At the beginning of a dynamic game, players may have exogenous theories about how the opponents are going to play. Suppose that these theories are commonly known. Then, players will refine their first-order beliefs, and challenge their own theories, through strategic reasoning. I develop and characterize epistemically a new solution concept, Selective Rationalizability, which accomplishes this task under the following assumption: when the observed behavior is not compatible with the beliefs in players' rationality and theories of all orders, players keep the orders of belief in rationality that are per se compatible with the observed behavior, and drop the incompatible beliefs in the theories. Thus, Selective Rationalizability captures Common Strong Belief in Rationality (Battigalli and Siniscalchi, 2002) and refines Extensive-Form Rationalizability (Pearce, 1984; BS, 2002), whereas Strong-$Delta$-Rationalizability (Battigalli, 2003; Battigalli and Siniscalchi, 2003) captures the opposite epistemic priority choice. Selective Rationalizability can be extended to encompass richer epistemic priority orderings among different theories of opponents' behavior. This allows to establish a surprising connection with strategic stability (Kohlberg and Mertens, 1986).
{"title":"Rationalizability and Epistemic Priority Orderings","authors":"Emiliano Catonini","doi":"10.4204/EPTCS.251.8","DOIUrl":"https://doi.org/10.4204/EPTCS.251.8","url":null,"abstract":"At the beginning of a dynamic game, players may have exogenous theories about how the opponents are going to play. Suppose that these theories are commonly known. Then, players will refine their first-order beliefs, and challenge their own theories, through strategic reasoning. I develop and characterize epistemically a new solution concept, Selective Rationalizability, which accomplishes this task under the following assumption: when the observed behavior is not compatible with the beliefs in players' rationality and theories of all orders, players keep the orders of belief in rationality that are per se compatible with the observed behavior, and drop the incompatible beliefs in the theories. Thus, Selective Rationalizability captures Common Strong Belief in Rationality (Battigalli and Siniscalchi, 2002) and refines Extensive-Form Rationalizability (Pearce, 1984; BS, 2002), whereas Strong-$Delta$-Rationalizability (Battigalli, 2003; Battigalli and Siniscalchi, 2003) captures the opposite epistemic priority choice. Selective Rationalizability can be extended to encompass richer epistemic priority orderings among different theories of opponents' behavior. This allows to establish a surprising connection with strategic stability (Kohlberg and Mertens, 1986).","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128933991","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}
A notion of pi-tolerant equilibrium is defined that takes into account that players have some tolerance regarding payoffs in a game. This solution concept generalizes Nash and refines epsilon-Nash equilibrium in a natural way. We show that pi-tolerant equilibrium can explain cooperation in social dilemmas such as Prisoner's Dilemma and the Public Good game. We then examine the structure of particularly cooperative pi-tolerant equilibria, where players are as cooperative as they can be, subject to their tolerances, in Prisoner's Dilemma. To the extent that cooperation is due to tolerance, these results provide guidance to a mechanism designer who has some control over the payoffs in a game, and suggest ways in which cooperation can be increased.
{"title":"Games With Tolerant Players","authors":"Arpita Ghosh, Joseph Y. Halpern","doi":"10.4204/EPTCS.251.18","DOIUrl":"https://doi.org/10.4204/EPTCS.251.18","url":null,"abstract":"A notion of pi-tolerant equilibrium is defined that takes into account that players have some tolerance regarding payoffs in a game. This solution concept generalizes Nash and refines epsilon-Nash equilibrium in a natural way. We show that pi-tolerant equilibrium can explain cooperation in social dilemmas such as Prisoner's Dilemma and the Public Good game. We then examine the structure of particularly cooperative pi-tolerant equilibria, where players are as cooperative as they can be, subject to their tolerances, in Prisoner's Dilemma. To the extent that cooperation is due to tolerance, these results provide guidance to a mechanism designer who has some control over the payoffs in a game, and suggest ways in which cooperation can be increased.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114635113","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 an axiomatic approach to group recommendations, in line of previous work on the axiomatic treatment of trust-based recommendation systems, ranking systems, and other foundational work on the axiomatic approach to internet mechanisms in social choice settings. In group recommendations we wish to recommend to a group of agents, consisting of both opinionated and undecided members, a joint choice that would be acceptable to them. Such a system has many applications, such as choosing a movie or a restaurant to go to with a group of friends, recommending games for online game players, & other communal activities. Our method utilizes a given social graph to extract information on the undecided, relying on the agents influencing them. We first show that a set of fairly natural desired requirements (a.k.a axioms) leads to an impossibility, rendering mutual satisfaction of them unreachable. However, we also show a modified set of axioms that fully axiomatize a group variant of the random-walk recommendation system, expanding a previous result from the individual recommendation case.
