This article examines the preservation of structural properties in epistemic and doxastic logic, with a particular focus on action model logic and the dynamics of group belief. Two central questions guide the analysis: (a) which frame conditions remain invariant under the execution of epistemic actions? and (b) do group conditions—properties allowing groups to be modeled as unified agents—persist after such actions? The study further explores specific subclasses of epistemic actions, including public announcements and unconditional actions, highlighting their distinctive preservation features. These findings contribute to a deeper understanding of the logical foundations of epistemic and doxastic reasoning, particularly within dynamic multi-agent frameworks.

Simulation and refinement are variations of the bisimulation relation, where in the former we keep only atoms and forth, and in the latter only atoms and back. Quantifying over simulations and refinements captures the effects of information change in a multi-agent system. In the case of quantification over refinements, we are looking at all the ways the agents in a system can become more informed. Similarly, in the case of quantification over simulations, we are dealing with all the ways the agents can become less informed, or in other words, could have been less informed, as we are at liberty how to interpret time in dynamic epistemic logic. While quantification over refinements has been well explored in the literature, quantification over simulations has received considerably less attention. In this paper, we explore the relationship between refinements and simulations. To this end, we also employ the notion of mutual factual ignorance that allows us to capture the state of a model before agents have learnt any factual information. In particular, we consider the extensions of multi-modal logic with the simulation and refinement modalities, as well as modalities for mutual factual ignorance. We provide reduction-based axiomatizations for several of the resulting logics that are built extending one another in a modular fashion.

Abstract We develop a proof-theoretic semantics—in particular, a base-extension semantics—for multi-agent $S5$ modal logic (and hence also for the usual unindexed $S5$). Following the inferentialist interpretation of logic, this gives us a semantics in which validity is based on proof rather than truth. In base-extension semantics, the validity of formulae is generated by provability in a ‘base’ of atomic rules and an inductive definition of the validity of the connectives. Base-extension semantics for many interesting logics has been explored by several authors and, in particular, a base-extension semantics for the modal logics $K$, $KT$, $K4$, and $S4$ has been developed by the present authors. Here, we give a base-extension semantics for multi-agent $S5$ with $\square _{a}$, for an agent $a$, as our primary operators, framed as the knowledge operator $K_{a}$. Similarly to Kripke semantics, we make use of relational structure between bases, allowing us to establish a correspondence between certain bases and worlds. We use this to establish the appropriate soundness and completeness results. We conclude by discussing how this semantics can be extended to Dynamic Epistemic Logics (DEL) starting with Public Announcement Logic (PAL). This note directly supplements [4] and does not repeat the discussion in it.

In today's rapidly changing and challenging world, complex interdisciplinary issues continue to emerge, such as environmental sustainability and artificial intelligence-driven adaptive learning. Understanding and resolving these problems require individuals to integrate knowledge, methodologies, and diverse ways of thinking. Within this problem-oriented process, the importance and potential necessity of interdisciplinary education and research become self-evident. However, how can we better promote interdisciplinary communication in the sense of transdisciplinary notions? This is a systematic endeavor involving multiple aspects, including cognition, methodology, team collaboration, and policy formulation. This paper focuses primarily on the cognitive level, first conducting an in-depth analysis of the cognitive challenges faced during interdisciplinary cooperation and communication. In response to these challenges, the paper introduces Logical Dynamics (a theoretical framework) and Dynamic Epistemic Logic (a formal tool). From three dimensions—perspective transformation, cognitive representation, and educational application—the article elaborates on "how Logical Dynamics provides guidance for interdisciplinary education and research at the level of cognitive thinking. "Moreover, artificial intelligence has been deeply integrated into interdisciplinary communication. Under the guidance of Logical Dynamics, AI can more accurately articulate problems and facilitate the generation of more creative solutions among interdisciplinary participants.

