Fitch addressed the issue for which formulas ϕ it holds that ϕ → ♦Kϕ, i.e., which truths are know... more Fitch addressed the issue for which formulas ϕ it holds that ϕ → ♦Kϕ, i.e., which truths are knowable or in other words can be learnt [2]. He observed that this requirement is inconsistent with the existence of an unknown truth, i.e., with ψ∧¬Kψ. For example, given a propositional variable p, one can easily compute that the sentence p∧¬Kp cannot be made known, as from this and (p∧¬Kp) → ♦K(p∧¬Kp) we derive that it is conceivable for K(p∧¬Kp) to be (become) true. But for knowledge, and also for introspective belief, this is an inconsistency. Clearly, this issue relates to the phenomenon of Moore-sentences. These are sentences such that Kϕ is inconsistent. The prime example is again p ∧ ¬Kp. In his recent paper What one may come to know [3] Van Benthem proposed to interpret the ♦ operator in Fitch’s ϕ → ♦Kϕ, that stands for ‘at some future stage, ’ as: ‘for some restriction of the information state, resulting from an announcement. ’ We have taken up this proposal. Public announcement ...
Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge - TARK '07, 2007
Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators t... more Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: ϕ expresses that ϕ is true after an arbitrary announcement ψ. As this includes the trivial announcement , one might as well say that ϕ expresses what remains true after any announcement: it therefore corresponds to truth persistence after (definable) relativisation. The dual operation ♦ϕ expresses that there is an announcement after which ϕ. This gives a perspective on Fitch's knowability issues: for which formulas ϕ does it hold that ϕ → ♦Kϕ? We give various semantic results, and we show completeness for a Hilbert-style axiomatisation of this logic.
The picture of information acquisition as the elimination of possibilities has proven fruitful in... more The picture of information acquisition as the elimination of possibilities has proven fruitful in many domains, serving as a foundation for formal models in philosophy, linguistics, computer science, and economics. While the picture appears simple, its formalization in dynamic epistemic logic reveals subtleties: given a valid principle of information dynamics in the language of dynamic epistemic logic, substituting complex epistemic sentences for its atomic sentences may result in an invalid principle. In this article, we explore such failures of uniform substitution. First, we give epistemic examples inspired by Moore, Fitch, and Williamson. Second, we answer a rmatively a question posed by van Benthem: can we e↵ectively decide when every substitution instance of a given dynamic epistemic principle is valid? In technical terms, we prove the decidability of this schematic validity problem for Public Announcement Logic (PAL and PAL-RC) over models for finitely many fully introspective agents, as well as models for infinitely many arbitrary agents. The proof of this result illuminates the reasons for the failure of uniform substitution.
one may argue that (logical) inference is the central topic of any logic. What we have in mind he... more one may argue that (logical) inference is the central topic of any logic. What we have in mind here is reasoning about agents that make inferences.
In epistemic logic, Kripke structures are used to model the distribution of information in a mult... more In epistemic logic, Kripke structures are used to model the distribution of information in a multi-agent system. In this paper, we present an approach to quantifying how much information each particular agent in a system has, or how important the agent is, with respect to some fact represented as a goal formula. It is typically the case that the goal formula is distributed knowledge in the system, but that no individual agent alone knows it. It might be that several different groups of agents can get to know the goal formula together by combining their individual knowledge. By using power indices developed in voting theory, such as the Banzhaf index, we get a measure of how important an agent is in such groups. We analyse the properties of this notion of information-based power in detail, and characterise the corresponding class of voting games. Although we mainly focus on distributed knowledge, we also look at variants of this analysis using other notions of group knowledge. An adv...
Reasoning about rational agents interacting over time is a central topic in many areas of philoso... more Reasoning about rational agents interacting over time is a central topic in many areas of philosophy, computer science and economics. An important challenge for the logician is to account for the many dynamic processes that govern the agents’ interaction over time. Inference, observation and communication are all examples of such processes that are the focus of current logics of informational update and belief revision (see, for example, van Benthem, 1996; van Ditmarsch et al., 2007; Parikh and Ramanujam, 2003). A recurring issue in any formal model that represents agents’ informational attitudes over time is how to account for the fact that the agents are limited in their access to the available inference steps, possible observations and available messages. This may be because the agents are not logically omniscient and so do not have unlimited reasoning ability. But it can also be because the agents are following a predefined protocol that explicitly limits statements available fo...
