A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces **generic theories** for propositional modal logic to address consistency results in a more robust way. As building blocks for background knowledge, generic theories provide a standard for categorical determinations of consistency. We argue that the results and methods of this paper help to elucidate problems in epistemology and enjoy sufficient scope and power to have purchase on problems bearing on modalities in judgement, inference, and decision making.
{"title":"Strengthening Consistency Results in Modal Logic","authors":"S. Alexander, Arthur Paul Pedersen","doi":"10.4204/EPTCS.379.4","DOIUrl":"https://doi.org/10.4204/EPTCS.379.4","url":null,"abstract":"A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces **generic theories** for propositional modal logic to address consistency results in a more robust way. As building blocks for background knowledge, generic theories provide a standard for categorical determinations of consistency. We argue that the results and methods of this paper help to elucidate problems in epistemology and enjoy sufficient scope and power to have purchase on problems bearing on modalities in judgement, inference, and decision making.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114331891","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}
Hierarchies of conditional beliefs (Battigalli and Siniscalchi 1999) play a central role for the epistemic analysis of solution concepts in sequential games. They are practically modelled by type structures, which allow the analyst to represent the players' hierarchies without specifying an infinite sequence of conditional beliefs. Here, we study type structures that satisfy a"richness"property, called completeness. This property is defined on the type structure alone, without explicit reference to hierarchies of beliefs or other type structures. We provide sufficient conditions under which a complete type structure represents all hierarchies of conditional beliefs. In particular, we present an extension of the main result in Friedenberg (2010) to type structures with conditional beliefs.
{"title":"Complete Conditional Type Structures (Extended Abstract)","authors":"Nicodemo De Vito","doi":"10.4204/EPTCS.379.15","DOIUrl":"https://doi.org/10.4204/EPTCS.379.15","url":null,"abstract":"Hierarchies of conditional beliefs (Battigalli and Siniscalchi 1999) play a central role for the epistemic analysis of solution concepts in sequential games. They are practically modelled by type structures, which allow the analyst to represent the players' hierarchies without specifying an infinite sequence of conditional beliefs. Here, we study type structures that satisfy a\"richness\"property, called completeness. This property is defined on the type structure alone, without explicit reference to hierarchies of beliefs or other type structures. We provide sufficient conditions under which a complete type structure represents all hierarchies of conditional beliefs. In particular, we present an extension of the main result in Friedenberg (2010) to type structures with conditional beliefs.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131693841","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 presents a logic-based framework to analyze responsibility, which I refer to as intentional epistemic act-utilitarian stit theory (IEAUST). To be precise, IEAUST is used to model and syntactically characterize various modes of responsibility, where by 'modes of responsibility' I mean instances of Broersen's three categories of responsibility (causal, informational, and motivational responsibility), cast against the background of particular deontic contexts. IEAUST is obtained by integrating a modal language to express the following components of responsibility on stit models: agency, epistemic notions, intentionality, and different senses of obligation. With such a language, I characterize the components of responsibility using particular formulas. Then, adopting a compositional approach -- where complex modalities are built out of more basic ones -- these characterizations of the components are used to formalize the aforementioned modes of responsibility.
{"title":"A Logic-Based Analysis of Responsibility","authors":"Aldo Iván Ramírez Abarca","doi":"10.4204/EPTCS.379.36","DOIUrl":"https://doi.org/10.4204/EPTCS.379.36","url":null,"abstract":"This paper presents a logic-based framework to analyze responsibility, which I refer to as intentional epistemic act-utilitarian stit theory (IEAUST). To be precise, IEAUST is used to model and syntactically characterize various modes of responsibility, where by 'modes of responsibility' I mean instances of Broersen's three categories of responsibility (causal, informational, and motivational responsibility), cast against the background of particular deontic contexts. IEAUST is obtained by integrating a modal language to express the following components of responsibility on stit models: agency, epistemic notions, intentionality, and different senses of obligation. With such a language, I characterize the components of responsibility using particular formulas. Then, adopting a compositional approach -- where complex modalities are built out of more basic ones -- these characterizations of the components are used to formalize the aforementioned modes of responsibility.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"233 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116173484","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}
Epistemic logics of intensional groups lift the assumption that membership in a group of agents is common knowledge. Instead of being represented directly as a set of agents, intensional groups are represented by a property that may change its extension from world to world. Several authors have considered versions of the intensional group framework where group-specifying properties are articulated using structured terms of a language, such as the language of Boolean algebras or of description logic. In this paper we formulate a general semantic framework for epistemic logics of structured intensional groups, develop the basic theory leading to completeness-via-canonicity results, and show that several frameworks presented in the literature correspond to special cases of the general framework.
