The simple substitution property provides a systematic and easy method for proving a theorem by an axiomatic way. The notion of the property was introduced in Hosoi [4] but without a definite name and he showed three examples of the axioms with the property. Later, the property was given it's name as above in Sasaki [7].Our main result here is that the necessary and sufficient condition for a logicL on a finite slice to have the simple substitution property is (...) thatL is finite. Here the necessity part is essentially new, for the sufficiency part has been proved in Hosoi and Sasaki [5]. Also the proof of sufficiency part is improved here. (shrink)

In the natural deduction system for classical propositional logic given by G. Gentzen, there are some inference rules with assumptions discharged by the rule. D. Prawitz calls such inference rules improper, and others proper. Improper inference rules are more complicated and are often harder to understand than the proper ones. In the present paper, we distinguish between proper and improper derivations by using sequent systems. Specifically, we introduce a sequent system $\vdash_{\bf Sc}$ for classical propositional logic with only structural rules, (...) and prove that $\vdash_{\bf Sc}$ does not allow improper derivations in general. For instance, the sequent $\Rightarrow p \to q$ cannot be derived from the sequent $p \Rightarrow q$ in $\vdash_{\bf Sc}$. In order to prove the failure of improper derivations, we modify the usual notion of truth valuation, and using the modified valuation, we prove the completeness of $\vdash_{\bf Sc}$. We also consider whether an improper derivation can be described generally by using $\vdash_{\bf Sc}$. (shrink)

This paper describes the situation of philosophy in Japan with respect to the question of internationalism. For more than a hundred years, Japan took Western culture as its model and European philosophy as the authentic philosophy. This tendency was paradoxically strengthened by the post‐war humanism. It gave us Japanese philosophers a clear discipline to work in but cut us off from our own native culture, history, and philosophical traditions. In wishing to recover this loss, I argue that it is necessary (...) to distinguish between two forms of internationalism: humanistic and merely fashionable. The latter in fact derives from domestic reasons. (shrink)

9th and 10th Nov. 2013 at Kyoto University. Organizers: Takeshi Sato and Shunsuke Sugimoto.

Hobbs (2010) introduced ‘clause-internal coherence’ (CIC) to describe inferences in, e.g., ‘A jogger was hit by a car,’ where the jogging is understood to have led to the car-hitting. Cohen & Kehler (2021) argue that well-known pragmatic tools cannot account for CIC, motivating an enrichment account familiar from discourse coherence research. An outstanding question is how to compositionally derive CIC from coherence relations. This paper takes strides in answering this question. It first provides experimental support for the existence of CIC (...) via offline evidence that attributive (non-)deverbal adjectives can trigger the same causal inferences within clauses that their predicative counterparts can trigger across clauses, albeit more weakly. To explain the experimental results, we use tools in Segmented Discourse Representation Theory (SDRT), which allows us to show that causal inferences can be derived in various ways, depending on whether deverbal adjectives are used attributively or predicatively. If the former, they are presupposition triggers and the coherence relations Elaboration/Continuation compete with Background; if the latter, Explanation/Result compete with Background. These different competitions -- cashed out in terms of interaction between default axioms -- correlate with the difference in the relative salience of the causal inferences. (shrink)

The simple substitution property provides a systematic and easy method for proving a theorem from the additional axioms of intermediate prepositional logics. There have been known only four intermediate logics that have the additional axioms with the property. In this paper, we reformulate the many valued logics S' n defined in Gödel [3] and prove the simple substitution property for them. In our former paper [9], we proved that the sets of axioms composed of one prepositional variable do not have (...) the property except two of them. Here we provide another proof for this theorem. (shrink)

The idea of interpretability logics arose in Visser [Vis90]. He introduced the logics as extensions of the provability logic GLwith a binary modality. The arithmetic realization of A B in a theory T will be that T plus the realization of B is interpretable in T plus the realization of A. More precisely, there exists a function f on the formulas of the language of T such that T + B C implies T + A f.The interpretability logics were considered (...) in several papers. An arithmetic completeness of the interpretability logic ILM, obtained by adding Montagna ''s axiom to the smallest interpretability logic IL, was proved in Berarducci [Ber90] and Shavrukov [Sha88]. [Vis90] proved that the interpretability logic ILP, an extension of IL, is also complete for another arithmetic interpretation. The completeness with respect to Kripke semantics due to Veltman was, for IL, ILMand ILP, proved in de Jongh and Veltman [JV90]. The fixed point theorem of GLcan be extended to ILand hence ILMand ILP. The unary pendant "T interprets T + A" is much less expressive and was studied in de Rijke [Rij92]. For an overview of interpretability logic, see Visser [Vis97], and Japaridze and de Jongh [JJ98]. (shrink)

