Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Simplicial Model for $KB4_n$: Epistemic Logic with Agents that May Die
134
0
0.0
(
0
)
Added by
Eric Goubault
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The standard semantics of multi-agent epistemic logic $S5$ is based on Kripke models whose accessibility relations are reflexive, symmetric and transitive. This one dimensional structure contains implicit higher-dimensional information beyond pairwise interactions, that has been formalized as pure simplicial models in previous work from the authors. Here we extend the theory to encompass all simplicial models - including the ones that are not pure. The corresponding Kripke models are those where the accessibility relation is symmetric and transitive, but might not be reflexive. This yields the epistemic logic $KB4$ which can reason about situations where some of the agents may die.
rate research
Read More
Collective adaptive systems (CAS) 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. The distribution of system entities determines a space that can be either physical or logical. The former is defined in terms of a physical relation among components. The latter depends on some logical relations such as being part of the same group. For these systems, specification and verification of spatial properties play a fundamental role to understand their behaviour and to support their design. Recently, different tools and languages have been introduced to specify and verify the properties of space. However, these formalisms are mainly based on graphs. This does not permit considering higher-order relations such as surfaces or volumes. In this work, we propose a spatial logic interpreted on simplicial complexes. These are topological objects able to represent surfaces and volumes efficiently and that generalise graphs with higher-order edges. The expressiveness of the proposed spatial logic is studied in terms of bisimulation and branching bisimulation relations defined over simplicial complexes. Finally, we discuss how the satisfaction of logical formulas can be verified by a correct and complete algorithm.
In this paper we introduce a computational-level model of theory of mind (ToM) based on dynamic epistemic logic (DEL), and we analyze its computational complexity. The model is a special case of DEL model checking. We provide a parameterized complexity analysis, considering several aspects of DEL (e.g., number of agents, size of preconditions, etc.) as parameters. We show that model checking for DEL is PSPACE-hard, also when restricted to single-pointed models and S5 relations, thereby solving an open problem in the literature. Our approach is aimed at formalizing current intractability claims in the cognitive science literature regarding computational models of ToM.
This paper revisits the multi-agent epistemic logic presented in [10], where agents and sets of agents are replaced by abstract, intensional names. We make three contributions. First, we study its model theory, providing adequate notions of bisimulation and frame morphisms, and use them to study the logics expressive power and definability. Second, we show that the logic has a natural neighborhood semantics, which in turn allows to show that the axiomatization in [10] does not rely on possibly controversial introspective properties of knowledge. Finally, we extend the logic with common and distributed knowledge operators, and provide a sound and complete axiomatization for each of these extensions. These results together put the original epistemic logic with names in a more modern context and opens the door for a logical analysis of epistemic phenomena where group membership is uncertain or variable.
We introduce a modal logic for describing statistical knowledge, which we call statistical epistemic logic. We propose a Kripke model dealing with probability distributions and stochastic assignments, and show a stochastic semantics for the logic. To our knowledge, this is the first semantics for modal logic that can express the statistical knowledge dependent on non-deterministic inputs and the statistical significance of observed results. By using statistical epistemic logic, we express a notion of statistical secrecy with a confidence level. We also show that this logic is useful to formalize statistical hypothesis testing and differential privacy in a simple and abstract manner.
The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behavior of said maps.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