{"title":"Epistemic Logics of Structured Intensional Groups","authors":"M. Bílková, I. Sedlár","doi":"10.4204/EPTCS.379.11","DOIUrl":"https://doi.org/10.4204/EPTCS.379.11","url":null,"abstract":"Epistemic logics of intensional groups lift the assumption that membership in a group of agents is common knowledge. Instead of being represented directly as a set of agents, intensional groups are represented by a property that may change its extension from world to world. Several authors have considered versions of the intensional group framework where group-specifying properties are articulated using structured terms of a language, such as the language of Boolean algebras or of description logic. In this paper we formulate a general semantic framework for epistemic logics of structured intensional groups, develop the basic theory leading to completeness-via-canonicity results, and show that several frameworks presented in the literature correspond to special cases of the general framework.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125927269","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 costs and benefits of selling data to a competitor. Although selling all consumers' data may decrease total firm profits, there exist other selling mechanisms -- in which only some consumers' data is sold -- that render both firms better off. We identify the profit-maximizing mechanism, and show that the benefit to firms comes at a cost to consumers. We then construct Pareto-improving mechanisms, in which each consumers' welfare, as well as both firms' profits, increase. Finally, we show that consumer opt-in can serve as an instrument to induce firms to choose a Pareto-improving mechanism over a profit-maximizing one.
{"title":"Selling Data to a Competitor","authors":"R. Gradwohl, Moshe Tennenholtz","doi":"10.4204/EPTCS.379.26","DOIUrl":"https://doi.org/10.4204/EPTCS.379.26","url":null,"abstract":"We study the costs and benefits of selling data to a competitor. Although selling all consumers' data may decrease total firm profits, there exist other selling mechanisms -- in which only some consumers' data is sold -- that render both firms better off. We identify the profit-maximizing mechanism, and show that the benefit to firms comes at a cost to consumers. We then construct Pareto-improving mechanisms, in which each consumers' welfare, as well as both firms' profits, increase. Finally, we show that consumer opt-in can serve as an instrument to induce firms to choose a Pareto-improving mechanism over a profit-maximizing one.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130449400","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}
C. Areces, Raul Fervari, Andrés R. Saravia, Fernando R. Vel'azquez-Quesada
We introduce a new semantics for a multi-agent epistemic operator of knowing how, based on an indistinguishability relation between plans. Our proposal is, arguably, closer to the standard presentation of knowing that modalities in classical epistemic logic. We study the relationship between this semantics and previous approaches, showing that our setting is general enough to capture them. We also define a sound and complete axiomatization, and investigate the computational complexity of its model checking and satisfiability problems.
{"title":"Uncertainty-Based Semantics for Multi-Agent Knowing How Logics","authors":"C. Areces, Raul Fervari, Andrés R. Saravia, Fernando R. Vel'azquez-Quesada","doi":"10.4204/EPTCS.335.3","DOIUrl":"https://doi.org/10.4204/EPTCS.335.3","url":null,"abstract":"We introduce a new semantics for a multi-agent epistemic operator of knowing how, based on an indistinguishability relation between plans. Our proposal is, arguably, closer to the standard presentation of knowing that modalities in classical epistemic logic. We study the relationship between this semantics and previous approaches, showing that our setting is general enough to capture them. We also define a sound and complete axiomatization, and investigate the computational complexity of its model checking and satisfiability problems.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122040706","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 the context of computational social choice, we study voting methods that assign a set of winners to each profile of voter preferences. A voting method satisfies the property of positive involvement (PI) if for any election in which a candidate x would be among the winners, adding another voter to the election who ranks x first does not cause x to lose. Surprisingly, a number of standard voting methods violate this natural property. In this paper, we investigate different ways of measuring the extent to which a voting method violates PI, using computer simulations. We consider the probability (under different probability models for preferences) of PI violations in randomly drawn profiles vs. profile-coalition pairs (involving coalitions of different sizes). We argue that in order to choose between a voting method that satisfies PI and one that does not, we should consider the probability of PI violation conditional on the voting methods choosing different winners. We should also relativize the probability of PI violation to what we call voter potency, the probability that a voter causes a candidate to lose. Although absolute frequencies of PI violations may be low, after this conditioning and relativization, we see that under certain voting methods that violate PI, much of a voter's potency is turned against them - in particular, against their desire to see their favorite candidate elected.
