The main purpose of this paper is to give alternative proofs of syntactical and semantical properties, i.e. the subformula property and the nite model property, of the sequent calculi for the modal logics K4.3, KD4.3, and S4.3. The application of the inference rules is said to be acceptable, if all the formulas in the upper sequents are subformula of the formulas in lower sequent. For some modal logics, Takano analyzed the relationships between the acceptable inference rules and semantical properties by (...) constructing models. By using these relationships, he showed Kripke completeness and subformula property. However, his method is difficult to apply to inference rules for the sequent calculi for K4.3, KD4.3, and S4.3. Lookinglosely at Takano's proof, we nd that his method can be modied to construct nite models based on the sequent calculus for K4.3, if the calculus has and all the applications of the inference rules are acceptable. Similarly, we can apply our results to the calculi for KD4.3 and S4.3. This leads not only to Kripke completeness and subformula property, but also to finite model property of these logics simultaneously. (shrink)

Islamic Mysticism and Abū Ṭālib al-Makkī: The Role of the Heart. By Saeko Yazaki. Routledge Sufi Series. London: Routledge, 2012. Pp. xx + 196. $145.

This volume discusses the origin and structure of the universe in mystical Islam (Sufism) and Islam's civilizational predecessors with special reference to parallel realms of existence and their interaction. Contributors address Sufi ideas about the fate of human beings in this and future life under three rubrics: (1) cosmogony and eschatology ("where do we come from?" and "where do we go?"); (2) conceptualizations of the world of the here-and-now ("where are we now?"); and (3) visualizations of realms of existence, their (...) hierarchy and mutual relationships ("where are we in relation to other times and places?"). Contributors are Christian Lange, Alexander Knysh, Noah Gardiner, Stephen Hirtenstein, Saeko Yazaki, Jean-Jacques Thibon, Leah Kinberg, Sara Sviri, Munjed M. Murad, Simon O'Meara, Pierre Lory, Mathieu Terrier, Michael Ebstein, Binyamin Abrahamov and Frederick Colby. (shrink)