36 found
Order:
  1.  22
    Residuated Lattices: An Algebraic Glimpse at Substructural Logics.Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski & Hiroakira Ono - 2007 - Elsevier.
    This is also where we begin investigating lattices of logics and varieties, rather than particular examples.
    Translate
      Direct download  
     
    Export citation  
     
    My bibliography   26 citations  
  2.  11
    Logics Without the Contraction Rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.
  3.  17
    Algebraic Aspects of Cut Elimination.Francesco Belardinelli, Peter Jipsen & Hiroakira Ono - 2004 - 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. (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   12 citations  
  4.  32
    Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics Over FL.Nikolaos Galatos & Hiroakira Ono - 2006 - 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.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   7 citations  
  5.  5
    Cut Elimination and Strong Separation for Substructural Logics: An Algebraic Approach.Nikolaos Galatos & Hiroakira Ono - 2010 - Annals of Pure and Applied Logic 161 (9):1097-1133.
    We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on substructural logics over the full Lambek Calculus [34], Galatos and Ono [18], Galatos et al. [17]). We present a Gentzen-style sequent system that lacks the structural rules of contraction, weakening, exchange and associativity, and can be considered a non-associative formulation of . Moreover, we introduce an equivalent Hilbert-style system and show that the logic associated (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  6.  18
    Closure Operators and Complete Embeddings of Residuated Lattices.Hiroakira Ono - 2003 - 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.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   6 citations  
  7. Intermediate Predicate Logics Determined by Ordinals.Pierluigi Minari, Mitio Takano & Hiroakira Ono - 1990 - 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 (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography  
  8.  19
    Glivenko Theorems for Substructural Logics Over FL.Nikolaos Galatos & Hiroakira Ono - 2006 - 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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  9.  30
    Kripke Semantics, Undecidability and Standard Completeness for Esteva and Godo's Logic MTL∀.Franco Montagna & Hiroakira Ono - 2002 - 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 (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  10.  27
    The Finite Model Property for BCK and BCIW.Robert K. Meyer & Hiroakira Ono - 1994 - Studia Logica 53 (1):107 - 118.
    This paper shows that both implicational logics BCK and BCIW have the finite model property. The proof of the finite model property for BCIW, which is equal to the relevant logic $\text{R}_{\rightarrow}$, was originally given by the first author in his unpublished paper [6] in 1973. The finite model property for BCK can be obtained by modifying the proof of that for BCIW. Here, both of these proofs will be given in a unified form and the difference between them will (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   6 citations  
  11.  31
    Craig's Interpolation Theorem for the Intuitionistic Logic and its Extensions—A Semantical Approach.Hiroakira Ono - 1986 - 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.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  12.  6
    On Involutive FL E-Monoids.Sándor Jenei & Hiroakira Ono - 2012 - 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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  13.  3
    Preface.Nikolaos Galatos, Peter Jipsen & Hiroakira Ono - 2012 - Studia Logica 100 (6):1059-1062.
  14.  5
    On Finite Linear Intermediate Predicate Logics.Hiroakira Ono - 1988 - 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.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  15.  20
    On the Size of Refutation Kripke Models for Some Linear Modal and Tense Logics.Hiroakira Ono & Akira Nakamura - 1980 - 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.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  16. The Variety Of Residuated Lattices Is Generated By Its Finite Simple Members.Tomasz Kowalski & Hiroakira Ono - 2000 - Reports on Mathematical Logic:59-77.
    We show that the variety of residuated lattices is generated by its finite simple members, improving upon a finite model property result of Okada and Terui. The reasoning is a blend of proof-theoretic and algebraic arguments.
     
    Export citation  
     
    My bibliography   2 citations  
  17.  15
    Reflection Principles in Fragments of Peano Arithmetic.Hiroakira Ono - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (4):317-333.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  18.  10
    Reflection Principles in Fragments of Peano Arithmetic.Hiroakira Ono - 1987 - Mathematical Logic Quarterly 33 (4):317-333.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  19. On Some Intuitionistic Modal Logics.Hiroakira Ono - 1977 - Bulletin of the Section of Logic 6 (4):182-184.
    Some modal logics based on logics weaker than the classical logic have been studied by Fitch [4], Prior [7], Bull [1], [2], [3], Prawitz [6] etc. Here we treat modal logics based on the intuitionistic propositional logic, which call intuitionistic modal logics.
     
    Export citation  
     
    My bibliography   4 citations  
  20.  11
    Non-Uniqueness of Normal Proofs for Minimal Formulas in Implication-Conjunction Fragment of BCK.Takahito Aoto & Hiroakira Ono - 1994 - Bulletin of the Section of Logic 23 (3):104-112.
    Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  21.  9
    Semantical Analysis of Predicate Logics Without the Contraction Rule.Hiroakira Ono - 1985 - 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.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  22.  2
    Logics Without the Contraction Rule and Residuated Lattices.Hiroakira Ono - 1930 - Australasian Journal of Philosophy 8:50-81.
    In this paper, we will develop an algebraic study of substructural propositional logics over FLew, i.e. the logic which is obtained from intuitionistic logics by eliminating the contraction rule. Our main technical tool is to use residuated lattices as the algebraic semantics for them. This enables us to study different kinds of nonclassical logics, including intermediate logics, BCK-logics, Lukasiewicz’s many-valued logics and fuzzy logics, within a uniform framework.
    Direct download  
     
