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Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 682/731 9. Agents based on FOL 5. (Concurrent-) MetaTeM The following connectives are defined ([finger-fisher-owens]): ○φ φ is true in the next state [⊥Uφ] ⊖φ the current state is not the initial state, and φ was true in the previous state [⊥Sφ] ⊚φ if the current state is not the initial state, then φ was true in the previous state [¬ ⊖¬φ] ♦φ φ will be true in some future state [⊤Uφ] φ φ was true in some past state [⊤Sφ] □φ φ will be true in all future states [¬ ♦¬φ] φ φ was true in all past states [¬¬φ]
Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 683/731 9. Agents based on FOL 5. (Concurrent-) MetaTeM Temporal formulae can be classified as follows. state-formula: is either a literal or a boolean combination of other state-formulae. Strict future-time: If A and B are either state or strict future-time formulae, then A UB is a strict future-time formula. If A and B are strict future-time formulae, then ¬A, A ∧ B, and (A) are strict future-time formulae. Strict past-time: past-time duals of strict future-time formulae. Non-strict: include state-formulae in their definition.
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