Public announcement logic (PAL) is a paradigm case of dynamic epistemic logic, which models how a... more Public announcement logic (PAL) is a paradigm case of dynamic epistemic logic, which models how agents’ epistemic states change when pieces of information are communicated publicly. PAL extends epistemic logic with the operator [A], where the intended reading of [A]φ is “After a public announcement that A, φ holds.” This logic has recently received two improvements. One improvement, studied in [1], is to extend PAL with a generalized public announcement operator that allows quantification over public announcements. The other, studied in [5, 6], is a semantic setting to model “announcement protocols” to restrict the announcable sequences of formulas, while whatever is true is assumed to be announcable in PAL itself. The purpose of the present paper is to merge these two kinds of improvements. We consider the extension of public announcement logic with the generalized public announcement operator in the semantic setting of restricted announcement protocols.
Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitu... more Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely many agents, PAL-Kω, as well as standard extensions thereof, e.g., PAL-Tω, PAL-S4ω, and PAL-S5ω. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL.
Publikationsansicht. 34964870. What has Chihara's mathematical nominalism gained over mathem... more Publikationsansicht. 34964870. What has Chihara's mathematical nominalism gained over mathematical realism? / (2003). Hoshi, Tomohiro. Abstract. Thesis (MA)--Texas A & M University, 2003.. Includes bibliographical references (leaves 61-62).. Vita.. ...
[8] merges the semantic frameworks of Dynamic Epistemic Logic DEL ([1, 3]) and Epistemic Temporal... more [8] merges the semantic frameworks of Dynamic Epistemic Logic DEL ([1, 3]) and Epistemic Temporal Logic ETL ([2, 6]). We consider the logic TDEL on the merged semantic framework and its extension with the labeled past-operator "P " ("The event has happened before which..."). To axiomatize the extension, we introduce a method to transform a given model into a normal form in a suitable sense. These logics suggest further applications of DEL in the theory of agency, the theory of learning, etc.
This paper surveys the interface between the two major logical trends that describe agents' intel... more This paper surveys the interface between the two major logical trends that describe agents' intelligent interaction over time: dynamic epistemic logic (DEL) and epistemic temporal logic (ETL). The initial attempt to "merge" DEL and ETL was made in van Benthem et al. (Merging frameworks for interaction: DEL and ETL, 2007) and followed up by van Benthem et al. (J Phil Logic 38(5):491-526, 2009) and Hoshi (Epistemic dynamics and protocol information. Ph.D. thesis, Stanford University, Stanford, 2009a). The merged framework provides a systematic comparison between these two logical systems and studies new logics of intelligent interaction. This paper presents the main results and the recent developments at the interface between DEL and ETL.
Fitch's paradox has presented a problem for recent vericationist ac- counts of semantic ... more Fitch's paradox has presented a problem for recent vericationist ac- counts of semantic anti-realism. Although various kinds of accounts have been produced to deal with the problem, each account has been at least con- troversial in some respects. The main purpose of this paper is to propose an alternative account that avoids the problematic features of the previ- ous approaches. We achieve this goal by undertaking two tasks. The rst task is to provide a philosophical framework for vericationism that does not imply the formulation of the knowability thesis, every truth is know- able, from which Fitch's paradox is derived. Consequently, it will also block another problem concerning the knowability thesis, which is known as the idealism problem. The second task is to formalize the proposed framework by suitably interpreting a logical system in dynamic epistemic logic. Not only will this make explicit our theoretical commitments, but also it will allow us (i) to present a new formulation of the vericationist knowability thesis as a provable statement and (ii) to give a ne-grained logical analysis of alternative formulations of vericationist commitments to knowability.
