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  1. Majid Alizadeh, Farzaneh Derakhshan & Hiroakira Ono (forthcoming). Uniform Interpolation in Substructural Logics. Review of Symbolic Logic:1-30.
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  2. Hiroakira Ono (forthcoming). Logics Without the Contraction Rule and Residuated Lattices. Australasian Journal of Logic.
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  3. Hadi Farahani & Hiroakira Ono (2012). Glivenko Theorems and Negative Translations in Substructural Predicate Logics. Archive for Mathematical Logic 51 (7-8):695-707.
    Along the same line as that in Ono (Ann Pure Appl Logic 161:246–250, 2009), a proof-theoretic approach to Glivenko theorems is developed here for substructural predicate logics relative not only to classical predicate logic but also to arbitrary involutive substructural predicate logics over intuitionistic linear predicate logic without exponentials QFL e . It is shown that there exists the weakest logic over QFL e among substructural predicate logics for which the Glivenko theorem holds. Negative translations of substructural predicate logics are (...)
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  4. Nikolaos Galatos, Peter Jipsen & Hiroakira Ono (2012). Preface. Studia Logica 100 (6):1059-1062.
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  5. Sándor Jenei & Hiroakira Ono (2012). On Involutive FL E-Monoids. Archive for Mathematical Logic 51 (7-8):719-738.
    The paper deals with involutive FL e -monoids, that is, commutative residuated, partially-ordered monoids with an involutive negation. Involutive FL e -monoids over lattices are exactly involutive FL e -algebras, the algebraic counterparts of the substructural logic IUL. A cone representation is given for conic involutive FL e -monoids, along with a new construction method, called twin-rotation. Some classes of finite involutive FL e -chains are classified by using the notion of rank of involutive FL e -chains, and a kind (...)
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  6. Hiroakira Ono (2012). Crawley Completions of Residuated Lattices and Algebraic Completeness of Substructural Predicate Logics. Studia Logica 100 (1-2):339-359.
    This paper discusses Crawley completions of residuated lattices. While MacNeille completions have been studied recently in relation to logic, Crawley completions (i.e. complete ideal completions), which are another kind of regular completions, have not been discussed much in this relation while many important algebraic works on Crawley completions had been done until the end of the 70’s. In this paper, basic algebraic properties of ideal completions and Crawley completions of residuated lattices are studied first in their conncetion with the join (...)
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  7. Nikolaos Galatos & Hiroakira Ono (2010). Cut Elimination and Strong Separation for Substructural Logics: An Algebraic Approach. Annals of Pure and Applied Logic 161 (9):1097-1133.
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  8. Hiroakira Ono (2009). Glivenko Theorems Revisited. Annals of Pure and Applied Logic 161 (2):246-250.
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  9. Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski & Hiroakira Ono (2007). Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Elsevier.
    This is also where we begin investigating lattices of logics and varieties, rather than particular examples.
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  10. Nikolaos Galatos & Hiroakira Ono (2006). Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics Over FL. Studia Logica 83 (1-3):279 - 308.
    Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.
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  11. Nikolaos Galatos & Hiroakira Ono (2006). Glivenko Theorems for Substructural Logics Over FL. Journal of Symbolic Logic 71 (4):1353 - 1384.
    It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko's theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko's theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via a double negation interpretation. Our presentation is algebraic and is formulated in the context of residuated lattices. In the last part (...)
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  12. Hiroakira Ono (2006). Nikolaos Galatos. Studia Logica 83:1-32.
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  13. Francesco Belardinelli, Peter Jipsen & Hiroakira Ono (2004). Algebraic Aspects of Cut Elimination. Studia Logica 77 (2):209 - 240.
    We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. (...)
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  14. Hiroakira Ono (2003). Closure Operators and Complete Embeddings of Residuated Lattices. Studia Logica 74 (3):427 - 440.
    In this paper, a theorem on the existence of complete embedding of partially ordered monoids into complete residuated lattices is shown. From this, many interesting results on residuated lattices and substructural logics follow, including various types of completeness theorems of substructural logics.
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  15. Hiroakira Ono & Masaki Ueda (2003). A Classification of Logics Over FLew and Almost Maximal Logics. In. In A. Rojszczak, J. Cachro & G. Kurczewski (eds.), Philosophical Dimensions of Logic and Science. Kluwer Academic Publishers. 3--13.
