Geometric Aspects of Multiagent Systems

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

Multi-agent system (MAS) requires coordination mechanisms to facilitate dynamic collaboration of the intelligent components, with the goal of meeting local and global objectives. This paper deals with the issue of using dynamic epistemic default logic to offer a natural way of communication policies for the management of inter-agent exchanges in MAS. We first explore the communication protocols in MAS that operate in dynamic and highly uncertain environments, and then we add the constrained default sets to realize the extension of dynamic epistemic logic theory and restrict the agent’s inference behavior via constrained epistemic default reasoning. We also specify and reason the characteristic of the dynamic updating when agent meets incompatible knowledge in the logical framework that show the usefulness of logical tools carried out in the dynamic process of information acquisition.

From point of view of power engineering the successful commercial market with electric vehicles demands a completely new concept of their integration into contemporary electrical network. The electric vehicles have very limited range, so they have to be charged in short periods, that means for the grid problems with peaks in the daily load profile. The paper outlined one of the most promising - decentralization of the network with help of multiagent systems. Each agent collects and evaluates data about vehicles from small area, manages such area relative independently, so the main problem is to create an algorithm for optimal cooperation and communication with the other agents. The example of such cooperation is shown, firstly as the simple linear programming problem, the secondly more complex, with using the game theory which is the mathematical basis for multiagent systems. The system is connected with the smart grid, so the possibilities of altering the load profile are shown. The last chapter explores the necessity of the shift of such grid to artificial intelligence and the epistemic modal logic is presented as a possible solution.

In multi-agent systems, an agent generally forms her belief based on information from multiple sources, such as messages from other agents or perception of the external environment. While modal epistemic logic has been a standard formalism for reasoning about agent's belief, it lacks the expressive power for tracking information sources. Justification logic (JL) provides the missing expressivity by using justification terms to keep track of the belief formation process. However, because JL does not make a clear distinction between potential and actual evidence, the interpretation of justification formulas in JL turns out to be ambiguous. In this paper, we present a justification-based multi-source reasoning formalism built upon second-order propositional modal logic. Our framework not only inherits the source-tracking advantage of JL but also allows the distinction between the actual observation and simply potential admissibility of evidence.

This paper deals with the computation of the rank and some integer Smith forms of a series of sparse matrices arising in algebraic K-theory. The number of non zero entries in the considered matrices ranges from 8 to 37 millions. The largest rank computation took more than 35 days on 50 processors. We report on the actual algorithms we used to build the matrices, their link to the motivic cohomology and the linear algebra and parallelizations required to perform such huge computations. In particular, these results are part of the first computation of the cohomology of the linear group GL 7(Z).

In this paper, we exploit epistemic logic (or the modal logic of knowledge) for multiagent systems to discuss the compositionality of several privacy-related information-hiding/disclosure properties. The properties considered here are anonymity, privacy, onymity, and identity. Our initial observation reveals that anonymity/privacy properties are not necessarily sequentially compositional. This means that even though a system comprising several sequential phases satisfies a certain unlinkability property in each phase, the entire system does not always enjoy a desired unlinkability property. We show that the compositionality can be guaranteed provided that the phases of the system satisfy what we call independence assumptions. More specifically, we develop a series of theoretical case studies of what assumptions are sufficient to guarantee the sequential compositionality of various degrees of anonymity, privacy, onymity, and/or identity properties. Similar results for parallel composition are also discussed. Further, we use the probabilistic extension of epistemic logic to consider the compositionality of probabilistic anonymity/privacy. We show that the compositionality can also be guaranteed in the probabilistic setting, provided that the phases of the system satisfy a probabilistic independence assumption.