Logics for dynamics of information and preferences
Public Announcement Logic with Protocol Constraints Tomohiro Hoshi Department of Philosophy, Stan... more Public Announcement Logic with Protocol Constraints Tomohiro Hoshi Department of Philosophy, Stanford University. thoshi@ stanford. edu Abstract There are two important ingredients in describing multi-agent intelligent interaction: one concerns how agents' epistemic ...
This paper surveys the interface between the two major logical trends that describe agents’ intel... more This paper surveys the interface between the two major logical trends that describe agents’ intelligent interaction over time: dynamic epistemic logic (DEL) and epistemic temporal logic (ETL). The initial attempt to “merge” DEL and ETL was made in van Benthem et al. (Merging frameworks for interaction: DEL and ETL, 2007) and followed up by van Benthem et al. (J Phil Logic 38(5):491–526,
ABSTRACT This paper investigates strategies for responding rationally to opponents who make mista... more ABSTRACT This paper investigates strategies for responding rationally to opponents who make mistakes. We identify two distinct interpretations of mistakes in the game theory literature: trembling hand and risk averse mistakes. We introduce the concept of an EFG Scenario, a game plus strategy profile, in order to probe the properties of these different types of mistake. An analysis of equivalence preserving transformations over EFG Scenarios reveals that risk averse mistakes are a form of rational play, while trembling hand mistakes are equivalent to moves by nature.
merges the semantic frameworks of Dynamic Epis- temic Logic DEL ((1, 3)) and Epistemic Temporal L... more merges the semantic frameworks of Dynamic Epis- temic Logic DEL ((1, 3)) and Epistemic Temporal Logic ETL ((2, 6)). We consider the logic TDEL on the merged semantic framework and its extension with the labeled past-operator "P! " ("The event ! has happened before which..."). To axiomatize the extension, we introduce a method to transform a given model into a normal form in a suitable sense. These logics suggest further applications of DEL in the theory of agency, the theory of learning, etc.
Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitu... more Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely many agents, PAL-K_omega, as well as standard extensions thereof, e.g., PAL-T_omega, PAL-S4_omega, and PAL-S5_omega. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL.
Fitch addressed the issue for which formulas ϕ it holds that ϕ → ♦Kϕ, i.e., which truths are know... more Fitch addressed the issue for which formulas ϕ it holds that ϕ → ♦Kϕ, i.e., which truths are knowable or in other words can be learnt [2]. He observed that this requirement is inconsistent with the existence of an unknown truth, i.e., with ψ∧¬Kψ. For example, given a propositional variable p, one can easily compute that the sentence p∧¬Kp cannot be made known, as from this and (p∧¬Kp) → ♦K(p∧¬Kp) we derive that it is conceivable for K(p∧¬Kp) to be (become) true. But for knowledge, and also for introspective belief, this is an inconsistency. Clearly, this issue relates to the phenomenon of Moore-sentences. These are sentences such that Kϕ is inconsistent. The prime example is again p ∧ ¬Kp. In his recent paper What one may come to know [3] Van Benthem proposed to interpret the ♦ operator in Fitch’s ϕ → ♦Kϕ, that stands for ‘at some future stage, ’ as: ‘for some restriction of the information state, resulting from an announcement. ’ We have taken up this proposal. Public announcement ...
Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge - TARK '07, 2007
Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators t... more Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: ϕ expresses that ϕ is true after an arbitrary announcement ψ. As this includes the trivial announcement , one might as well say that ϕ expresses what remains true after any announcement: it therefore corresponds to truth persistence after (definable) relativisation. The dual operation ♦ϕ expresses that there is an announcement after which ϕ. This gives a perspective on Fitch's knowability issues: for which formulas ϕ does it hold that ϕ → ♦Kϕ? We give various semantic results, and we show completeness for a Hilbert-style axiomatisation of this logic.
