This paper gives new confluence proofs for several lambda calculi with permutation-like reduction, including lambda calculi corresponding to intuitionistic and classical natural deduction with disjunction and permutative conversions, and a lambda calculus with explicit substitutions. For lambda calculi with permutative conversion, naïve parallel reduction technique does not work, and traditional notion of residuals is required as Ando pointed out. This paper shows that the difficulties can be avoided by extending the technique proposed by Dehornoy and van Oostrom, called the Z (...) theorem: existence of a mapping on terms with the Z property concludes the confluence. Since it is still hard to directly define a mapping with the Z property for the lambda calculi with permutative conversions, this paper extends the Z theorem to compositional functions, called compositional Z, and shows that we can adopt it to the calculi. (shrink)

This paper applies Dehornoy et al.’s Z theorem and its variant, called the compositional Z theorem, to prove confluence of Parigot’s \-calculi extended by the simplification rules. First, it is proved that Baba et al.’s modified complete developments for the call-by-name and the call-by-value variants of the \-calculus with the renaming rule, which is one of the simplification rules, satisfy the Z property. It gives new confluence proofs for them by the Z theorem. Secondly, it is shown that the compositional (...) Z theorem can be applied to prove confluence of the call-by-name and the call-by-value \-calculi with both simplification rules, the renaming and the \-rules, whereas it is hard to apply the ordinary parallel reduction technique or the original Z theorem by one-pass definition of mappings for these variants. (shrink)

日本、中国、韓国はそれぞれの伝統に依拠しつつ西洋哲学を受容することで近代哲学を形成してきた。哲学や思想における特徴や制限は、他の思想を鏡として、そこに映し出すことで明らかになる。なぜ違いが生まれたのか 。互いの違いをどう克服するのか。西田幾多郎、吉田松陰、九鬼周造、西周、和辻哲郎、土田杏村、大西克礼、戸坂潤...。受容から対話へと続く道から、いま、東アジアにおける哲学的創造の新たな意義と可能性が拓か れる。.

Possible worlds have revolutionised philosophy and some related fields. But, in recent years, tools based on possible worlds have been found to be limited in many respects. Impossible worlds have been introduced to overcome these limitations. This Element aims to raise and answer the neglected question of what is characteristically impossible about impossible worlds. The Element sheds new light on the nature of impossible worlds. It also aims to analyse the main features and utility of impossible worlds and examine how (...) impossible worlds can capture distinctions which are unavailable if we limit ourselves to possible world-based tools. (shrink)

" L'argent est l'envers de toutes les images que le cinéma montre et monte à l'endroit " écrit Gilles Deleuze dans le deuxième volet de Cinéma. Le capital est toujours derrière le cinéma. Le Capital hante Cinéma du début à la fin. C'est donc une lecture marxiste du diptyque composé de L'Image-mouvement et L'Image-temps que propose Jun Fujita dans Ciné-capital. Comment fonctionne le mode de production ciné-capitaliste? Comment celui-ci fait-il produire de la plus-value aux images? Pourquoi et comment s'approprie-t-il (...) le travail même du spectateur? En quel sens peut-on soutenir qu'Eisenstein et Hitchcock ont anticipé l'arrivée de la New Economy des années 1990 (dématérialisation du travail et financiarisation de l'économie)? Quand et comment les images s'insurgent-elles contre l'exploitation ciné-capitaliste? Comment se mettent-elles à valoir pour elles-mêmes? Pourquoi le cinéma politique, depuis Straub et Huillet, a-t-il cessé de privilégier le tournage au bord de la mer? Qu'est-ce qui permet à Deleuze d'affirmer qu'Ozu est un cinéaste de gauche? Telles sont quelques-unes des questions abordées dans Ciné-capital. (shrink)

東洋の思想的な伝統を踏まえ、広い視野で哲学の新しい眺望を切り開いた『善の研究』。難解で知られるこの名著を丁寧に、深く掘り下げて読み解く西田哲学入門。 『善の研究』は西田の最初の著作ながら、晩年に至るまでの思索全体を貫く考え方が示されている主著。その魅力は、西洋の哲学と格闘しながら、その不十分性を乗り越えて物事の真相に迫ろうとする西田の思いがそのまま 表現されている点にある。仏教や儒教など、東洋の思想的な伝統をも踏まえた広い視野で哲学の世界に新しい眺望を切り開いた本書の面白さや意義を分かりやすく解説。西田の思考を丁寧に読み解き、西田が何を語ろうとし たのかを深く掘り下げて明らかにする、格好の西田哲学入門。.