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  16. Franco Montagna & Hiroakira Ono (2002). Kripke Semantics, Undecidability and Standard Completeness for Esteva and Godo's Logic MTL∀. Studia Logica 71 (2):227-245.
    The present paper deals with the predicate version MTL of the logic MTL by Esteva and Godo. We introduce a Kripke semantics for it, along the lines of Ono''s Kripke semantics for the predicate version of FLew (cf. [O85]), and we prove a completeness theorem. Then we prove that every predicate logic between MTL and classical predicate logic is undecidable. Finally, we prove that MTL is complete with respect to the standard semantics, i.e., with respect to Kripke frames on the (...)
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  17. Kazumi Nakamatsu, Marek Nasieniewski, Volodymyr Navrotskiy, Sergey Pavlovich Odintsov, Carlos Oiler, Mieczyslaw Omyla, Hiroakira Ono, Ewa Orlowska, Katarzyna Palasihska & Francesco Paoli (2001). List of Participants 17 Robert K. Meyer (Camberra, Australia) Barbara Morawska (Gdansk, Poland) Daniele Mundici (Milan, Italy). Logic and Logical Philosophy 7:16.
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  18. Hiroakira Ono (2001). Francesco Belardinelli Peter Jipsen. Studia Logica 68:1-32.
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  19. Takahito Aoto & Hiroakira Ono (1994). Non-Uniqueness of Normal Proofs for Minimal Formulas in Implication-Conjunction Fragment of BCK. Bulletin of the Section of Logic 23 (3):104-112.
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  20. Robert K. Meyer & Hiroakira Ono (1994). The Finite Model Property for BCK and BCIW. Studia Logica 53 (1):107 - 118.
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  21. Pierluigi Minari, Mitio Takano & Hiroakira Ono (1990). Intermediate Predicate Logics Determined by Ordinals. Journal of Symbolic Logic 55 (3):1099-1124.
    For each ordinal $\alpha > 0, L(\alpha)$ is the intermediate predicate logic characterized by the class of all Kripke frames with the poset α and with constant domain. This paper will be devoted to a study of logics of the form L(α). It will be shown that for each uncountable ordinal of the form α + η with a finite or a countable $\eta (> 0)$ , there exists a countable ordinal of the form β + η such that L(α (...)
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  22. Hiroakira Ono (1988). On Finite Linear Intermediate Predicate Logics. Studia Logica 47 (4):391 - 399.
    An intermediate predicate logicS + n (n>0) is introduced and investigated. First, a sequent calculusGS n is introduced, which is shown to be equivalent toS + n and for which the cut elimination theorem holds. In § 2, it will be shown thatS + n is characterized by the class of all linear Kripke frames of the heightn.
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  23. Hiroakira Ono (1987). Reflection Principles in Fragments of Peano Arithmetic. Mathematical Logic Quarterly 33 (4):317-333.
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  24. Hiroakira Ono (1986). Craig's Interpolation Theorem for the Intuitionistic Logic and its Extensions—a Semantical Approach. Studia Logica 45 (1):19 - 33.
    A semantical proof of Craig's interpolation theorem for the intuitionistic predicate logic and some intermediate prepositional logics will be given. Our proof is an extension of Henkin's method developed in [4]. It will clarify the relation between the interpolation theorem and Robinson's consistency theorem for these logics and will enable us to give a uniform way of proving the interpolation theorem for them.
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  25. Hiroakira Ono (1985). Semantical Analysis of Predicate Logics Without the Contraction Rule. Studia Logica 44 (2):187 - 196.
    In this paper, a semantics for predicate logics without the contraction rule will be investigated and the completeness theorem will be proved. Moreover, it will be found out that our semantics has a close connection with Beth-type semantics.
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  26. Hiroakira Ono & Yuichi Komori (1985). Logics Without the Contraction Rule. Journal of Symbolic Logic 50 (1):169-201.
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  27. Hiroakira Ono & Akira Nakamura (1980). On the Size of Refutation Kripke Models for Some Linear Modal and Tense Logics. Studia Logica 39 (4):325 - 333.
    LetL be any modal or tense logic with the finite model property. For eachm, definer L (m) to be the smallest numberr such that for any formulaA withm modal operators,A is provable inL if and only ifA is valid in everyL-model with at mostr worlds. Thus, the functionr L determines the size of refutation Kripke models forL. In this paper, we will give an estimation ofr L (m) for some linear modal and tense logicsL.
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