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  1. Satoko Titani, Heiji Kodera & Hiroshi Aoyama (2013). Systems of Quantum Logic. Studia Logica 101 (1):193-217.
    Logical implications are closely related to modal operators. Lattice-valued logic LL and quantum logic QL were formulated in Titani S (1999) Lattice Valued Set Theory. Arch Math Logic 38:395–421, Titani S (2009) A Completeness Theorem of Quantum Set Theory. In: Engesser K, Gabbay DM, Lehmann D (eds) Handbook of Quantum Logic and Quantum Structures: Quantum Logic. Elsevier Science Ltd., pp. 661–702, by introducing the basic implication → which represents the lattice order. In this paper, we fomulate a predicate orthologic provided (...)
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  2. Satoko Titani (1999). A Lattice-Valued Set Theory. Archive for Mathematical Logic 38 (6):395-421.
    A lattice-valued set theory is formulated by introducing the logical implication $\to$ which represents the order relation on the lattice.
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  3. Satoko Titani (1997). Completeness of Global Intuitionistic Set Theory. Journal of Symbolic Logic 62 (2):506-528.
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  4. Gaisi Takeuti & Satoko Titani (1992). Fuzzy Logic and Fuzzy Set Theory. Archive for Mathematical Logic 32 (1):1-32.
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  5. Gaisi Takeuti & Satoko Titani (1987). Globalization of Intui Tionistic Set Theory. Annals of Pure and Applied Logic 33:195-211.
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  6. Gaisi Takeuti & Satoko Titani (1986). Global Intuitionistic Analysis. Annals of Pure and Applied Logic 31:307-339.
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  7. Gaisi Takeuti & Satoko Titani (1984). Intuitionistic Fuzzy Logic and Intuitionistic Fuzzy Set Theory. Journal of Symbolic Logic 49 (3):851-866.
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  8. Satoko Titani (1973). A Proof of the Cut-Elimination Theorem in Simple Type Theory. Journal of Symbolic Logic 38 (2):215-226.
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