We give a general-purpose programming language in which programs can reason about their own knowledge. To specify what these intelligent programs know, we define a “program epistemic” logic, akin to a dynamic epistemic logic for programs. Our logic properties are complex, including programs introspecting into future state of affairs, i.e., reasoning now about facts that hold only after they and other threads will execute. To model aspects anchored in privacy, our logic is interpreted over partial observability of variables, thus capturing that each thread can “see” only a part of the global space of variables. We verify program-epistemic properties on such AI-centred programs. To this end, we give a sound translation of the validity of our program-epistemic logic into first-order validity, using a new weakest-precondition semantics and a book-keeping of variable assignment. We implement our translation and fully automate our verification method for well-established examples using SMT solvers.

Abstract Knowledge representation is one way to exploit expertise in a given domain by logical means. But, what kind of knowledge does one acquire from an inference (or inference on a query result over a knowledge base)? Such a question may appear awkward since the answer seems so obvious: from an inference, one simply acquires knowledge. This is undoubtedly the case when only one type of knowledge (for instance, expert knowledge) is involved in an inference. What if several types of knowledge are involved? What type of knowledge can one deduce from a plurality of knowledge types? I claim that reasoning with different knowledge concepts requires a fine-grained representation of knowledge in which every knowledge type finds a singular expression in order to avoid some epistemic equivocity associated with a coarse-grained representation of knowledge. In the first part of the paper, I revisit the Muddy Children Puzzle, which usually serves to illustrate common knowledge in dynamic epistemic logic. I try to show that this problem also shows some sort of epistemic equivocity between concepts of knowledge and, consequently, that the problem calls for some epistemological refinements concerning the representation of the types of knowledge at play in an inference. In the second part, I address this issue from a semantic point of view, and I develop a fragment of epistemic logic capable of providing a solution to the problem of epistemic equivocity.

Abstract Communication within groups of agents has been lately the focus of research in dynamic epistemic logic. This paper studies a recently introduced form of partial (more precisely, topic-based) communication. This type of communication allows for modelling scenarios of multi-agent collaboration and negotiation, and it is particularly well-suited for situations in which sharing all information is not feasible/advisable. The paper can be divided into two parts. In the first part, we present results on invariance and complexity of model checking. Moreover, we compare partial communication with the public announcement and arrow update settings in terms of both language-expressivity and update-expressivity. Regarding the former, the three settings are equivalent, their languages being equally expressive. Regarding the latter, all three modes of communication are incomparable in terms of update-expressivity. In the second part, we shift our attention to strategic topic-based communication. We do so by extending the language with a modality that quantifies over the topics the agents can ‘talk about’, thus allowing a form of arbitrary partial communication. For this new framework, we provide a complete axiomatisation, showing also that the new language’s model checking problem is PSPACE-complete. Finally, we argue that, in terms of expressivity, this new language of arbitrary partial communication is incomparable to that of arbitrary public announcements and also to that of arbitrary arrow updates.

Abstract We introduce pattern models, a dynamic epistemic logic for analyzing distributed systems. First, we present a version of pattern models where the full-information protocol, widely studied in distributed computability, is static in the product definition of pattern models. Next, we parametrize such a logic so as to add the capability to model dynamics of arbitrary deterministic protocols. We thus give a systematic construction of pattern models for a large variety of distributed-computing models called dynamic-network models. Using pattern models, the epistemic dynamics of a proper subclass of dynamic-network models called oblivious can be described using a static pattern model, hence using constant space. For this case, we present a sufficient unsolvability condition for the consensus task that can be easily verified analyzing the structure of the initial epistemic model and the pattern model for a given oblivious dynamic-network model.

When something is said by an agent, addressees and other agents in the audience may sometimes be uncertain what specific illocutionary act the agent intends to perform even if what is said and the context in which it is said are perfectly clear.Yet which illocutionary act is performed can make a great difference in what the addressees should do in response to the utterance.The well-known method for analyzing how the different (un)certainties different agents have about what has been done affect the outcome is the method of the product update by action models.This method is used in developing various systems in DEL (Dynamic Epistemic Logic) that deal with acts that affect epistemic states of agents.Illocutionary acts, however, usually affect deontic aspects of the situations in which they are performed.We will define a deontic version of the method of product update by importing ideas from dynamic deontic logics that deal with acts of commanding and acts of requesting.We then show (1) that the deontic version of product update works when uptake (the understanding of the force and the content of an illocutionary act) is secured, but (2) that it doesn't work when uptake is not secured, and (3) that a twist is needed to represent what is going on in such a case.

