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  1.  6
    Substructural Negations.Takuro Onishi - 2015 - Australasian Journal of Logic 12 (4).
    We present substructural negations, a family of negations classified in terms of structural rules of an extended kind of sequent calculus, display calculus. In considering the whole picture, we emphasize the duality of negation. Two types of negative modality, impossibility and unnecessity, are discussed and "self-dual" negations like Classical, De Morgan, or Ockham negation are redefined as the fusions of two negative modalities. We also consider how to identify, using intuitionistic and dual intuitionistic negations, two accessibility relations associated with impossibility (...)
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  2.  26
    Understanding Negation Implicationally in the Relevant Logic R.Takuro Onishi - 2016 - Studia Logica 104 (6):1267-1285.
    A star-free relational semantics for relevant logic is presented together with a sound and complete sequent proof theory. It is an extension of the dualist approach to negation regarded as modality, according to which de Morgan negation in relevant logic is better understood as the confusion of two negative modalities. The present work shows a way to define them in terms of implication and a new connective, co-implication, which is modeled by respective ternary relations. The defined negations are confused by (...)
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  3.  5
    Deductive Inference as Indirect Verification.Takuro Onishi - 2015 - Journal of the Japan Association for Philosophy of Science 42 (2):81-95.
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