Тип публикации: статья из журнала
Год издания: 2009
Идентификатор DOI: 10.1093/logcom/exp027
Ключевые слова: Linear temporal logic, modal logics multi-agent logic, interacting agents, decidability, algorithms, inference rules, Algorithms, Decidability, Inference rules, Interacting agents, Linear temporal logic, Modal logics multi-agent logic, Inference rules, Interacting agents, Linear temporal logic, Modal logic, Modal logics multi-agent logic, Multi-agent logic, Communication channels (information theory), Computability and decidability, Inference engines, Multi agent systems, Recursive functions, Temporal logic
Аннотация: We study an extension LTLK of the linear temporal logic LTL by implementing multi-agent knowledge logic KD45(m) (which is often referred as multi-modal logic S5(m)). The temporal language of our logic adapts the operations U (until) and N (next) and uses new temporal operations: U-w-weak until, and U-s-strong until. We also employ the standard agents' knowledge operations K-i from the multi-agent logic KD45(m) and extend them with an operation IntK responsible for knowledge obtained via interaction of agents. The semantic models for LTLK are Kripke/Hintikka-like structures N-C based on the linear time. Structures N-C use i is an element of N as indexes for time, and the base set of any N-C consists of clusters C(i) (for all i is an element of N) containing all possible states at the time i. Agents' knowledge is modelled in time clusters C(i) via agents' knowledge accessibility relations R-j. The logic LTLK is the set of all formulas which are valid (true) in all such models N-C w.r.t. all possible valuations. We prove that LTLK is decidable: we reduce the decidability problem to verification of validity for special normal reduced forms of rules in specific models (not LTLK models) of size single-exponential in size of the rules. Furthermore. we extend these results to a linear temporal logic LTLK(Z) based on the time flow indexed by all integer numbers (with additional operations Since and Previous). Also we show that LTLK has the finite model property (fmp) while LTLK(Z) has no standard fmp.
Журнал: JOURNAL OF LOGIC AND COMPUTATION
Выпуск журнала: Vol. 19, Is. 6
Номера страниц: 989-1017
ISSN журнала: 0955792X
Место издания: OXFORD
Издатель: OXFORD UNIV PRESS
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