This paper presents a class of epistemic logics that captures the dynamics of acquiring knowledge and descending into oblivion, while incorporating concepts of group knowledge. The approach is grounded in a system of weighted models, introducing an ``epistemic skills'' metric to represent the epistemic capacities tied to knowledge updates. Within this framework, knowledge acquisition is modeled as a process of upskilling, whereas oblivion is represented as a consequence of downskilling. The framework further enables exploration of ``knowability'' and ``forgettability,'' defined as the potential to gain knowledge through upskilling and to lapse into oblivion through downskilling, respectively. Additionally, it supports a detailed analysis of the distinctions between epistemic de re and de dicto expressions. The computational complexity of the model checking and satisfiability problems is examined, offering insights into their theoretical foundations and practical implications.

This special issue of the Journal of Logic and Computation presents 11 carefully selected articles in the field of Logic and Argumentation. Authors of the strongest contributions to 4th International Conference on Logic and Argumentation (CLAR 2021) were invited to submit extended versions of their papers for inclusion in this special issue. All articles in this volume were carefully reviewed by two or three expert reviewers before acceptance was finally granted. CLAR 2021 was held in Hangzhou, 20–22 October 2021 at the Zhejiang University City College in China. This special issue was made possible by the numerous strong submissions (58 in total) we received for the conference, from which 30 presentations and 4 additional invited talks were selected for presentation at the conference and for publication in the CLAR 2021 proceedings published as volume 13040 in the Springer series Lecture Notes in Computer Science. The contributions to this special issue, and more generally to CLAR 2021, cover a wide range of topics that are the focus of the CLAR conference series, including in particular abstract and structured argumentation, logic and argumentation, argumentation with qualitative and quantitative uncertainty, knowledge representation and reasoning, modal and non-classical logics and non-monotonic logics, with applications in a variety of fields like law, ethics, game theory, linguistics and medical reasoning.

Several different notions of group knowledge have been extensively studied in the epistemic and doxastic logic literature, including common knowledge, general knowledge (everybody-knows) and distributed knowledge. In this paper we study a natural notion of group knowledge between general and distributed knowledge: somebody-knows. While something is general knowledge if and only if it is known by everyone, this notion holds if and only if it is known by someone. This is stronger than distributed knowledge, which is the knowledge that follows from the total knowledge in the group. We introduce a modality for somebody-knows in the style of standard group knowledge modalities, and study its properties. Unlike the other mentioned group knowledge modalities, somebody-knows is not a normal modality; in particular it lacks the conjunctive closure property. We provide an equivalent neighbourhood semantics for the language with a single somebody-knows modality, together with a completeness result: the somebody-knows modalities are completely characterised by the modal logic EMN extended with a particular weak conjunctive closure axiom. We also show that the satisfiability problem for this logic is PSPACE-complete. The neighbourhood semantics and the completeness and complexity results also carry over to logics for so-called local reasoning (Fagin et al. 1995) with bounded ``frames of mind'', correcting an existing completeness result in the literature (Allen 2005).

Abstract While logical formalizations of group notions of knowledge such as common and distributed knowledge have received considerable attention in the literature, most approaches being based on modal logic, group notions of belief have received much less attention. In this paper we systematically study standard notions of group belief under different assumptions about the properties of belief. In particular, we map out (lack of) preservation of belief properties against different standard definitions of group belief. It turns out that what is called group belief most often is not actually belief, i.e. does not have the properties of belief. In fact, even what is called group knowledge is sometimes not actually knowledge either. For example, under the common assumption that belief has the KD45 properties, neither common belief (does not satisfy the negative introspection axiom 5) nor distributed belief (does not satisfy the consistency axiom D) are not actually belief. There has been some confusion in the literature regarding soundness of proposed axiomatizations of logics with distributed knowledge, related to the mentioned lack of preservation. In this paper we also present detailed completeness proofs of sound and complete axiomatizations of KD45 with distributed belief, both with and without common belief.

With the development of next generation artificial intelligence, the interplay between knowledge-based approaches and machine learning approaches is gaining momentum. This trend drives the researchers to pay attention to possible and novel developments in relevant areas, either based on their theoretical foundations or based on their efficient applications. This special issue collects the newly developed works from logic, argumentation and artificial intelligence, to stimulate possible outcomes from their interactions. This volume includes 14 papers selected from 25 submissions accepted to the 2020 International Conferences on Logic and Artificial Intelligence at Zhejiang University (ZJULogAI). ZJULogAI was jointly organized by the University of Luxembourg and Zhejiang University as a three-day digital online event. It consists of three sub-events: the 5th Asian Workshop on Philosophical Logic (AWPL 2020), the 3rd International Conference on Logic and Argumentation (CLAR 2020) and the 6th Global Conference on Artificial Intelligence (GCAI 2020). Five experts (Christoph Benzmüller, Claude Sammut, Dag Westerståhl, Fei Wu and Marc van Zee) in logic and AI were invited to present their current work, covering the topics of ethical-legal AI systems, logic-based robots, big data intelligence and natural language and AI.

Abstract We introduce a logic of knowledge in a framework in which knowledge is treated as a kind of belief. The framework is based on a standard KD45 characterization of belief, and the characterization of knowledge undergoes the classical tripartite analysis that knowledge is justified true belief, which has a natural link to the studies of logics of evidence and justification. The interpretation of knowledge avoids the unwanted properties of logical omniscience, independent of the choice of the base logic of belief. We axiomatize the logic, prove its soundness and completeness and study the computational complexity results of the model checking and satisfiability problems. We extend the logic to a multi-agent setting and introduce a variant in which belief is characterized in a weaker system to avoid the problem of logical omniscience.

We combine social balance theory with temporal logic to obtain a Logic of Allies and Enemies (LAE), which formally describes the likely changes to a social network due to social pressure. We demonstrate how the rich language of LAE can be used to describe various interesting concepts, and show that both model checking and validity checking are PSPACE-complete.