Optimal control is one of the most powerful, important and advantageous topics in control engineering. The two challenges in every optimal control problem are defining the proper cost function and obtaining the best method to minimize it. In this study, innovative optimal control approaches are developed to solve the two problems of consensus and path planning in multi-agent systems (MASs). The consensus problem for general Linear-Time Invariant systems is solved by implementing an inverse optimal control approach which enables us to start by deriving a control law based on the stability and optimality condition and then according to the derived control define the cost function. We will see that this method in which the cost function is not specified a priori as the conventional optimal control design has the benefit that the resulting control law is guaranteed to be both stabilizing and optimal. Three new theorems in related linear algebra are developed to enable us to use the algorithm for all the general LTI systems. The designed optimal control is distributed and only needs local neighbor-to-neighbor information based on the communication topology to make the agents achieve consensus and track a desired trajectory. Path planning problem is solved for a group are Unmanned Aerial Vehicles (UAVs) that are assigned to track the fronts of a fires in a process of wildfire management. We use Partially Observable Markov Decision Process (POMDP) in order to minimize the cost function that is defined according to the tracking error. Here the challenge is designing the algorithm such that (1) the UAVs are able to make decisions autonomously on which fire front to track and (2) they are able to track the fire fronts which evolve over time in random directions. We will see that by defining proper models, the designed algorithms provides real-time calculation of control variables which enables the UAVs to track the fronts and find their way autonomously. Furthermore, by implementing Nominal Belief-state Optimization (NBO) method, the dynamic constraints of the UAVs is considered and challenges such as collision avoidance is addressed completely in the context of POMDP.

Linear Algebra Linear algebra studies linear transformations and vector spaces, or in another language, matrix multiplication and the vector space R n . You should know how to translate between the language of abstract vector spaces and the language of matrices. In particular, given a basis for a vector space, you should know how to represent any linear transformation as a matrix. Further, given two matrices, you should know how to determine if these matrices actually represent the same linear transformation, but under different choices of bases. The key theorem of linear algebra is a statement that gives many equivalent descriptions for when a matrix is invertible. These equivalences should be known cold. You should also know why eigenvectors and eigenvalues occur naturally in linear algebra. Real Analysis The basic definitions of a limit, continuity, differentiation and integration should be known and understood in terms of ∈'s and δ's. Using this ∈ and δ language, you should be comfortable with the idea of uniform convergence of functions. Differentiating Vector-Valued Functions The goal of the Inverse Function Theorem is to show that a differentiable function f : R n → R n is locally invertible if and only if the determinant of its derivative (the Jacobian) is non-zero. You should be comfortable with what it means for a vector-valued function to be differentiable, why its derivative must be a linear map (and hence representable as a matrix, the Jacobian) and how to compute the Jacobian.

There are many real-time situations which can be effectively solved by optimizing the basics of linear algebra by infusing it through latest AI models. This research paper is intended to bring into use the basic concepts of linear algebra along with the nuances of AI/ML to bring about optimization for solving supply chain scenario across industry. The challenge lies in Modeling disruptions (e.g., geopolitical events, pandemics) across global supply chains in real time. Linear Algebra’s Role lies in Matrix representations of supplier–buyer networks, eigenvalue analysis for systemic risk. The frontier lies in combining linear algebra with adaptive AI (reinforcement learning, quantum ML, and multi-agent systems).

With recent advances in mobile technologies and e-commerce infrastructures, there have been increasing demands for the expansion of collaboration services within and across systems. In particular, human collaboration requirements should be considered together with those for systems and their components. Agent technologies have been deployed in order to model and implement e-commerce activities as multi-agent systems (MAS). Agents are able to provide assistance on behalf of their users or systems in collaboration services. As such, we advocate the engineering of e-collaboration support by means of MAS in the following three key dimensions: (i) across multiple platforms, (ii) across organization boundaries, and (iii) agent-based intelligent support. To archive this, we present a MAS infrastructure to facilitate systems and human collaboration (or e-collaboration) activities based on the belief-desire-intension (BDI) agent architecture, constraint technology, and contemporary Web Services. Further, the MAS infrastructure also provides users with different options of agent support on different platforms. Motivated by the requirements of mobile professional workforces in large enterprises, the authors present their development and adaptation methodology for e-collaboration services with a case study of constraint-based collaboration protocol from a three-tier implementation architecture aspect. They evaluate our approach from the perspective of three main stakeholders of e-collaboration, which include users, management, and systems developers.