{"title":"Measuring Violations of Positive Involvement in Voting","authors":"W. Holliday, E. Pacuit","doi":"10.4204/EPTCS.335.17","DOIUrl":"https://doi.org/10.4204/EPTCS.335.17","url":null,"abstract":"In the context of computational social choice, we study voting methods that assign a set of winners to each profile of voter preferences. A voting method satisfies the property of positive involvement (PI) if for any election in which a candidate x would be among the winners, adding another voter to the election who ranks x first does not cause x to lose. Surprisingly, a number of standard voting methods violate this natural property. In this paper, we investigate different ways of measuring the extent to which a voting method violates PI, using computer simulations. We consider the probability (under different probability models for preferences) of PI violations in randomly drawn profiles vs. profile-coalition pairs (involving coalitions of different sizes). We argue that in order to choose between a voting method that satisfies PI and one that does not, we should consider the probability of PI violation conditional on the voting methods choosing different winners. We should also relativize the probability of PI violation to what we call voter potency, the probability that a voter causes a candidate to lose. Although absolute frequencies of PI violations may be low, after this conditioning and relativization, we see that under certain voting methods that violate PI, much of a voter's potency is turned against them - in particular, against their desire to see their favorite candidate elected.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"06 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129615461","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 formalization of action and obligation using logic languages is a topic of increasing relevance in the field of ethics for AI. Having an expressive syntactic and semantic framework to reason about agents' decisions in moral situations allows for unequivocal representations of components of behavior that are relevant when assigning blame (or praise) of outcomes to said agents. Two very important components of behavior in this respect are belief and belief-based action. In this work we present a logic of doxastic oughts by extending epistemic deontic stit theory with beliefs. On one hand, the semantics for formulas involving belief operators is based on probability measures. On the other, the semantics for doxastic oughts relies on a notion of optimality, and the underlying choice rule is maximization of expected utility. We introduce an axiom system for the resulting logic, and we address its soundness, completeness, and decidability results. These results are significant in the line of research that intends to use proof systems of epistemic, doxastic, and deontic logics to help in the testing of ethical behavior of AI through theorem-proving and model-checking.
{"title":"A Deontic Stit Logic Based on Beliefs and Expected Utility","authors":"Aldo Iván Ramírez Abarca, J. Broersen","doi":"10.4204/EPTCS.335.27","DOIUrl":"https://doi.org/10.4204/EPTCS.335.27","url":null,"abstract":"The formalization of action and obligation using logic languages is a topic of increasing relevance in the field of ethics for AI. Having an expressive syntactic and semantic framework to reason about agents' decisions in moral situations allows for unequivocal representations of components of behavior that are relevant when assigning blame (or praise) of outcomes to said agents. Two very important components of behavior in this respect are belief and belief-based action. In this work we present a logic of doxastic oughts by extending epistemic deontic stit theory with beliefs. On one hand, the semantics for formulas involving belief operators is based on probability measures. On the other, the semantics for doxastic oughts relies on a notion of optimality, and the underlying choice rule is maximization of expected utility. We introduce an axiom system for the resulting logic, and we address its soundness, completeness, and decidability results. These results are significant in the line of research that intends to use proof systems of epistemic, doxastic, and deontic logics to help in the testing of ethical behavior of AI through theorem-proving and model-checking.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128501304","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 Savage’s classic decision-theoretic framework [12], actions are formally defined as functions from states to outcomes. But where do the state space and outcome space come from? Expanding on recent work by Blume, Easley, and Halpern [3], we consider a language-based framework in which actions are identified with (conditional) descriptions in a simple underlying language, while states and outcomes (along with probabilities and utilities) are constructed as part of a representation theorem. Our work expands the role of language from that in [3] by using it not only for the conditions that determine which actions are taken, but also the effects. More precisely, we take the set of actions to be built from those of the form do(φ), for formulas φ in the underlying language. This presents a problem: how do we interpret the result of do(φ) when φ is underspecified (i.e., compatible with multiple states)? We answer this using tools familiar from the semantics of counterfactuals [13]: roughly speaking, do(φ) maps each state to the “closest” φ-state. This notion of “closest” is also something we construct as part of the representation theorem; in effect, then, we prove that (under appropriate assumptions) the agent is acting as if each underspecified action is first made definite and then evaluated (i.e., by maximizing expected utility). Of course, actions in the real world are often not presented in a fully precise manner, yet agents reason about and form preferences among them all the same. Our work brings the abstract tools of decision theory into closer contact with such real-world scenarios.