{"title":"Group Recommendations: Axioms, Impossibilities, and Random Walks","authors":"Omer Lev, Moshe Tennenholtz","doi":"10.4204/EPTCS.251.28","DOIUrl":"https://doi.org/10.4204/EPTCS.251.28","url":null,"abstract":"We introduce an axiomatic approach to group recommendations, in line of previous work on the axiomatic treatment of trust-based recommendation systems, ranking systems, and other foundational work on the axiomatic approach to internet mechanisms in social choice settings. In group recommendations we wish to recommend to a group of agents, consisting of both opinionated and undecided members, a joint choice that would be acceptable to them. Such a system has many applications, such as choosing a movie or a restaurant to go to with a group of friends, recommending games for online game players, & other communal activities. \u0000Our method utilizes a given social graph to extract information on the undecided, relying on the agents influencing them. We first show that a set of fairly natural desired requirements (a.k.a axioms) leads to an impossibility, rendering mutual satisfaction of them unreachable. However, we also show a modified set of axioms that fully axiomatize a group variant of the random-walk recommendation system, expanding a previous result from the individual recommendation case.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115163196","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}
Legal probabilism (LP) claims the degrees of conviction in juridical fact-finding are to be modeled exactly the way degrees of beliefs are modeled in standard bayesian epistemology. Classical legal probabilism (CLP) adds that the conviction is justified if the credence in guilt given the evidence is above an appropriate guilt probability threshold. The views are challenged on various counts, especially by the proponents of the so-called narrative approach, on which the fact-finders' decision is the result of a dynamic interplay between competing narratives of what happened. I develop a way a bayesian epistemologist can make sense of the narrative approach. I do so by formulating a probabilistic framework for evaluating competing narrations in terms of formal explications of the informal evaluation criteria used in the narrative approach.
{"title":"Reconciling Bayesian Epistemology and Narration-based Approaches to Judiciary Fact-finding","authors":"R. Urbaniak","doi":"10.4204/EPTCS.251.37","DOIUrl":"https://doi.org/10.4204/EPTCS.251.37","url":null,"abstract":"Legal probabilism (LP) claims the degrees of conviction in juridical fact-finding are to be modeled exactly the way degrees of beliefs are modeled in standard bayesian epistemology. Classical legal probabilism (CLP) adds that the conviction is justified if the credence in guilt given the evidence is above an appropriate guilt probability threshold. The views are challenged on various counts, especially by the proponents of the so-called narrative approach, on which the fact-finders' decision is the result of a dynamic interplay between competing narratives of what happened. I develop a way a bayesian epistemologist can make sense of the narrative approach. I do so by formulating a probabilistic framework for evaluating competing narrations in terms of formal explications of the informal evaluation criteria used in the narrative approach.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123555423","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}
A natural way to represent beliefs and the process of updating beliefs is presented by Bayesian probability theory, where belief of an agent a in P can be interpreted as a considering that P is more probable than not P. This paper attempts to get at the core logical notion underlying this. The paper presents a sound and complete neighbourhood logic for conditional belief and knowledge, and traces the connections with probabilistic logics of belief and knowledge. The key notion in this paper is that of an agent a believing P conditionally on having information Q, where it is assumed that Q is compatible with what a knows. Conditional neighbourhood logic can be viewed as a core system for reasoning about subjective plausibility that is not yet committed to an interpretation in terms of numerical probability. Indeed, every weighted Kripke model gives rise to a conditional neighbourhood model, but not vice versa. We show that our calculus for conditional neighbourhood logic is sound but not complete for weighted Kripke models. Next, we show how to extend the calculus to get completeness for the class of weighted Kripke models. Neighbourhood models for conditional belief are closed under model restriction (public announcement update), while earlier neighbourhood models for belief as `willingness to bet' were not. Therefore the logic we present improves on earlier neighbourhood logics for belief and knowledge. We present complete calculi for public announcement and for publicly revealing the truth value of propositions using reduction axioms. The reductions show that adding these announcement operators to the language does not increase expressive power.
