Actualizing distributed knowledge in bounded groups

What do epistemic logic and cognitive science have to do with each other?

Dynamic epistemic logic (\(\mathbf {DEL}\)) is known as a large family of logics that extend standard epistemic logic with dynamic operators. Such dynamic operators can be regarded as epistemic actions over Kripke semantics (or its variant). Therefore, \(\mathbf {DEL}\) is often used to model changes of agents’ knowledge, belief or preference over Kripke semantics in terms of dynamic operators in many literatures. As a variant of \(\mathbf {DEL}\), (van Benthem and Liu, J Appl Non-Classical Logics 17(2):157–18 2007; Liu, Reasoning about preference dynamics, Springer Science & Business Media, Berlin 2011) proposed dynamic logic of relation changers (\(\mathbf {DLRC}\)). They provided a general framework to capture many dynamic operators in terms of relation changing operation written in programs of propositional dynamic logic, and they also provided a sound and complete Hilbert-style axiomatization for \(\mathbf {DLRC}\). While \(\mathbf {DLRC}\) can cover many dynamic operators in a uniform manner, proof theory for \(\mathbf {DLRC}\) is not well-studied except the Hilbert-style axiomatization. Therefore, we propose a cut-free labelled sequent calculus for \(\mathbf {DLRC}\). We show that our sequent calculus is equipollent with the Hilbert-style axiomatization.

Existing epistemic logics such as the logic of implicit and explicit belief and the logic of awareness adopt a deductive-theoretic approach for characterizing belief. In this approach, an agent represents the state of the world with a conjunction of axioms in its knowledge base (KB) and evaluates queries by trying to prove or disprove that they follow from KB. This paper presents a multivalued epistemic logic (MEL) that allows agents to reason both deductively and model theoretically about implicit and explicit belief. By characterizing an agent's KB with a class of finite models, the set of formulas that an agent believes can be determined by checking their validity in all these models. This rests on the fact that MEL has a complete axiomatization (sentences that are true in all these models will also be provable). In this paper, the soundness, completeness, and decidability of MEL are proven. Furthermore, a polynomial time model-checking algorithm for determining the satisfiability of a sentence at a particular state in a given model of MEL is also presented. © 2000 John Wiley & Sons, Inc.

This paper presents a logic of questions developed as an extension of (S5) epistemic logic. We discuss many features that are important for erotetic logic (formalization and semantics of questions, answerhood conditions, and inferential structures with questions). The aim is to introduce an erotetic system which corresponds well with epistemic terms and can form an appropriate background for dynamic approaches in epistemic logic.

The aim of this paper is to explore the advantages deriving from the application of relating semantics in epistemic logic. As a first step, I will discuss two versions of relating semantics and how they can be differently exploited for studying modal and epistemic operators. Next, I consider several standard frameworks which are suitable for modelling knowledge and related notions, in both their implicit and their explicit form and present a simple strategy by virtue of which they can be associated with intuitive systems of relating logic. As a final step, I will focus on the logic of knowledge based on justification logic and show how relating semantics helps us to provide an elegant solution to some problems related to the standard interpretation of the explicit epistemic operators.

We study imagination as reality-oriented mental simulation (ROMS): the activity of simulating nonactual scenarios in one’s mind, to investigate what would happen if they were realized. Three connected questions concerning ROMS are: What is the logic, if there is one, of such an activity? How can we gain new knowledge via it? What is voluntary in it and what is not? We address them by building a list of core features of imagination as ROMS, drawing on research in cognitive psychology and the philosophy of mind. We then provide a logic of imagination as ROMS which models such features, combining techniques from epistemic logic, action logic, and subject matter semantics. Our logic comprises a modal propositional language with non-monotonic imagination operators, a formal semantics, and an axiomatization.

Geometric Aspects of Multiagent Systems

In epistemic logic we are not only interested in the propositional knowledge expressed by “knowing that” operators, but also care about other types of knowledge used in natural language. In [1], Plaza proposed the “knowing value” operators and gave the complete axiomatization for the logic of knowledge with nonrigid designators. Moreover, in [2] Halpern and colleagues holds that, when analyzing a system in terms of knowledge, not only is the current state of knowledge of the agents in the system relevant, but also how that state of knowledge changes over time. So we introduce temporal logic operators ‘next’ and ‘until’ to extend Plaza’s system. The completeness proof is highly non-trivial and we referred to the work of [2, 3].