Graphs of the usual kind display functions. Graphs of a different kind (these have m edges connecting n nodes) lead to matrices. What y=f(x) is to calculus, matrices and subspaces are to linear algebra. Those are the central ideas, which students struggle with and to some extent master. This paper is about the incidence matrix A of a connected graph?and especially about its associated subspaces. For any m by n matrix there are four fundamental subspaces?two in Rn and two in Rm. They are the column spaces and nullspaces of A and AT. Their dimensions are related by the most important theorem in linear algebra. The second part of that theorem is the orthogonality of the subspaces. For the matrices we study, the dimensions and the orthogonality have a special meaning. Our goal is to show how examples from graphs illuminate the fundamental theorem of linear algebra. We start with the four subspaces (for any matrix). Then we state the theorem and construct a directed graph. For incidence matrices, the dimensions are easy to discover. But the subspaces themselves?this is where orthogonality helps. It is essential to connect the subspaces to the graph they come from. By specializing to incidence matrices, the laws of linear algebra become KirchhofFs laws. Every entry of an incidence matrix is 0 or 1 or -1. This continues to hold during elimination. All pivots and multipliers are ? 1. Therefore both factors in A =LU (lower triangular L and upper triangular U) also contain 0,1, -1. Remarkably this persists for the nullspaces of A and AT. All four subspaces have basis vectors with these exceptionally simple components. The matrices are not concocted for a textbook, they come from a model that is absolutely essential in pure and applied mathematics.

We explore when finite epistemic models are definable up to simulation or bisimulation, either over the basic multi-agent epistemic language L or over its extension L-C with common knowledge operators. Our main results are the following: (1) Bisimulation to finite epistemic states (i.e. pointed models) is not definable in L. (2) Global bisimulation to finite epistemic models is definable using model validity in L. (3) Simulation by finite epistemic states is not always definable, even over L-C. (4) We identify a class of epistemic models called well-multifounded for which simulation to finite epistemic states is definable over L. The first two results contrasts with that of van Benthem that finite epistemic states are definable up to bisimulation in L-C by so-called characteristic formulae. Our results have applications in the logical specification of multi-agent systems. Characteristic formulae, which define states up to bisimulation, fully capture all modally definable properties of models, and can for example be used to give complete calculi for validity over fixed structures. Meanwhile, simulation is a 'substructure' relation that is appropriate for epistemic logic, as it preserves positive existential formulae. Simulation formulae are useful in giving a dynamic description of models subject to epistemic actions.

The last ten years witnessed a sustained effort aimed at developing a formalism appropriate for rigorous reasoning about information hiding related properties. Among the various existent proposals one can distinguish the highly general approach of Halpern and O'Neil that employs a simple epistemic logic in the context of a multi-agent system. Still, in the context of the same formalism, basic concepts like unlink ability, undetectability, unobservability or pseudonymity are very scarcely discussed in the literature. The goal of this paper is to fill this gap by using the same epistemic logic based framework. Here we extend the aforementioned formalism to include group epistemic operators (everyone knows, common knowledge and distributed knowledge) and prove that the inference system that is thus obtained is compatible with the S5 axiomatic system and the conjunctivity axiom. We propose epistemic formalizations not only for anonymity (Halpern and O'Neil), privacy, onymity and identity (Tsukada et al.) but also for a wide spectrum of information hiding related concepts: protocol, (un) link ability, (un) traceability, (un) detectability, (un) identifiability, unobservability, pseudonymity, dissimulation. To provide an overview, we organize a large number of terms related to computer security in a comprehensive hierarchical structure divided in three sections: setting, ends and means. Basic properties and relationships between these concepts are also provided.

One of the challenges for designing multi-agent systems is how to capture and reason about agent knowledge and knowledge evolution in a highly abstract and modular way. Hence it is very desirable to have a generic framework in which such systems can be conveniently specified and the properties verified under one umbrella. As a classical reasoning support, the model checking technique has proved to be applicable for systems of reasonable size. However current model checkers for epistemic logics suffer from the state explosion problem and their inability to handle infinite state problems. Prototype Verification System (PVS) is an environment for the development of formal specifications. It integrates a highly expressive specification language and a well supported theorem prover. In this paper, we demonstrate our attempt towards mechanizing epistemic logic reasoning by building a formal, sound and complete verification framework in PVS for reasoning about a spectrum of (dynamic) epistemic logics.KeywordsModal LogicMultiagent SystemProof SystemKripke ModelReasoning SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

While temporal logic in its various forms has proven essential to reason about reactive systems, agent-based scenarios are typically specified by considering high-level agents attitudes. In particular, specification languages based on epistemic logic [7], or logics for knowledge, have proven useful in a variety of areas including robotics, security protocols, web-services, etc. For example, security specifications involving anonymity [4] are known to be naturally expressible in epistemic formalisms as they explicitly state the lack of different kinds of knowledge of the principals.