{"title":"Conditional Belief, Knowledge and Probability","authors":"J. Eijck, K. Li","doi":"10.4204/EPTCS.251.14","DOIUrl":"https://doi.org/10.4204/EPTCS.251.14","url":null,"abstract":"A natural way to represent beliefs and the process of updating beliefs is presented by Bayesian probability theory, where belief of an agent a in P can be interpreted as a considering that P is more probable than not P. This paper attempts to get at the core logical notion underlying this. \u0000The paper presents a sound and complete neighbourhood logic for conditional belief and knowledge, and traces the connections with probabilistic logics of belief and knowledge. The key notion in this paper is that of an agent a believing P conditionally on having information Q, where it is assumed that Q is compatible with what a knows. \u0000Conditional neighbourhood logic can be viewed as a core system for reasoning about subjective plausibility that is not yet committed to an interpretation in terms of numerical probability. Indeed, every weighted Kripke model gives rise to a conditional neighbourhood model, but not vice versa. We show that our calculus for conditional neighbourhood logic is sound but not complete for weighted Kripke models. Next, we show how to extend the calculus to get completeness for the class of weighted Kripke models. \u0000Neighbourhood models for conditional belief are closed under model restriction (public announcement update), while earlier neighbourhood models for belief as `willingness to bet' were not. Therefore the logic we present improves on earlier neighbourhood logics for belief and knowledge. We present complete calculi for public announcement and for publicly revealing the truth value of propositions using reduction axioms. The reductions show that adding these announcement operators to the language does not increase expressive power.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133687702","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 construct the universal type structure for conditional probability systems without any topological assumption, namely a type structure that is terminal, belief-complete, and non-redundant. In particular, in order to obtain the belief-completeness in a constructive way, we extend the work of Meier [An Infinitary Probability Logic for Type Spaces. Israel Journal of Mathematics, 192, 1-58] by proving strong soundness and strong completeness of an infinitary conditional probability logic with truthful and non-epistemic conditioning events.
我们构造了不带拓扑假设的条件概率系统的普适型结构，即一种终端型、信念完备型和非冗余型结构。特别地，为了以建设性的方式获得相信完备性，我们推广了Meier [a∞Probability Logic for Type Spaces]的工作。数学学报，1999,19 (1):1- 8 [j] .用数学方法证明了具有真实和非认知条件事件的无限概率逻辑的强完备性。
{"title":"The Topology-Free Construction of the Universal Type Structure for Conditional Probability Systems","authors":"Pierfrancesco Guarino","doi":"10.4204/EPTCS.251.20","DOIUrl":"https://doi.org/10.4204/EPTCS.251.20","url":null,"abstract":"We construct the universal type structure for conditional probability systems without any topological assumption, namely a type structure that is terminal, belief-complete, and non-redundant. In particular, in order to obtain the belief-completeness in a constructive way, we extend the work of Meier [An Infinitary Probability Logic for Type Spaces. Israel Journal of Mathematics, 192, 1-58] by proving strong soundness and strong completeness of an infinitary conditional probability logic with truthful and non-epistemic conditioning events.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125409818","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}
H. V. Ditmarsch, M. Hartley, Barteld P. Kooi, J. Welton, Joseph B. W. Yeo
We present four logic puzzles and after that their solutions. Joseph Yeo designed 'Cheryl's Birthday'. Mike Hartley came up with a novel solution for 'One Hundred Prisoners and a Light Bulb'. Jonathan Welton designed 'A Blind Guess' and 'Abby's Birthday'. Hans van Ditmarsch and Barteld Kooi authored the puzzlebook 'One Hundred Prisoners and a Light Bulb' that contains other knowledge puzzles, and that can also be found on the webpage http://personal.us.es/hvd/lightbulb.html dedicated to the book.
我们提出了四个逻辑难题，然后，他们的解决方案。“谢丽尔的生日”由约瑟夫·杨设计。迈克·哈特利为《一百个囚犯和一个灯泡》想出了一个新颖的解决方案。乔纳森·韦尔顿设计了“盲目猜测”和“艾比的生日”。Hans van Ditmarsch和Barteld Kooi撰写了益智书《一百个囚犯和一个灯泡》，其中包含其他知识难题，也可以在专门为该书设计的网页http://personal.us.es/hvd/lightbulb.html上找到。
{"title":"Cheryl's Birthday","authors":"H. V. Ditmarsch, M. Hartley, Barteld P. Kooi, J. Welton, Joseph B. W. Yeo","doi":"10.4204/EPTCS.251.1","DOIUrl":"https://doi.org/10.4204/EPTCS.251.1","url":null,"abstract":"We present four logic puzzles and after that their solutions. Joseph Yeo designed 'Cheryl's Birthday'. Mike Hartley came up with a novel solution for 'One Hundred Prisoners and a Light Bulb'. Jonathan Welton designed 'A Blind Guess' and 'Abby's Birthday'. Hans van Ditmarsch and Barteld Kooi authored the puzzlebook 'One Hundred Prisoners and a Light Bulb' that contains other knowledge puzzles, and that can also be found on the webpage http://personal.us.es/hvd/lightbulb.html dedicated to the book.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"528 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116706399","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}
Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other secrets. Recently a number of authors studied distributed epistemic gossip protocols. These protocols use as guards formulas from a simple epistemic logic, which makes their analysis and verification substantially easier. We study here common knowledge in the context of such a logic. First, we analyze when it can be reduced to iterated knowledge. Then we show that the semantics and truth for formulas without nested common knowledge operator are decidable. This implies that implementability, partial correctness and termination of distributed epistemic gossip protocols that use non-nested common knowledge operator is decidable, as well. Given that common knowledge is equivalent to an infinite conjunction of nested knowledge, these results are non-trivial generalizations of the corresponding decidability results for the original epistemic logic, established in (Apt & Wojtczak, 2016). K. R. Apt & D. Wojtczak (2016): On Decidability of a Logic of Gossips. In Proc. of JELIA 2016, pp. 18-33, doi:10.1007/ 978-3-319-48758-8_2.