    Export citation  
     
    My bibliography   6 citations  
  23.  18
    Uniform Interpolation in Substructural Logics.Majid Alizadeh, Farzaneh Derakhshan & Hiroakira Ono - 2014 - Review of Symbolic Logic 7 (3):455-483.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  24.  13
    Francesco Belardinelli Peter Jipsen.Hiroakira Ono - 2001 - Studia Logica 68:1-32.
    Translate
      Direct download  
     
    Export citation  
     
    My bibliography  
  25.  14
    Glivenko Theorems and Negative Translations in Substructural Predicate Logics.Hadi Farahani & Hiroakira Ono - 2012 - 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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  26. Cut Elimination In Noncommutative Substructural Logics.Bayu Surarso & Hiroakira Ono - 1996 - Reports on Mathematical Logic:13-29.
    The present paper is concerned with the cut eliminability for some sequent systems of noncommutative substructural logics, i.e. substructural logics without exchange rule. Sequent systems of several extensions of noncommutative logics FL and LBB'I, which is sometimes called $\tw$, will be introduced. Then, the cut elimination theorem and the decision problem for them will be discussed in comparison with their commutative extensions.
     
    Export citation  
     
    My bibliography   1 citation  
  27.  12
    Nikolaos Galatos.Hiroakira Ono - 2006 - Studia Logica 83:1-32.
    No categories
    Direct download  
     
    Export citation  
     
    My bibliography  
  28.  20
    Crawley Completions of Residuated Lattices and Algebraic Completeness of Substructural Predicate Logics.Hiroakira Ono - 2012 - 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 (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  29.  4
    A Classification of Logics Over FLew and Almost Maximal Logics.Hiroakira Ono & Masaki Ueda - 2003 - In A. Rojszczak, J. Cachro & G. Kurczewski (eds.), Philosophical Dimensions of Logic and Science. Kluwer Academic Publishers. pp. 3--13.
    Direct download  
     
    Export citation  
     
    My bibliography  
  30.  3
    Glivenko Theorems Revisited.Hiroakira Ono - 2009 - Annals of Pure and Applied Logic 161 (2):246-250.
    Glivenko-type theorems for substructural logics are comprehensively studied in the paper [N. Galatos, H. Ono, Glivenko theorems for substructural logics over FL, Journal of Symbolic Logic 71 1353–1384]. Arguments used there are fully algebraic, and based on the fact that all substructural logics are algebraizable 279–308] and also [N. Galatos, P. Jipsen, T. Kowalski, H. Ono, Residuated Lattices: An Algebraic Glimpse at Substructural Logics, in: Studies in Logic and the Foundations of Mathematics, vol. 151, Elsevier, 2007] for the details). As (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  31.  1
    Closure Operators and Complete Embeddings of Residuated Lattices.Hiroakira Ono - 2003 - 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.
    Direct download  
     
    Export citation  
     
    My bibliography  
  32. Algebraic Characterizations of Variable Separation Properties.Hitoshi Kihara & Hiroakira Ono - 2008 - Reports on Mathematical Logic.
    This paper gives algebraic characterizations of Halld\'{e}n completeness , and of Maksimova's variable separation property and its deductive form. Though algebraic characterizations of these properties have been already studied for modal and superintuitionistic logics, e.g. in Wro\'{n}ski [12] , pp.126--129), Maksimova [7] , pp.168--184), [9] , pp.99--112), a deeper analysis of these properties and non-trivial modifications of these results are needed to extend them to those for substructural logics, because of the lack of some structural rules in them. The first (...)
     
    Export citation  
     
    My bibliography  
  33. Remarks on Splittings in the Variety of Residuated Lattices.Tomasz Kowalski & Hiroakira Ono - 2000 - Reports on Mathematical Logic:133-140.
     
    Export citation  
     
    My bibliography  
  34. List of Participants 17 Robert K. Meyer (Camberra, Australia) Barbara Morawska (Gdansk, Poland) Daniele Mundici (Milan, Italy).Kazumi Nakamatsu, Marek Nasieniewski, Volodymyr Navrotskiy, Sergey Pavlovich Odintsov, Carlos Oiler, Mieczyslaw Omyla, Hiroakira Ono, Ewa Orlowska, Katarzyna Palasihska & Francesco Paoli - 2001 - Logic and Logical Philosophy 7:16.
    No categories
     
    Export citation  
     
    My bibliography  
  35. Algebraic Logic.Hiroakira Ono - 2012 - Journal of the Indian Council of Philosophical Research 1.
     
    Export citation  
     
    My bibliography  
  36. Logics Without the Contraction Rule and Residuated Lattices.Hiroakira Ono - 2011 - Australasian Journal of Logic 8 (2).
    In this paper, we will develop an algebraic study of substructural propositional logics over FLew, i.e. the logic which is obtained from intuitionistic logics by eliminating the contraction rule. Our main technical tool is to use residuated lattices as the algebraic semantics for them. This enables us to study different kinds of nonclassical logics, including intermediate logics, BCK-logics, Lukasiewicz’s many-valued logics and fuzzy logics, within a uniform framework.
    Direct download  
     
    Export citation  
     
    My bibliography