The picture of information acquisition as the elimination of possibilities has proven fruitful in... more The picture of information acquisition as the elimination of possibilities has proven fruitful in many domains, serving as a foundation for formal models in philosophy, linguistics, computer science, and economics. While the picture appears simple, its formalization in dynamic epistemic logic reveals subtleties: given a valid principle of information dynamics in the language of dynamic epistemic logic, substituting complex epistemic sentences for its atomic sentences may result in an invalid principle. In this article, we explore such failures of uniform substitution. First, we give epistemic examples inspired by Moore, Fitch, and Williamson. Second, we answer a rmatively a question posed by van Benthem: can we e↵ectively decide when every substitution instance of a given dynamic epistemic principle is valid? In technical terms, we prove the decidability of this schematic validity problem for Public Announcement Logic (PAL and PAL-RC) over models for finitely many fully introspective agents, as well as models for infinitely many arbitrary agents. The proof of this result illuminates the reasons for the failure of uniform substitution.
one may argue that (logical) inference is the central topic of any logic. What we have in mind he... more one may argue that (logical) inference is the central topic of any logic. What we have in mind here is reasoning about agents that make inferences.
In epistemic logic, Kripke structures are used to model the distribution of information in a mult... more In epistemic logic, Kripke structures are used to model the distribution of information in a multi-agent system. In this paper, we present an approach to quantifying how much information each particular agent in a system has, or how important the agent is, with respect to some fact represented as a goal formula. It is typically the case that the goal formula is distributed knowledge in the system, but that no individual agent alone knows it. It might be that several different groups of agents can get to know the goal formula together by combining their individual knowledge. By using power indices developed in voting theory, such as the Banzhaf index, we get a measure of how important an agent is in such groups. We analyse the properties of this notion of information-based power in detail, and characterise the corresponding class of voting games. Although we mainly focus on distributed knowledge, we also look at variants of this analysis using other notions of group knowledge. An adv...
Reasoning about rational agents interacting over time is a central topic in many areas of philoso... more Reasoning about rational agents interacting over time is a central topic in many areas of philosophy, computer science and economics. An important challenge for the logician is to account for the many dynamic processes that govern the agents’ interaction over time. Inference, observation and communication are all examples of such processes that are the focus of current logics of informational update and belief revision (see, for example, van Benthem, 1996; van Ditmarsch et al., 2007; Parikh and Ramanujam, 2003). A recurring issue in any formal model that represents agents’ informational attitudes over time is how to account for the fact that the agents are limited in their access to the available inference steps, possible observations and available messages. This may be because the agents are not logically omniscient and so do not have unlimited reasoning ability. But it can also be because the agents are following a predefined protocol that explicitly limits statements available fo...
Public announcement logic (PAL) is a paradigm case of dynamic epistemic logic, which models how a... more Public announcement logic (PAL) is a paradigm case of dynamic epistemic logic, which models how agents’ epistemic states change when pieces of information are communicated publicly. PAL extends epistemic logic with the operator [A], where the intended reading of [A]φ is “After a public announcement that A, φ holds.” This logic has recently received two improvements. One improvement, studied in [1], is to extend PAL with a generalized public announcement operator that allows quantification over public announcements. The other, studied in [5, 6], is a semantic setting to model “announcement protocols” to restrict the announcable sequences of formulas, while whatever is true is assumed to be announcable in PAL itself. The purpose of the present paper is to merge these two kinds of improvements. We consider the extension of public announcement logic with the generalized public announcement operator in the semantic setting of restricted announcement protocols.
Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitu... more Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely many agents, PAL-Kω, as well as standard extensions thereof, e.g., PAL-Tω, PAL-S4ω, and PAL-S5ω. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL.
Publikationsansicht. 34964870. What has Chihara's mathematical nominalism gained over mathem... more Publikationsansicht. 34964870. What has Chihara's mathematical nominalism gained over mathematical realism? / (2003). Hoshi, Tomohiro. Abstract. Thesis (MA)--Texas A & M University, 2003.. Includes bibliographical references (leaves 61-62).. Vita.. ...
[8] merges the semantic frameworks of Dynamic Epistemic Logic DEL ([1, 3]) and Epistemic Temporal... more [8] merges the semantic frameworks of Dynamic Epistemic Logic DEL ([1, 3]) and Epistemic Temporal Logic ETL ([2, 6]). We consider the logic TDEL on the merged semantic framework and its extension with the labeled past-operator "P " ("The event has happened before which..."). To axiomatize the extension, we introduce a method to transform a given model into a normal form in a suitable sense. These logics suggest further applications of DEL in the theory of agency, the theory of learning, etc.