0 From Sansui to Keshiki My subject here is the nature of landscape. The word “landscape” is to be understood in what follows in the aesthetic sense: I wish to clarify what we experience in landscape as a typical scene of natural beauty. For most people, the nature of this experience may be so transparent that its analysis is superfluous. I don’t, however, find the matter so straightforward. The fact that “a landscape” can also signify a landscape painting would seem (...) to indicate that landscap... (shrink)

『不思議の国のアリス』の数学観から、古代ギリシャから現代への懐疑主義思想との格闘をたどって、数学的知識の成立根拠を探る。.

Examining the interconnections between genes and culture is crucial for a more complete understanding of psychological processes. Genetic predispositions may predict different outcomes depending on one's cultural context, and culture may predict different outcomes depending on genetic predispositions - that is, genes and culture interact. Less is understood, however, about how genes and culture interact, or the psychological mechanisms through which gene–culture interactions occur. In this Element, Joni Y. Sasaki and Heewon Kwon review key findings and theories in gene–culture (...) interaction research. They then go on to discuss current issues and future directions in gene–culture research that may illuminate the path toward an explanatory framework. (shrink)

Volume 20, Issue 8, August 2020, Page 32-36.

In this paper, we discuss semantical properties of the logic $\textbf{GL}$ of provability. The logic $\textbf{GL}$ is a normal modal logic which is axiomatized by the the Löb formula $\Box (\Box p\supset p)\supset \Box p$, but it is known that $\textbf{GL}$ can also be axiomatized by an axiom $\Box p\supset \Box \Box p$ and an $\omega$ -rule $(\Diamond ^{*})$ which takes countably many premises $\phi \supset \Diamond ^{n}\top$ $(n\in \omega )$ and returns a conclusion \(\phi \supset (...) \bot \). We show that the class of transitive Kripke frames which validates $(\Diamond ^{*})$ and the class of transitive Kripke frames which strongly validates $(\Diamond ^{*})$ are equal, and that the following three classes of transitive Kripke frames, the class which validates $(\Diamond ^{*})$, the class which weakly validates $(\Diamond ^{*})$, and the class which is defined by the Löb formula, are mutually different, while all of them characterize $\textbf{GL}$. This gives an example of a proof system _P_ and a class _C_ of Kripke frames such that _P_ is sound and complete with respect to _C_ but the soundness cannot be proved by simple induction on the height of the derivations in _P_. We also show Kripke completeness of the proof system with $(\Diamond ^{*})$ in an algebraic manner. As a corollary, we show that the class of modal algebras which is defined by equations $\Box x\le \Box \Box x$ and $\bigwedge _{n\in \omega }\Diamond ^{n}1=0$ is not a variety. (shrink)

In this paper, we discuss semantical properties of the logic $\textbf{GL}$ of provability. The logic $\textbf{GL}$ is a normal modal logic which is axiomatized by the the Löb formula $\Box (\Box p\supset p)\supset \Box p$, but it is known that $\textbf{GL}$ can also be axiomatized by an axiom $\Box p\supset \Box \Box p$ and an $\omega$ -rule $(\Diamond ^{*})$ which takes countably many premises $\phi \supset \Diamond ^{n}\top$ $(n\in \omega )$ and returns a conclusion \(\phi \supset (...) \bot \). We show that the class of transitive Kripke frames which validates $(\Diamond ^{*})$ and the class of transitive Kripke frames which strongly validates $(\Diamond ^{*})$ are equal, and that the following three classes of transitive Kripke frames, the class which validates $(\Diamond ^{*})$, the class which weakly validates $(\Diamond ^{*})$, and the class which is defined by the Löb formula, are mutually different, while all of them characterize $\textbf{GL}$. This gives an example of a proof system _P_ and a class _C_ of Kripke frames such that _P_ is sound and complete with respect to _C_ but the soundness cannot be proved by simple induction on the height of the derivations in _P_. We also show Kripke completeness of the proof system with $(\Diamond ^{*})$ in an algebraic manner. As a corollary, we show that the class of modal algebras which is defined by equations $\Box x\le \Box \Box x$ and $\bigwedge _{n\in \omega }\Diamond ^{n}1=0$ is not a variety. (shrink)

