By Godfried T. Toussaint

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1]) because this would leave the important intentional notions unformalized. On the other hand, execution states cannot be identical to environment states, because the reachability graph construction algorithm relies on termination through eventually revisiting execution states, so all the information relevant to the execution state must be used when identifying execution states. Our approach is to distinguish between the information explicitly associated with a node in the reachability graph and the information used for identifying execution states, which is also represented in the graph but not as information explicitly encoded in states.

Ding, Y. and Zhang, Y. (2005). A logic approach for LTL system modiﬁcation. In Proceedings of the 15th International Symposium on Methodologies for Intelligent Systems (ISMIS 2005). LNAI3488. Pp. 436-444. 6. Gammie, P. (2004). MCK-Model checking the logic of knowledge. In the Proceeding of the 16th International Conference on Computer Aided Veriﬁcation. Pp. 479 - 483. 7. Harris,H. and Ryan,M. (2003). Theoretical foundations of updating systems. In the Prodeeding of the 18th IEEE International Conference on Automated Software Engineering.

M , ∃π = [s0 , s1 , · · · , si , si+1 , · · ·] ∈ M such that si = m−1 (si ), where i = 0, 1, · · ·; S = S ∪ {sss |sss ∈ S, sss ∈ S } − {si |si ∈ S, si ∈ S }; R = R ∪ {(si−1 , sss )(sss , si+1 )|si−1 ∈ S, si−1 ∈ S , si+1 ∈ S, si+1 ∈ S } −{(si−1 , si ), (si , si+1 )}; L :→ 2AP , where ∀s ∈ S , if s ∈ S,then L (s) = L(s), else L (sss ) =τ (sss ), where τ is the truth assignment related to sss , where the associated relations of si (or sss ) are its incoming and outgoing relations. PU4: Adding a state and its associated relation(s) only Given M = (S, R, L), its updated model M = (S , R , L ) is the result of M having only added a new state and its associated relation(s), iﬀ S = S ∪ {sas |sas ∈ S, sas ∈ S }; R = R ∪ {(sas−1 , sas )(sas , sas+1 )|sas−1 ∈ S, sas−1 ∈ S , sas+1 ∈ S, sas+1 ∈ S }; L :→ 2AP , where ∀s ∈ S , if s ∈ S,then L (s) = L(s), else L (sas ) =τ (sas ), where τ is the truth assignment related to sas , where the associated incoming and outgoing relations of sas are added.