On bimodal logics of provability

In this paper we attempt to shed light on the concept of an agent’s knowledge after a non-deterministic action is executed. We start by making a comparison between notions of non-deterministic choice, and between notions of sequential composition, of settings with dynamic and/or epistemic character; namely Propositional Dynamic Logic (PDL), Dynamic Epistemic Logic (DEL), and the more recent logic of Semi-Public Environments (SPE). These logics represent two different approaches for defining the aforementioned actions, and in order to provide unified frameworks that encompass both, we define the logics DELVO (DEL+Vision+Ontic change) and PDLVE (PDL+Vision+Epistemic operators). DELVO is given a sound and complete axiomatisation.

Public announcement logic (PAL) extends multi-agent epistemic logic with dynamic operators modelling the effects of public communication. Allowing quantification over public announcements lets us reason about the existence of an announcement that reaches a certain epistemic goal. Two notable examples of logics of quantified announcements are arbitrary public announcement logic (APAL) and group announcement logic (GAL). While the notion of common knowledge plays an important role in PAL, and in particular in characterisations of epistemic states that an agent or a group of agents might make come about by performing public announcements, extensions of APAL and GAL with common knowledge still haven’t been studied in detail. That is what we do in this paper. In particular, we consider both conservative extensions, where the semantics of the quantifiers is not changed, as well as extensions where the scope of quantification also includes common knowledge formulas. We compare the expressivity of these extensions relative to each other and other connected logics, and provide sound and complete axiomatisations. Finally, we show how the completeness results can be used for other logics with quantification over information change.

Ever since [4]. systems of spheres have been considered to give an intuitive and elegant way to give a semantics for logics of theory- or belief- change. Several authors [5, 11] have considered giving up the rather strong assumption that systems of spheres be linearly ordered by inclusion. These more general structures are calledhypertheoriesafter [8]. It is shown that none of the proposed logics induced by these weaker structures are compact and thus cannot be given a strongly complete axiomatization in a finitary logic. Complete infinitary axiomatizations are given for several intuitive logics based on hypertheories that are not linearly ordered by inclusion.

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.

This work presents three increasingly expressive Dynamic Logics in which the programs are described in a language based on CCS. Our goal is to build dynamic logics that are suitable for the description and verification of properties of communicating concurrent systems, in a similar way as PDL is used for the sequential case. In order to accomplish that, CCS’s operators and constructions are added to a basic modal logic. Doing this, the semantics of CCS’s parallel operator allows us to build dynamic logics that support communicating and concurrent programs. We build a simple Kripke semantics for these logics, provide complete axiomatizations for them and show that they have the finite model property. This contrasts with other dynamic logics with parallel operators presented in the literature, such as Peleg’s Concurrent PDL with Channels, where either the parallel programs cannot communicate, or at least one of the properties mentioned above (simple Kripke semantics, complete axiomatization and finite model property) is missing.

Research relevance: the article talks about the significance of changes in the modern era of globalization in human life, including the significant impact on the culture of communication and communication of the future generation. Research objectives: to determine the factors influencing the culture of communication of the younger generation in the context of globalization. Research materials and methods: analysis of the influence of harmful factors of globalization such as the Internet, the rapid development of technology, which negatively affect the speech culture of the younger generation and the formation of communicative abilities. Research results: in the context of globalization, it is noted that the Internet is the main source of development, education, assimilation of information, friendship and cooperation with people from all over the world. As a positive side of Internet sources, such achievements as solving many problems, easy search for necessary information, learning new things, and the ability to quickly find answers to questions are analyzed. At the same time, it is noted that in the context of today’s rapid development of globalization, the Internet has made an unprecedented turn in the life of mankind and, along with its relief, has created a number of problems. Conclusions: the future generation gets used to solving problems easily, is constantly in the virtual world and loses the ability to satisfy real needs and communicate with real people. This has become a problem in modern society. It is also noted that in a developing society, teaching the future generation the art of speech, which is considered a national value, will contribute to the creation of quality speech, communication, as well as the formation and development of communication skills. Development of communication skills is a relevant necessity.