It provides a step-by-step introduction to possible worlds semantics and by that to modal and other nonclassical logics via the tableaux method. This basically amounts to trying to build a model for the formula by building a tree. In such a setting, what an agent will do, i. The tableau calculi has been implemented in Lotrecscheme. The proof systems for modal logics come in various styles: Hilbert style, natural deduction, sequents, and resolution.
This chapter is about the model construction problem in some classes of models: models satisfying the conditions of reflexivity, seriality, symmetry, and combinations thereof. We prove that announcement finding in this setting is not only decidable, but that it is simpler than the corresponding problem in the most simplified modal logics. We give some words about model-checking, satisfiability problem and common knowledge. Basically, a possible worlds model is nothing but a graph with labelled nodes and labelled edges. After proving that what we can infer about ii given i and iii and what we can infer about i given ii and iii are both reducible to what we can infer about iii given i and ii , we provide a tableau method deciding whether such an inference is valid. All these logics have been studied intensively in philosophical and mathematical logic and in computer science, and have been applied increasingly in various domains such as program semantics, artificial intelligence, and more recently in the semantic web. We provide a multi-agent spatially grounded epistemic logical framework to reason about the knowledge of perception agent a sees agent b whose potential applications are video games and robotics.
This book follows a more general approach by trying to build a graph, the advantage being that a graph is closer to a Kripke model than a tree. They can also reason about each other's observation abilities and knowledge derived from these observations. In the end of the chapter we present another general termination theorem guaranteeing that the tableau construction does not loop and which applies to all these logics. We consider distributed gossip protocols wherein the agents themselves instead of a global scheduler determine whom to call. In this paper the problem of designing and analyzing gossip protocols is given a dynamic twist by assuming that when a call is established not only secrets are exchanged but also telephone numbers. We also consider effects of public announcements.
To capture asynchrony, we introduce two different modal operators for sending and receiving messages. An attention-based announcement can also be described as an action model. It can be used as an easy-going introduction for all who are interested in automated reasoning and need some formal tools for playing with modal logics. It provides a step-by-step introduction to possible worlds semantics and by that to modal and other nonclassical logics via the tableaux method. We define various such distributed dynamic gossip protocols, and we characterize them in terms of the class of graphs where they terminate successfully.
In this paper we investigate a concrete epistemic situation: there are agents humans, robots, cameras,. Every agent human, camera etc. Possible worlds models were introduced by Saul Kripke in the early 1960s. We also consider models whose accessibility relation is confluent logic K. In this work, we propose a version of public announcement logic wherein it is encoded in the states of the epistemic model which agents pay attention to the announcement. Euler diagrams are described as set of circles.
The natural approach to defining the semantics leads to a circular definition, but we describe two restricted cases in which we solve this problem. However, it is fair to say that the most uniform and most successful such systems are tableaux systems. Additionally, all these logics were also studied proof theoretically. Concerning interaction, the local search approach is not suitable but hybrid method and gradient method give both good results in terms of quality of drawings and stability. Concerning Flatland, we show that both model-checking and satisfiability problem are decidable but the exact complexities and the axiomatization remain open problems.
The first case requires the Kripke model representing the initial epistemic situation to be a finite tree, and the second one only allows announcements from the existential fragment. This book provides a step-by-step introduction to possible worlds semantics and by that to modal and other nonclassical logics via the tableaux method. A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. This basically amounts to trying to build a model for the formula by building a tree. At the end of the article we present an application of our formalization of counterfactual emotions to a concrete example. This book provides a step-by-step introduction to possible worlds semantics and by that to modal and other nonclassical logics via the tableaux method.
We propose a logical framework for reasoning about the sets of arguments owned by other agents, their knowledge about other agents' arguments, etc. This axiomatization also employs the auxiliary notion of attention-based relativized common belief. We also experimentally compare the different methods. In this work, we propose a version of public announcement logic wherein it is encoded in the states of the epistemic model which agents pay attention to the announcement. We introduce suitable logical languages for reasoning about such scenarios which involve atomic formulae stating what agents can see, multi-agent epistemic operators for individual, distributed and common knowledge, as well as dynamic operators re-flecting the ability of cameras to turn around in order to reach positions satisfying formulae in the language. We introduce a general formal language in order to talk about properties of Kripke models. Concerning Lineland, we provide a complete axiomatization and an optimal procedure for model-checking and satisfiability problem.