On the semantics of knowledge update

2006

Abstract. In this paper, we show how to establish correctness and time bounds (eg, quality of service guarantees) for multi-agent systems composed of communicating rule-based agents. The formal models of multi-agent systems we study are transition systems where each transition corresponds to either a rule firing or an act of communication by an agent. We present a complete and sound modal logic which formalises how the beliefs of communicating rule-based agents change over time.

In Proceedings of the 7th annual ACM symposium on …, 1985

In Kripke semantics for modal logic, "possible world^" and the possibility relation are both primitive notions. This has both technical and conceptual shortcomings. From a technical point of view, the mathematics associated with Kripke. semantics is often quite complicated. From a conceptual point of view, it is not clear how to use Kripke structures to model know!edge and belief, where one wants a clearer understanding of the notions that are primitive in Kripke semantics. We introduce modal structures as models for modal logic. We use the idea of possible worlds, but by directly describing the "internal semantics" of each possible world. It is much easier to study the standard logical questions, such as completeness, decidability, and compactness, ushg modal structures. Furthermore, modal structures offer a much more intuitive approach to modelling knowledge and belief.

Lecture Notes in Computer Science, 2008

The possible worlds semantics is a fruitful approach used in Artificial Intelligence (AI) for both modelling as well as reasoning about knowledge in agent systems via modal logics. In this work our main idea is not to model/reason about knowledge but to provide a theoretical framework for knowledge assessment (KA) with the help of Monatague-Scott (MS) semantics of modal logic. In KA questions asked and answers collected are the central elements and knowledge notions will be defined from these (i.e., possible states of knowledge of subjects in a population with respect to a field of information).

2011

We develop an algebraic modal logic that combines epistemic and dynamic modalities with a view to modelling information acquisition (learning) by automated agents in a changing world. Unlike most treatments of dynamic epistemic logic, we have transitions that “change the state” of the underlying system and not just the state of knowledge of the agents.

2010

Abstract We develop an algebraic modal logic that combines epistemic modalities with dynamic modalities with a view to modelling information acquisition (learning) by automated agents in a changing world. Unlike most treatments of dynamic epistemic logic, we have transitions that “change the state” of the underlying system and not just the state of knowledge of the agents.

ACM Transactions on Computational Logic, 2004

KLAIM is an experimental programming language that supports a programming paradigm where both processes and data can be moved across different computing environments. The language relies on the use of explicit localities. This paper presents a temporal logic for specifying properties of Klaim programs. The logic is inspired by Hennessy-Milner Logic (HML) and the µ−calculus, but has novel features that permit dealing with state properties and impact of actions and movements over the different sites. The logic is equipped with a complete proof system that enables one to prove properties of mobile systems.

Studies in Logic and Practical Reasoning, 2007

This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimulations) which underly it. We introduce the syntax and semantics of basic modal logic, discuss its expressivity at the level of models, examine its computational properties, and then consider what it can say at the level of frames. We then move beyond the basic modal language, examine the kinds of expressivity offered by a number of richer modal logics, and try to pin down what it is that makes them all 'modal'. We conclude by discussing an example which brings many of the ideas we discuss into play: games. Contents 1 Introduction 2 Basic modal logic 2.1 First steps in relational semantics 2.2 The standard translation 3 Simulation and definability 3.1 Drawing distinctions 3.2 Structural invariances: bisimulation 3.3 Invariance and definability in first-order logic 3.4 Invariance and definability in modal logic 3.5 Modal logic and first-order logic compared 3.6 Bisimulation as a game 4 Computation and complexity 4.1 Model checking 4.2 Decidability 4.3 Complexity 4.4 Other reasoning tasks 5 Richer logics 5.1 Axioms and relational frame properties 5.2 Frame correspondence and second-order logic 5.3 First-order definable modal axioms 5.4 Correspondence in richer languages: fixed-point extensions 5.5 Modally definable frame classes 5.6 First-order logic as modal logic 6 Richer languages 6.1 The universal modality 6.2 Hybrid logic 6.3 Temporal logic with Until and Since operators 6.4 Conditional logic 6.5 The guarded fragment 38 6.6 Propositional Dynamic Logic 40 6.7 Modal µ-calculus 42 6.8 General perspectives 45 7 New descriptive challenges 46 7.1 An example where it all comes together: games 46 References 48

Dutch-German workshop on Non-Monotonic Reasoning (DGNMR 2001), 2001

An agent acquiring information about its environment, either by observation or by communication with other agents, must update its beliefs about the environment. In this way the agent keeps track of the changes in its environment. Usually the agent will not be able to perceive the environment completely. Since most environments do not change very fast over time, the agent may assume that everything about which the agent does not learn that it has changed, will still be the same. This minimal change assumption results in counter intuitive conclusions if an agent has background knowledge describing general (causal) relations between aspects of the environment. To avoid these counter intuitive conclusions, this paper proposes instead of the minimal change assumption, a minimal intervention assumption . Here, an inter- vention is an action of an agent that changes the environment. A Kripke semantics that formalizes the update process based on the minimal intervention assumption, will be...

Logic Journal of IGPL, 2005

This paper introduces a two-dimensional modal logic to represent agents' concurrent common knowledge in distributed systems. Unlike common knowledge, concurrent common knowledge is a kind of agreement reachable in asynchronous environments. As a proper semantics to concurrent common knowledge we present the closed sub-product of modal logics. We axiomatize the presented logic issuing an idea of the soundness and completeness proofs.

This paper introduces a twodimensional modal logic to represent agents' knowledge in distributed environments. The agent's knowledge was formally defined in [5], where modal logic was used to model knowledge in synchronous distributed message-passing systems. The logic we present here can properly describe the properties of the agent's knowledge in asynchronous environments. An axiomatic system to describe such kind of knowledge is also presented.