This paper surveys the interface between the two major logical trends that describe agents' intel... more This paper surveys the interface between the two major logical trends that describe agents' intelligent interaction over time: dynamic epistemic logic (DEL) and epistemic temporal logic (ETL). The initial attempt to "merge" DEL and ETL was made in van Benthem et al. (Merging frameworks for interaction: DEL and ETL, 2007) and followed up by van Benthem et al. (J Phil Logic 38(5):491-526, 2009) and Hoshi (Epistemic dynamics and protocol information. Ph.D. thesis, Stanford University, Stanford, 2009a). The merged framework provides a systematic comparison between these two logical systems and studies new logics of intelligent interaction. This paper presents the main results and the recent developments at the interface between DEL and ETL.
Fitch's paradox has presented a problem for recent vericationist ac- counts of semantic ... more Fitch's paradox has presented a problem for recent vericationist ac- counts of semantic anti-realism. Although various kinds of accounts have been produced to deal with the problem, each account has been at least con- troversial in some respects. The main purpose of this paper is to propose an alternative account that avoids the problematic features of the previ- ous approaches. We achieve this goal by undertaking two tasks. The rst task is to provide a philosophical framework for vericationism that does not imply the formulation of the knowability thesis, every truth is know- able, from which Fitch's paradox is derived. Consequently, it will also block another problem concerning the knowability thesis, which is known as the idealism problem. The second task is to formalize the proposed framework by suitably interpreting a logical system in dynamic epistemic logic. Not only will this make explicit our theoretical commitments, but also it will allow us (i) to present a new formulation of the vericationist knowability thesis as a provable statement and (ii) to give a ne-grained logical analysis of alternative formulations of vericationist commitments to knowability.
Logics for dynamics of information and preferences
Public Announcement Logic with Protocol Constraints Tomohiro Hoshi Department of Philosophy, Stan... more Public Announcement Logic with Protocol Constraints Tomohiro Hoshi Department of Philosophy, Stanford University. thoshi@ stanford. edu Abstract There are two important ingredients in describing multi-agent intelligent interaction: one concerns how agents' epistemic ...
This paper surveys the interface between the two major logical trends that describe agents’ intel... more This paper surveys the interface between the two major logical trends that describe agents’ intelligent interaction over time: dynamic epistemic logic (DEL) and epistemic temporal logic (ETL). The initial attempt to “merge” DEL and ETL was made in van Benthem et al. (Merging frameworks for interaction: DEL and ETL, 2007) and followed up by van Benthem et al. (J Phil Logic 38(5):491–526,
ABSTRACT This paper investigates strategies for responding rationally to opponents who make mista... more ABSTRACT This paper investigates strategies for responding rationally to opponents who make mistakes. We identify two distinct interpretations of mistakes in the game theory literature: trembling hand and risk averse mistakes. We introduce the concept of an EFG Scenario, a game plus strategy profile, in order to probe the properties of these different types of mistake. An analysis of equivalence preserving transformations over EFG Scenarios reveals that risk averse mistakes are a form of rational play, while trembling hand mistakes are equivalent to moves by nature.
merges the semantic frameworks of Dynamic Epis- temic Logic DEL ((1, 3)) and Epistemic Temporal L... more merges the semantic frameworks of Dynamic Epis- temic Logic DEL ((1, 3)) and Epistemic Temporal Logic ETL ((2, 6)). We consider the logic TDEL on the merged semantic framework and its extension with the labeled past-operator "P! " ("The event ! has happened before which..."). To axiomatize the extension, we introduce a method to transform a given model into a normal form in a suitable sense. These logics suggest further applications of DEL in the theory of agency, the theory of learning, etc.
Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitu... more Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely many agents, PAL-K_omega, as well as standard extensions thereof, e.g., PAL-T_omega, PAL-S4_omega, and PAL-S5_omega. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL.
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Papers by Tomohiro Hoshi