Computer Science – Logic in Computer Science
Scientific paper
2002-08-20
Computer Science
Logic in Computer Science
To appear, SIAM Journal on Computing
Scientific paper
Sound and complete axiomatizations are provided for a number of different logics involving modalities for knowledge and time. These logics arise from different choices for various parameters. All the logics considered involve the discrete time linear temporal logic operators `next' and `until' and an operator for the knowledge of each of a number of agents. Both the single agent and multiple agent cases are studied: in some instances of the latter there is also an operator for the common knowledge of the group of all agents. Four different semantic properties of agents are considered: whether they have a unique initial state, whether they operate synchronously, whether they have perfect recall, and whether they learn. The property of no learning is essentially dual to perfect recall. Not all settings of these parameters lead to recursively axiomatizable logics, but sound and complete axiomatizations are presented for all the ones that do.
der Meyden Ron van
Halpern Joseph Y.
Vardi Moshe Y.
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