八卦协议旨在通过点对点或群体通信的方式，达到一种所有特工都知道彼此秘密的状态。最近，许多作者研究了分布式认知八卦协议。这些协议使用来自简单认知逻辑的保护公式，这使得它们的分析和验证更加容易。我们在这里研究这种逻辑背景下的常识。首先，我们分析了它何时可以被简化为迭代知识。然后证明了没有嵌套公共知识算子的公式的语义和真值是可判定的。这意味着使用非嵌套公共知识算子的分布式知识八卦协议的可实现性、部分正确性和终止性也是可确定的。鉴于共同知识等同于嵌套知识的无限结合，这些结果是对(Apt & Wojtczak, 2016)中建立的原始认知逻辑的相应可判定性结果的非平凡推广。K. R. Apt & D. Wojtczak(2016):论八卦逻辑的可决性。中国生物医学工程学报，2016,pp. 18-33, doi:10.1007/ 978-3-319-48758-8_2。
{"title":"Common Knowledge in a Logic of Gossips","authors":"K. Apt, D. Wojtczak","doi":"10.4204/EPTCS.251.2","DOIUrl":"https://doi.org/10.4204/EPTCS.251.2","url":null,"abstract":"Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other secrets. Recently a number of authors studied distributed epistemic gossip protocols. These protocols use as guards formulas from a simple epistemic logic, which makes their analysis and verification substantially easier. \u0000We study here common knowledge in the context of such a logic. First, we analyze when it can be reduced to iterated knowledge. Then we show that the semantics and truth for formulas without nested common knowledge operator are decidable. This implies that implementability, partial correctness and termination of distributed epistemic gossip protocols that use non-nested common knowledge operator is decidable, as well. Given that common knowledge is equivalent to an infinite conjunction of nested knowledge, these results are non-trivial generalizations of the corresponding decidability results for the original epistemic logic, established in (Apt & Wojtczak, 2016). \u0000K. R. Apt & D. Wojtczak (2016): On Decidability of a Logic of Gossips. In Proc. of JELIA 2016, pp. 18-33, doi:10.1007/ 978-3-319-48758-8_2.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121569768","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}
Willem Conradie, S. Frittella, A. Palmigiano, M. Piazzai, A. Tzimoulis, N. Wijnberg
Categorization systems are widely studied in psychology, sociology, and organization theory as information-structuring devices which are critical to decision-making processes. In the present paper, we introduce a sound and complete epistemic logic of categories and agents' categorical perception. The Kripke-style semantics of this logic is given in terms of data structures based on two domains: one domain representing objects (e.g. market products) and one domain representing the features of the objects which are relevant to the agents' decision-making. We use this framework to discuss and propose logic-based formalizations of some core concepts from psychological, sociological, and organizational research in categorization theory.
{"title":"Toward an Epistemic-Logical Theory of Categorization","authors":"Willem Conradie, S. Frittella, A. Palmigiano, M. Piazzai, A. Tzimoulis, N. Wijnberg","doi":"10.4204/EPTCS.251.12","DOIUrl":"https://doi.org/10.4204/EPTCS.251.12","url":null,"abstract":"Categorization systems are widely studied in psychology, sociology, and organization theory as information-structuring devices which are critical to decision-making processes. In the present paper, we introduce a sound and complete epistemic logic of categories and agents' categorical perception. The Kripke-style semantics of this logic is given in terms of data structures based on two domains: one domain representing objects (e.g. market products) and one domain representing the features of the objects which are relevant to the agents' decision-making. We use this framework to discuss and propose logic-based formalizations of some core concepts from psychological, sociological, and organizational research in categorization theory.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115342131","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}
Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic, and characterise inquisitive modal logic as the bisimulation invariant fragments of first-order logic over various classes of two-sorted relational structures. These results crucially require non-classical methods in studying bisimulations and first-order expressiveness over non-elementary classes.
{"title":"Bisimulation in Inquisitive Modal Logic","authors":"Ivano Ciardelli, M. Otto","doi":"10.4204/EPTCS.251.11","DOIUrl":"https://doi.org/10.4204/EPTCS.251.11","url":null,"abstract":"Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic, and characterise inquisitive modal logic as the bisimulation invariant fragments of first-order logic over various classes of two-sorted relational structures. These results crucially require non-classical methods in studying bisimulations and first-order expressiveness over non-elementary classes.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"156 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114107719","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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