This paper studies a combined system of intuitionistic and classical propositional logic from proof-theoretic viewpoints. Based on the semantic treatment of Humberstone (J Philos Log 8:171–196, 1979) and del Cerro and Herzig (Frontiers of combining systems: FroCoS, Springer, 1996), a sequent calculus $$\textsf{G}(\textbf{C}+\textbf{J})$$ is proposed. An approximate idea of obtaining $$\textsf{G}(\textbf{C}+\textbf{J})$$ is adding rules for classical implication on top of the intuitionistic multi-succedent sequent calculus by Maehara (Nagoya Math J 7:45–64, 1954). However, in the semantic treatment, some formulas do not (...) satisfy heredity, which leads to the necessity of a restriction on the right rule for intuitionistic implication to keep the soundness of the calculus. The calculus $$\textsf{G}(\textbf{C}+\textbf{J})$$ enjoys cut elimination and Craig interpolation, whose detailed proofs are described in this paper. Cut elimination enables us to show the decidability of this combination both directly and syntactically. This paper also employs a canonical model argument to establish the strong completeness of Hilbert system $$\mathbf {C+J}$$ proposed by del Cerro and Herzig (Frontiers of combining systems: FroCoS, Springer, 1996). (shrink)

This paper shows Hilbert system (C+J)-, given by del Cerro and Herzig (1996) is semantically incomplete. This system is proposed as a proof theory for Kripke semantics for a combination of intuitionistic and classical propositional logic, which is obtained by adding the natural semantic clause of classical implication into intuitionistic Kripke semantics. Although Hilbert system (C+J)- contains intuitionistic modus ponens as a rule, it does not contain classical modus ponens. This paper gives an argument ensuring that the system (C+J)- is (...) semantically incomplete because of the absence of classical modus ponens. Our method is based on the logic of paradox, which is a paraconsistent logic proposed by Priest (1979). (shrink)

大地から生まれた自然農法の極意。米麦・野菜・果樹、あらゆる農の実践を縦横無尽に説く。「無」三部作実践篇。.

科挙のような儒教的制度を有さない他方、仏教によって葬儀や祭祀が主導されていた近世日本社会。そうした社会を生きる儒者達は、儒教儀礼、殊に東アジアで絶大な影響力を誇った『家礼』記載の喪祭礼を、どのように捉 え、そしていかにして実践しようと試みていたのか。長期間にわたってこの問題と真摯に向き合い続けた、山崎闇斎を学祖とする闇斎学派に着目、思想と社会とが様々に交錯する現場に立ち入ることで、これまで見落とされ てきた近世日本儒教の新しい一面を照らし出す。.

The cellular basis of motor learning in the cerebellum has been attributed mostly to long-term depression (LTD) at excitatory parallel fiber (PF)-Purkinje cell (PC) synapses. LTD is induced when PFs are activated in conjunction with a climbing fiber (CF), the other excitatory input to PCs. Recently, by using whole-cell patch-clamp recording from PCs in cerebellar slices, a new form of synaptic plasticity was discovered. Stimulation of excitatory CFs induced a long-lasting (usually longer than 30 min) of 30 sec) and the (...) durations of RP (>30 min) strongly suggests that some intracellular biochemical machinery is involved. Pharmacological evidence suggests that protein kinases are involved in RP of inhibitory synapses and LTD of excitatory PF synapses. Besides the well-described LTD, RP could be a cellular mechanism that plays an important role in motor learning. (shrink)