Many philosophical discussions hinge on the concept of knowability. For example, there is a blooming literature on the so-called paradox of knowability. How to understand this notion, however? In this paper, we examine several approaches to the notion: the naive approach to take knowability as the possibility to know, the counterfactual approach endorsed by Edgington (1985) and Schlöder (2019) , approaches based on the notion of a capacity or ability to know (Fara 2010, Humphreys 2011), and finally, approaches that make use of the resources of dynamic epistemic logic (van Benthem 2004, Holliday 2017).

Any kind of dynamics in dynamic epistemic logic can be represented as an action model. Right? Wrong! In this contribution we prove that the update expressivity of communication patterns is incomparable to that of action models. Action models, as update mechanisms, were proposed by Baltag, Moss, and Solecki in 1998 and have remained the nearly universally accepted update mechanism in dynamic epistemic logics since then. Alternatives, such as arrow updates that were proposed by Kooi and Renne in 2011, have update equivalent action models. More recently, the picture is shifting. Communication patterns are update mechanisms originally proposed in some form or other by Agotnes and Wang in 2017 (as resolving distributed knowledge), by Baltag and Smets in 2020 (as reading events), and by Velazquez, Castaneda, and Rosenblueth in 2021 (as communication patterns). All these logics have the same expressivity as the base logic of distributed knowledge. However, their update expressivity, the relation between pointed epistemic models induced by such an update, was conjectured to be different from that of action model logic. Indeed, we show that action model logic and communication pattern logic are incomparable in update expressivity. We also show that, given a history-based semantics and when restricted to (static) interpreted systems, action model logic is (strictly) more update expressive than communication pattern logic. Our results are relevant for distributed computing wherein oblivious models involve arbitrary iteration of communication patterns.

Abstract In this paper, I develop an algorithmic impossible-worlds model of belief and knowledge that provides a middle ground between models that entail that everyone is logically omniscient and those that are compatible with even the most egregious kinds of logical incompetence. In outline, the model entails that an agent believes (knows)$\phi $just in case she can easily (and correctly) compute that$\phi $is true and thus has the capacity to make her actions depend on whether$\phi $. The model thereby captures the standard view that belief and knowledge ground are constitutively connected to dispositions to act. As I explain, the model improves upon standard algorithmic models developed by Parikh, Halpern, Moses, Vardi, and Duc, among other ways, by integrating them into an impossible-worlds framework. The model also avoids some important disadvantages of recent candidate middle-ground models based on dynamic epistemic logic or step logic, and it can subsume their most important advantages.

Abstract Dynamic epistemic logic (DEL) is a multi-modal logic for reasoning about the change of knowledge in multi-agent systems. It extends epistemic logic by a modal operator for actions which announce logical formulas to other agents. In Hilbert-style proof calculi for DEL, modal action formulas are reduced to epistemic logic, whereas current sequent calculi for DEL are labelled systems which internalize the semantic accessibility relation of the modal operators, as well as the accessibility relation underlying the semantics of the actions. We present a novel cut-free ordinary sequent calculus, called $ \textbf{G4}_{P,A}[] $, for propositional DEL. In contrast to the known sequent calculi, our calculus does not internalize the accessibility relations, but—similar to Hilbert style proof calculi—action formulas are reduced to epistemic formulas. Since no ordinary sequent calculus for full S5 modal logic is known, the proof rules for the knowledge operator and the Boolean operators are those of an underlying S4 modal calculus. We show the soundness and completeness of $ \textbf{G4}_{P,A}[] $ and prove also the admissibility of the cut-rule and of several other rules for introducing the action modality.

