A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic event (...) models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall , No Miracles , and Bisimulation Invariance . We then focus on new issues of completeness . One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL. (shrink)

Public announcement logic is an extension of multiagent 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: after which , does it hold that Kφ? We give various semantic results and show completeness for a Hilbert-style axiomatization of this logic. There is a natural generalization to a logic for arbitrary events.

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic event (...) models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall, No Miracles, and Bisimulation Invariance. We then focus on new issues of completeness. One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL. (shrink)

van Bentham et al. (Merging frameworks for interaction: DEL and ETL, 2007) provides a framework for generating the models of Epistemic Temporal Logic ( ETL : Fagin et al., Reasoning about knowledge, 1995; Parikh and Ramanujam, Journal of Logic, Language, and Information, 2003) from the models of Dynamic Epistemic Logic ( DEL : Baltag et al., in: Gilboa (ed.) Tark 1998, 1998; Gerbrandy, Bisimulations on Planet Kripke, 1999). We consider the logic TDEL on the merged semantic framework, and its extension (...) with the labeled past-operator “ P ϵ ” (“The event ϵ has happened before which. . .”). To axiomatize the extension, we introduce a method for transforming 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. (shrink)

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 affirmatively a question posed by van Benthem: can we effectively 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. (shrink)

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. (shrink)

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. (shrink)

Diachronic uncertainty, uncertainty about where an agent falls in time, poses interesting conceptual difficulties. Although the agent is uncertain about where she falls in time, this uncertainty can only obtain at a particular moment in time. We resolve this conceptual tension by providing a transformation from models with diachronic uncertainty relations into “equivalent” models with only synchronic uncertainty relations. The former are interpreted as capturing the causal structure of a situation, while the latter are interpreted as capturing its epistemic structure. (...) The models are equivalent in the sense that agents pass through the same information sets in the same order, In this paper, we investigate how such a transformation may be used to define an appropriate notion of equivalence, which we call epistemic equivalence. Although our project is motivated by problems which have arisen in a variety of disciplines, especially philosophy and game theory, our formal development takes place within the general and flexible framework provided by epistemic temporal logic. (shrink)

A recurring issue in any formal model representing agents' (changing) informational attitudes 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 for observation and/or communication. Within the broad literature (...) on epistemic logic, there are a variety of accounts that make precise a notion of an agent's "limited access" (for example, Awareness Logics, Justification Logics, and Inference Logics). This paper interprets the agents' access set of formulas as a constraint on the agents' information gathering process limiting which formulas can be observed. (shrink)

Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitu- tion 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. (shrink)

The indispensability argument, which claims that science requires beliefs in mathematical entities, gives a strong motivation for mathematical realism. However, mathematical realism bears Benacerrafian ontological and epistemological problems. Although recent accounts of mathematical realism have attempted to cope with these problems, it seems that, at least, a satisfactory account of epistemology of mathematics has not been presented. For instance, Maddy's realism with perceivable sets and Resnik's and Shapiro's structuralism have their own epistemological problems. This fact has been a reason to (...) rebut the indispensability argument and adopt mathematical nominalism. Since mathematical nominalism purports to be committed only to concretia, it seems that mathematical nominalism is epistemically friendlier than mathematical realism. However, when it comes to modal mathematical nominalism, this claim is not trivial. There is a reason for doubting the modal primitives that it invokes. In this thesis, this doubt is investigated through Chihara's Constructibility Theory. Chihara's Constructibility Theory purports not to be committed to abstracta by replacing existential assertions of the standard mathematics with ones of constructibility. However, the epistemological status of the primitives in Chihara's system can be doubted. Chihara might try to argue that the problem would dissolve by using possible world semantics as a didactic device to capture the primitive notions. Nonetheless, his analysis of possible world semantic is not plausible, when considered as a part of the project of nominalizing mathematics in terms of the Constructibility Theory. (shrink)