1. Kō to shi no shisōshi -- 2. Kō to shi no shakai kagaku -- 3. Nihon ni okeru kō to shi -- 4. Ō-Bei ni okeru kō to shi -- 5. Kokka to ningen to kōkyōsei -- 6. Keizai kara mita kōshi mondai -- 7. Chūkan shūdan ga hiraku kōkyōsei -- 8. Kagaku gijutsu to kōkyōsei -- 9. chikyū kankyō to kōkyōsei -- 10. 21-seiki kōkyō tetsugaku no chihei -- 14. Rīdāshippu kara kangaeru kōkyōsei.

Ageing is basically a natural or physical phenomenon. For a human being, it belongs to the body. When this fact is noticed, a drama of oldness and life/death begins: ageing is a problem of experience. There are losses and gains in this experience. Indeed, a particular respect was paid to a rhapsodist/bard and a hermit because of their memory power and deep wisdom respectively. Since we recognize in these cases accumulation and maturation, the core subject in the experience of ageing (...) is memory and the time structure. Vis-à-vis the hard memories such as stone monuments and IC memory, the live memory is characterised by a creativity, which vivifies our past time. I pay a particular attention to friendship, because one of the most painful experiences of ageing consists in the loss of dear friends. Recollecting creatively the time shared with them, we can vivify our past, i.e. our being: that is the appropriation of ourselves. (shrink)

We introduce a Gentzen style formulation of Basic Propositional Calculus(BPC), the logic that is interpreted in Kripke models similarly tointuitionistic logic except that the accessibility relation of eachmodel is not necessarily reflexive. The formulation is presented as adual-context style system, in which the left hand side of a sequent isdivided into two parts. Giving an interpretation of the sequents inKripke models, we show the soundness and completeness of the system withrespect to the class of Kripke models. The cut-elimination theorem isproved (...) in a syntactic way by modifying Gentzen's method. Thisdual-context style system exemplifies the effectiveness of dual-contextformulation in formalizing various non-classical logics. (shrink)

Objective:This study aimed to investigate the effect of robot-assisted gait training therapy combined with non-invasive brain stimulation on lower limb function in patients with stroke and spinal cord injury.Data sourcesPubMed, Cochrane Central Register of Controlled Trials, Ovid MEDLINE, and Web of Science were searched.Study selectionRandomized controlled trials published as of 3 March 2021. RCTs evaluating RAGT combined with NIBS, such as transcranial direct current stimulation and repetitive transcranial magnetic stimulation, for lower limb function and activities in patients with stroke and (...) SCI were included.Data extractionTwo reviewers independently screened the records, extracted the data, and assessed the risk of bias.Data synthesisA meta-analysis of five studies and risk of bias were conducted. Pooled estimates demonstrated that RAGT combined with NIBS significantly improved lower limb function [standardized mean difference = 0.52; 95% confidence interval = 0.06–0.99] but not lower limb activities. Subgroup analyses also failed to find a greater improvement in lower limb function of RAGT with tDCS compared to sham stimulation. No significant differences between participant characteristics or types of NIBS were observed.ConclusionThis meta-analysis demonstrated that RAGT therapy in combination with NIBS was effective in patients with stroke and SCI. However, a greater improvement in lower limb function and activities were not observed using RAGT with tDCS compared to sham stimulation. (shrink)

Here, we provide a detailed description of the mutual relation of formulas with finite propositional variables p1, …, pm in modal logic S4. Our description contains more information on S4 than those given in Shehtman (1978) and Moss (2007); however, Shehtman (1978) also treated Grzegorczyk logic and Moss (2007) treated many other normal modal logics. Specifically, we construct normal forms, which behave like the principal conjunctive normal forms in the classical propositional logic. The results include finite and effective methods to (...) find a normal form equivalent to a given formula A by clarifying the behavior of connectives and giving a finite method to list all exact models. (shrink)