Abstract The paper introduces a broad family of metrics applicable to finite and countably infinite strings, or, by extension, to formal structures serving as semantics for countable languages. The main focus is on applications to sets of pointed Kripke models, a semantics for modal logics. For the resulting metric spaces, the paper classifies topological properties including which metrics are topologically equivalent, providing sufficient conditions for compactness, characterizing clopen sets and isolated points, and characterizing the metrical topologies by a concept of logical convergence. We then apply the approach to maps from dynamic epistemic logic, showing that product updates with action models yield continuous maps, hence allowing for an interpretation of the iterated updates as discrete time dynamical systems.

Inquisitive logic as an epistemic logic of knowing how

In this paper we design a new logical system to explicitly model the different deductive reasoning steps of a boundedly rational agent. We present an adequate system in line with experimental findings about an agent’s reasoning limitations and the cognitive effort that is involved. Inspired by Dynamic Epistemic Logic, we work with dynamic operators denoting explicit applications of inference rules in our logical language. Our models are supplemented by (a) impossible worlds (not closed under logical consequence), suitably structured according to the effect of inference rules, and (b) quantitative components capturing the agent’s cognitive capacity and the cognitive costs of rules with respect to certain resources (e.g. memory, time). These ingredients allow us to avoid problematic logical closure principles, while at the same time deductive reasoning is reflected in our dynamic truth clauses. We further show that our models can be reduced to awareness-like plausibility structures that validate the same formulas and we give a sound and complete axiomatization with respect to them. This approach to the agent’s internal deductive reasoning is finally combined with actions of external information.

Abstract Logics for social networks have been studied in the recent literature. This paper presents a framework based on dynamic term-modal logic ($\textsf {DTML}$), a quantified variant of dynamic epistemic logic (DEL). In contrast with DEL where it is commonly known to whom agent names refer, $\textsf {DTML}$ can represent dynamics with uncertainty about agent identity. We exemplify dynamics where such uncertainty and de re/de dicto distinctions are key to social network epistemics. Technically, we show that $\textsf {DTML}$ semantics can represent a popular class of hybrid logic epistemic social network models. We also show that $\textsf {DTML}$ can encode previously discussed dynamics for which finding a complete logic was left open. As complete reduction axioms systems exist for $\textsf {DTML}$, this yields a complete system for the dynamics in question.

There are two approaches to merging temporal and epistemic models. The first one consists in starting with a temporal model and enriching it with epistemic dimension (as temporal epistemic logic), while the second one is supposed to start with an epistemic model introducing temporal dimension (dynamic epistemic logic, epistemic temporal logic). The proposed evolutionary epistemic model (EEM) is based on the standard epistemic model with an evolutionary relation. EEM captures knowledge changes in terms of the evolution of worlds included in different epistemic contexts. Unlike other temporal-epistemic models, EEM is free from the concept of history and enriched with quantification operators over the worlds’ evolution stages.

Abstract Dynamic Belief Update is a model checking problem in Dynamic Epistemic Logic concerning the effect of applying a number of epistemic actions on an initial epistemic model. It can also be considered as a plan verification problem in epistemic planning. The problem is known to be PSPACE-hard. To better understand the source of complexity of the problem, previous research has investigated the complexity of 128 parameterized versions of the problem with parameters such as number of agents and size of epistemic actions. The complexity of many parameter combinations has been determined, but previous research left 14 parameter combinations open. In this paper, we solve all of these open problems. Most of the parameter combinations turns out to be fixed-parameter intractable, except for 3 that are fixed-parameter tractable.

I propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the representational focus of doxastic models from belief sets to collections of information, and by defining changes of beliefs as artifacts of changes of information, we can achieve a more realistic account of belief representation and belief change. The proposed dynamic operation suggests a non-classical way of changing beliefs: belief revision occurs in non-explosive environments which allow for a non-monotonic and hyperintensional belief dynamics. A logic that is sound with respect to the semantics is also provided.