Related papers: Cayley structures and common knowledge

We study an intuitionistic version of common knowledge logic (CK), called ICK, which was introduced by J\"ager and Marti. ICK extends intuitionistic propositional logic (IPL) by multiple box modalities interpreted as knowledge operators for…

The famous van Benthem theorem states that modal logic corresponds exactly to the fragment of first-order logic that is invariant under bisimulation. In this article we prove an exact analogue of this theorem in the framework of modal…

Categorization systems are widely studied in psychology, sociology, and organization theory as information-structuring devices which are critical to decision-making processes. In the present paper, we introduce a sound and complete…

In standard epistemic logic, agent names are usually assumed to be common knowledge implicitly. This is unreasonable for various applications. Inspired by term modal logic and assignment operators in dynamic logic, we introduce a…

The correlations that can be observed between a set of variables depend on the causal structure underpinning them. Causal structures can be modeled using directed acyclic graphs, where nodes represent variables and edges denote functional…

The basic idea of quantum complexity geometry is to endow the space of unitary matrices with a metric, engineered to make complex operators far from the origin, and simple operators near. By restricting our attention to a finite subgroup of…

We develop a conceptually clear, intuitive, and feasible decision procedure for testing satisfiability in the full multi-agent epistemic logic CMAEL(CD) with operators for common and distributed knowledge for all coalitions of agents…

We consider two simple variants of a framework for reasoning about knowledge amongst communicating groups of players. Our goal is to clarify the resulting epistemic issues. In particular, we investigate what is the impact of common…

Epistemic logic is known as a logic that captures the knowledge and beliefs of agents and has undergone various developments since Hintikka (1962). In this paper, we propose a new logic called agent-knowledge logic by taking the product of…

Correspondence theory allows us to create sound and complete axiomatizations for modal logic on frames with certain properties. For example, if we restrict ourselves to transitive frames we should add the axiom $\square \phi \rightarrow…

The study of group knowledge concepts such as mutual, common, and distributed knowledge is well established within the discipline of epistemic logic. In this work, we incorporate epistemic abilities of agents to refine the formal definition…

We expound a concise construction of finite groups and groupoids whose Cayley graphs satisfy graded acyclicity requirements. Our acyclicity criteria concern cyclic patterns formed by coset-like configurations w.r.t. subsets of the generator…

The paper investigates epistemic properties of information flow under communication protocols with a given topological structure of the communication network. The main result is a sound and complete logical system that describes all such…

This note sketches the extension of the basic characterisation theorems as the bisimulation-invariant fragment of first-order logic to modal logic with graded modalities and matching adaptation of bisimulation. We focus on showing…

Collective Adaptive Systems often consist of many heterogeneous components typically organised in groups. These entities interact with each other by adapting their behaviour to pursue individual or collective goals. In these systems, the…

We develop a theory of covering digraphs, similar to the theory of covering spaces. By applying this theory to Cayley digraphs, we build a "bridge" between GLMY-theory and group homology theory, which helps to reduce path homology…

The paper treats 4 different fragments of first-order logic induced by their respective versions of Kripke style semantics for modal intuitionistic logic. In order to capture these fragments, the notion of asimulation is modified and…

We introduce a topological property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a particular finite presentation. We also define…

The paper presents an extension of temporal epistemic logic with operators that quantify over strategies. The language also provides a natural way to represent what agents would know were they to be aware of the strategies being used by…

In this paper we study finite groups which have Cayley isomorphism property with respect to Cayley maps, CIM-groups for a brief. We show that the structure of the CIM-groups is very restricted. It is described in Theorem~\ref{111015a} where…