(2);Caleiro et al. (2005, Electron)。定理指出。第一版。科学。(中国科学院学报，125,67-89)。
{"title":"Bounded model checking distributed temporal logic","authors":"A. Peres, J. Ramos, F. Dionísio","doi":"10.1093/logcom/exac042","DOIUrl":"https://doi.org/10.1093/logcom/exac042","url":null,"abstract":"\u0000 The distributed temporal logic (DTL) is a logic for reasoning about temporal properties of distributed systems from the local point of view of the system’s agents, which are assumed to execute sequentially and to interact by means of synchronous event sharing. Different versions of DTL have been proposed over the years for a number of different applications, reflecting different perspectives on how non-local information can be accessed by each agent. In a recent paper, an automata-theoretic approach to model check DTL was proposed Subtil et al. (2020, Technical Report). Herein, we follow a different approach and adapt the bounded model-checking (BMC) algorithm for linear temporal logic to the case of DTL (see Biere et al. (2003, Adv. Comput., 58, 117–148) and Biere et al. (1999, TACAS 1999, 193–207)). For that purpose, a new notion of bounded semantics for DTL is proposed. In the BMC approach, the witness problem is translated to the satisfiability of a propositional formula that can be addressed (efficiently) by SAT solvers. An important application for this approach is verification of security protocols (Basin et al. (2011, Theoret. Comput. Sci., 412, 4007–4043); Caleiro et al. (2005, Electron. Notes Theor. Comput. Sci., 125, 67–89)).","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117239738","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 provide a semantic framework to specify information propagation in social networks; our semantic framework features both the operational description of information propagation and the epistemic aspects in social networks. In our framework, based on annotated labelled transition systems, actions are decorated with function views to specify different types of announcements. Our function views enforce various common types of local privacy policies, i.e. those policies concerning a single action. Furthermore, we specify global privacy policies, those concerning multiple actions, using a combination of modal $mu $-calculus and epistemic logic. To illustrate the applicability of our framework, we apply it to the specification of a real-world case study. As a fundamental property for the epistemic aspect of our semantic model, we prove that its indistinguishability relations are equivalence relations, namely they are reflexive, symmetric and transitive. We also study the complexity bounds for the model-checking problem concerning a subset of our logic and show that model checking is PSPACE-complete for the studied subset.
{"title":"A policy-aware epistemic framework for social networks","authors":"Zahra Moezkarimi, F. Ghassemi, M. Mousavi","doi":"10.1093/logcom/exac025","DOIUrl":"https://doi.org/10.1093/logcom/exac025","url":null,"abstract":"\u0000 We provide a semantic framework to specify information propagation in social networks; our semantic framework features both the operational description of information propagation and the epistemic aspects in social networks. In our framework, based on annotated labelled transition systems, actions are decorated with function views to specify different types of announcements. Our function views enforce various common types of local privacy policies, i.e. those policies concerning a single action. Furthermore, we specify global privacy policies, those concerning multiple actions, using a combination of modal $mu $-calculus and epistemic logic. To illustrate the applicability of our framework, we apply it to the specification of a real-world case study. As a fundamental property for the epistemic aspect of our semantic model, we prove that its indistinguishability relations are equivalence relations, namely they are reflexive, symmetric and transitive. We also study the complexity bounds for the model-checking problem concerning a subset of our logic and show that model checking is PSPACE-complete for the studied subset.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126236242","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 study the dynamics of information sharing in web-based social networks and analyse in a stochastic manner some aspects of this phenomenon. We define the stochastic sharing calculus by considering probabilistic factors and stochastic evolutions that could be analysed statistically. A rate-based operational semantics allows specific observations and results regarding sharing in web-based social networks. To reason about the dynamics of the social networks, we verify statistically various aspects of information sharing expressed in CTL by employing an existing statistical model checker (after a translation of our processes into stochastic automata). Some queries related to the stochastic behaviours in social networks are illustrated by a running example.
{"title":"Stochastic sharing calculus for reasoning about social networks","authors":"Bogdan Aman, Gabriel Ciobanu","doi":"10.1093/logcom/exac017","DOIUrl":"https://doi.org/10.1093/logcom/exac017","url":null,"abstract":"\u0000 We study the dynamics of information sharing in web-based social networks and analyse in a stochastic manner some aspects of this phenomenon. We define the stochastic sharing calculus by considering probabilistic factors and stochastic evolutions that could be analysed statistically. A rate-based operational semantics allows specific observations and results regarding sharing in web-based social networks. To reason about the dynamics of the social networks, we verify statistically various aspects of information sharing expressed in CTL by employing an existing statistical model checker (after a translation of our processes into stochastic automata). Some queries related to the stochastic behaviours in social networks are illustrated by a running example.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"47 11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133230533","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 : 2022-03-10DOI: 10.48550/arXiv.2203.05250
D. Normann, Sam Sanders
. We investigate the computational properties of basic mathematical notions pertaining to R → R -functions and subsets of R , like finiteness , countability , ( absolute ) continuity , bounded variation , suprema , and regular- ity . We work in higher-order computability theory based on Kleene’s S1-S9 schemes. We show that the aforementioned italicised properties give rise to two huge and robust classes of computationally equivalent operations, the latter based on well-known theorems from the mainstream mathematics literature. As part of this endeavour, we develop an equivalent λ -calculus formulation of S1-S9 that accommodates partial objects. We show that the latter are essen- tial to our enterprise via the study of countably based and partial functionals of type 3.
{"title":"On the computational properties of basic mathematical notions","authors":"D. Normann, Sam Sanders","doi":"10.48550/arXiv.2203.05250","DOIUrl":"https://doi.org/10.48550/arXiv.2203.05250","url":null,"abstract":". We investigate the computational properties of basic mathematical notions pertaining to R → R -functions and subsets of R , like finiteness , countability , ( absolute ) continuity , bounded variation , suprema , and regular- ity . We work in higher-order computability theory based on Kleene’s S1-S9 schemes. We show that the aforementioned italicised properties give rise to two huge and robust classes of computationally equivalent operations, the latter based on well-known theorems from the mainstream mathematics literature. As part of this endeavour, we develop an equivalent λ -calculus formulation of S1-S9 that accommodates partial objects. We show that the latter are essen- tial to our enterprise via the study of countably based and partial functionals of type 3.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116940849","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 : 2021-12-16DOI: 10.1007/978-3-030-93100-1_4
Neil J. DeBoer
{"title":"Justification Logic and Type Theory as Formalizations of Intuitionistic Propositional Logic","authors":"Neil J. DeBoer","doi":"10.1007/978-3-030-93100-1_4","DOIUrl":"https://doi.org/10.1007/978-3-030-93100-1_4","url":null,"abstract":"","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130945247","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 : 2021-12-16DOI: 10.1007/978-3-030-93100-1_13
Eoin Moore
{"title":"Soundness and Completeness Results for LEA and Probability Semantics","authors":"Eoin Moore","doi":"10.1007/978-3-030-93100-1_13","DOIUrl":"https://doi.org/10.1007/978-3-030-93100-1_13","url":null,"abstract":"","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133369451","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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