We provide a natural extension of the intuitionistic natural deduction system NJ with at most two consequences, which we call a binary conclusion natural deduction system. The classical natural deduction system NK is defined as NJ together with the law of the excluded middle or the double negation principle. However, in contrast to NK, the new BCN system has no such classical rule, but has two kinds of rules managing two consequences. One is to eliminate one consequence and the other (...) is to introduce another consequence. Except on this point, BCN proofs are derived in exactly the same way as those in NJ. It is shown that with respect to the propositional fragment of NK, the BCN system is sound and sufficiently complete to prove classical propositional theorems. Moreover, as a corollary we obtain a general form of Glivenko's theorem and disjunction property for one of the two consequences. We also show the normalization theorem for BCN. Finally, we study some extensions of BCN to classical predicate logic. (shrink)

膨大な資料をもとに魅力あふれる西田の素顔を描きだし、彼の言葉に豊かな広がりを与える決定的評伝。.

Feinberg and Mallatt, in their presentation of neurobiological naturalism, have suggested that visual consciousness was acquired by early vertebrates and inherited by a wide range of descendants, and that its neural basis has shifted to nonhomologous nervous structures during evolution. However, their evolutionary scenario of visual consciousness relies on the assumption that visual consciousness is closely linked with survival, which is not commonly accepted in current consciousness research. We suggest an alternative idea that visual consciousness is linked to a specific (...) class of agency, consequently justifying their phylogenetic claim. We also examine the implication of their phylogenetic claim: visual consciousness is homologous across vertebrates, but its neural basis is not. This apparent incongruence illustrates a general phenomenon of homology, and that the resulting hierarchical view of visual consciousness and its neural basis can be straightforwardly accommodated by neurobiological naturalism. Throughout these discussions, we aim to address the potential theoretical issues in neurobiological naturalism and refine the picture illustrated by Feinberg and Mallatt regarding phylogenetic distribution and trajectories of visual consciousness. (shrink)

In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel (...) way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic. (shrink)

Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the eighteenth century. But it is quite recent (more precisely, in the 1990s) that logicians started to study them from a formal logical viewpoint. We propose a novel approach to the formalization of Euler diagrammatic reasoning, in which diagrams are defined not in terms of regions as in (...) the standard approach, but in terms of topological relations between diagrammatic objects. We formalize the unification rule, which plays a central role in Euler diagrammatic reasoning, in a style of natural deduction. We prove the soundness and completeness theorems with respect to a formal set-theoretical semantics. We also investigate structure of diagrammatic proofs and prove a normal form theorem. (shrink)

There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it (...) is designed to study. (shrink)

We propose a new information sharing system, named ``BisNet'', which automatically gathers information about the bookmarks stored in users' web browsers and helps the users exchange URIs of possibly interesting web pages with others who have similar interest with them. Being different from other typical agent services that gather and provide information according to pre-registered user profiles, BisNet is expected to share more relevant information because of its use of web browser bookmarks that are actively selected and ordered by many (...) humans. To enhance the relevance of information being shared, we developed a novel algorithm for directory evaluation. This algorithm only looks at the local referential structure between bookmark directories and URIs and calculates for each directory the ``order index'' that represents how well its content URIs are put in order with a focus on specific areas of interest. Then each directory receives new URIs from other related directories with large order indexes. The repetition of such URI exchanges makes the whole directory-URI networks dynamically form directory groups according to the commonness of the URIs they refer to. Our method is unique in that it pays no attention to the actual contents of web pages, and thus is much simpler and faster than other methods based on the result of content analysis. We carried out a field trial that involved 45 people who used a prototype version of BisNet clients. The result indicated that the relevance of shared URIs positively correlated with the ``order index'' of surrounding related directories, demonstrating the effectiveness of the method we proposed. (shrink)

What does it mean for the laws of logic to fail? My task in this paper is to answer this question. I use the resources that Routley/Sylvan developed with his collaborators for the semantics of relevant logics to explain a world where the laws of logic fail. I claim that the non-normal worlds that Routley/Sylvan introduced are exactly such worlds. To disambiguate different kinds of impossible worlds, I call such worlds logically impossible worlds. At a logically impossible world, the laws (...) of logic fail. In this paper, I provide a definition of logically impossible worlds. I then show that there is nothing strange about admitting such worlds. (shrink)

We define and investigate a uniformly locally o-minimal structure of the second kind in this paper. All uniformly locally o-minimal structures of the second kind have local monotonicity, which is a local version of monotonicity theorem of o-minimal structures. We also demonstrate a local definable cell decomposition theorem for definably complete uniformly locally o-minimal structures of the second kind. We define dimension of a definable set and investigate its basic properties when the given structure is a locally o-minimal structure which (...) admits local definable cell decomposition. (shrink)