{"title":"Language-based Decisions","authors":"Adam Bjorndahl, Joseph Y. Halpern","doi":"10.4204/EPTCS.335.5","DOIUrl":"https://doi.org/10.4204/EPTCS.335.5","url":null,"abstract":"In Savage’s classic decision-theoretic framework [12], actions are formally defined as functions from states to outcomes. But where do the state space and outcome space come from? Expanding on recent work by Blume, Easley, and Halpern [3], we consider a language-based framework in which actions are identified with (conditional) descriptions in a simple underlying language, while states and outcomes (along with probabilities and utilities) are constructed as part of a representation theorem. Our work expands the role of language from that in [3] by using it not only for the conditions that determine which actions are taken, but also the effects. More precisely, we take the set of actions to be built from those of the form do(φ), for formulas φ in the underlying language. This presents a problem: how do we interpret the result of do(φ) when φ is underspecified (i.e., compatible with multiple states)? We answer this using tools familiar from the semantics of counterfactuals [13]: roughly speaking, do(φ) maps each state to the “closest” φ-state. This notion of “closest” is also something we construct as part of the representation theorem; in effect, then, we prove that (under appropriate assumptions) the agent is acting as if each underspecified action is first made definite and then evaluated (i.e., by maximizing expected utility). Of course, actions in the real world are often not presented in a fully precise manner, yet agents reason about and form preferences among them all the same. Our work brings the abstract tools of decision theory into closer contact with such real-world scenarios.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"129 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133351530","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 provide an epistemic analysis of a simple variant of the fundamental consistent broadcasting primitive for byzantine fault-tolerant asynchronous distributed systems. Our Firing Rebels with Relay (FRR) primitive enables agents with a local preference for acting/not acting to trigger an action (FIRE) at all correct agents, in an all-or-nothing fashion. By using the epistemic reasoning framework for byzantine multi-agent systems introduced in our TARK’19 paper, we develop the necessary and sufficient state of knowledge that needs to be acquired by the agents in order to FIRE. It involves eventual common hope (a modality related to belief), which we show to be attained already by achieving eventual mutual hope in the case of FRR. We also identify subtle variations of the necessary and sufficient state of knowledge for FRR for different assumptions on the local preferences.
{"title":"Fire!","authors":"Krisztina Fruzsa, R. Kuznets, U. Schmid","doi":"10.4204/EPTCS.335.13","DOIUrl":"https://doi.org/10.4204/EPTCS.335.13","url":null,"abstract":"In this paper, we provide an epistemic analysis of a simple variant of the fundamental consistent broadcasting primitive for byzantine fault-tolerant asynchronous distributed systems. Our Firing Rebels with Relay (FRR) primitive enables agents with a local preference for acting/not acting to trigger an action (FIRE) at all correct agents, in an all-or-nothing fashion. By using the epistemic reasoning framework for byzantine multi-agent systems introduced in our TARK’19 paper, we develop the necessary and sufficient state of knowledge that needs to be acquired by the agents in order to FIRE. It involves eventual common hope (a modality related to belief), which we show to be attained already by achieving eventual mutual hope in the case of FRR. We also identify subtle variations of the necessary and sufficient state of knowledge for FRR for different assumptions on the local preferences.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115093962","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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