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INFORMATIONRELATIVE OPEN SYSTEMS
THE FORMAL LANGUAGE
7 other sections not shown
abstract model abstract semantics accessibility relation actually possible Assume atomic formula axiom axiomatic systems backwards consistent backwards identity relation backwards transitive Chapter defined definition ensemble for ft evaluation function example extensionally equivalent follows formulas of LT ft is backwards ft is reflexive game theory game-theoretic model game-theoretic semantics given H ftK H RK Hence I-sets iff a,H iff H implies information available information ensemble information in H information is perfect information set Kripke semantics Lemma limited forward transitive modal language LTD modal operators modal systems Montague semantics nonempty nonext nonextensional relation nonextensional sets open system perfect information play H player Proof propositional variables provable R-History reflexive and backwards relative Remark represents S-model semantics for tensed set of formulas subensemble temporal modal logics tense logics tense operators tensed language LT tensed modal language tion totally ordered tree structure U-relation universal index set vertex world H