Logic of knowledge and discovery via interacting agents - Decision algorithm for true and satisfiable statements

Тип публикации: статья из журнала

Год издания: 2009

Идентификатор DOI: 10.1016/j.ins.2008.12.008

Ключевые слова: Chance discovery (CD), Modal logic, Temporal logic, Agents' knowledge logic, Hybrid logics, Decidability, Kripke-Hintikka models, Inference rules, Rules in normal reduced form, Agents' knowledge logic, Chance discovery (CD), Decidability, Hybrid logics, Inference rules, Kripke-Hintikka models, Modal logic, Rules in normal reduced form, Temporal logic, Communication channels (information theory), Data storage equipment, Recursive functions, Set theory, Temporal logic, Chance discovery (CD), Decidability, Hybrid logics, Inference rules, Kripke-Hintikka models, Modal logic, Rules in normal reduced form, Computability and decidability

Аннотация: In this paper we study logical properties of the operation chance discovery (CD) via structures based on special Kripke/Hintikka models. These models use as bases partially ordered sets of indexes (indexes of steps in a computation, or ones indicating time points in a time flow), and clusters of states associated to each index. The language chosen to build the logical formulas includes modal/temporal operations, operations for the agents' knowledge, local and global operations for CID, operation of local common knowledge, and an operation for chance of discovery via agents' interactions. We introduce and study a logic (of knowledge and discovery via interaction of agents), LDK(A), which is defined by semantics, as the set of all formulas that are valid in all suggested models. The paper provides an algorithm to recognize logical laws (and satisfiable formulas) of LDK(A). The algorithm replaces a formula with a rule in a special, so-called reduced normal form, and, then it verifies the validity of this rule in specific models of exponential size in the size of the rule. We show that the problem of computing the true logical laws of LDK(A) is decidable. (C) 2008 Elsevier Inc. All rights reserved.

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Издание

Журнал: INFORMATION SCIENCES

Выпуск журнала: Vol. 179, Is. 11

Номера страниц: 1608-1614

ISSN журнала: 00200255

Место издания: NEW YORK

Издатель: ELSEVIER SCIENCE INC

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