Recently Lafont [6] showed the finite model property for the multiplicative additive fragment of linear logic and for affine logic, i.e., linear logic with weakening. In this paper, we shall prove the finite model property for intuitionistic versions of those, i.e. intuitionistic MALL, and intuitionistic LLW. In addition, we shall show the finite model property for contractive linear logic, i.e., linear logic with contraction, and for its intuitionistic version. The finite model property for related substructural logics also follow by our (...) method. In particular, we shall show that the property holds for all of FL and GL$^-$-systems except FL$_c$ and GL$^-_c$ of Ono [11], that will settle the open problems stated in Ono [12]. (shrink)

We present some ideas on logical process descriptions, using relations from the DIO (Drug Interaction Ontology) as examples and explaining how these relations can be naturally decomposed in terms of more basic structured logical process descriptions using terms from linear logic. In our view, the process descriptions are able to clarify the usual relational descriptions of DIO. In particular, we discuss the use of logical process descriptions in proving linear logical theorems. Among the types of reasoning supported by DIO one (...) can distinguish both (1) basic reasoning about general structures in reality and (2) the domain-specific reasoning of experts. We here propose a clarification of this important distinction between (realist) reasoning on the basis of an ontology and rule-based inferences on the basis of an expert’s view. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.4 (2003) 73-84 [Access article in PDF] Music-Picture:One Form of Synthetic Art Education"Music-picture (a picture drawn through musical perception)" has been widely accepted by art educators in Japan. The purpose of this essay is to propose the making of music-pictures as art education and to put it on afirm theoretical base. I first investigate three gestalt rules: adjacency, continuance, and resemblance, all of which (...) are applicable to the senses of both seeing and hearing. Next I present research on color hearing as one version ofsynaesthesia, which is the comprehensive faculty that binds the five senses in various ways. The well-organized music-picture program by Kaoru Sasaki 1 is introduced as an example. 2 The synthetic art-educational value of music-picture will become clearer through these examinations. The Interrelations between Visual Arts and Music It is exciting that the visual arts meet music in an art class, even if these subjects are entirely different in regard to media, expressive form, the category of perception, and mastery of techniques. Put simply, Picasso's works are visible, whereas Stravinsky's pieces are invisible. Nevertheless, both powerfully convey imaginative and often narrative messages. Relying on intuition alone, I firmly believe both are interchangeable.My research on common methods of organizing both recorded music and painting was my first observation of the mutual relationship between music and visual arts. 3 But what I considered then would not be applied to art class directly because the research was based on my practical experience. It did not have any educational goals. Now I recognize that instructive approaches are necessary to lay the foundation for art classes dealing with interaction between two distinct modalities.In Japan, the Ministry of Education and Science provides the government curriculum guidelines nearly every ten years. It contains descriptions on two subjects: The visual arts and music taught in these classes are at an elementary school level and a junior high school level, both located within a compulsory education system. The new version has been in force since April 2002 (the new school term starts in April in Japan). Objectives in the two educational fields are similar and ideas of what art and music education ought to be are almost the same. The aim common to both in the government curriculum guidelines: "Through expression and appreciation, we [End Page 73] cultivate students' sentiments" invites the linking of music and the visual arts across the curriculum.Many art educators in Japan are interested in this sort of idea and have actually put it into practice. 4 They are engaged in interrelating or even unifying music and the visual arts. Additionally I know other teachers who have designed and proposed many ideas toward this crossover. Listed below are general ideas that seek to combine visual arts with music in an art class.1) Music-picture: to make a pictorial description of impressions received from music.2) Sound map: to make a map of sounds heard at a given location. Each sound is visualized by simple marks like - - -, <<<, ~~~, ooo, and xxx.3) Graphic notation: to write a score which directs the details, whole form, and progression of music by graphics instead of staff notation. Using onomatopoeias or instructions by words are common. It can be improvised, based on intuitively translating visual impacts into sounds.4) Sound toy: to make an original musical instrument of familiar easil obtained materials. For instance, a corrugated cardboard ukulele whose strings are rubber bands, a pair of maracas made of empty cans and soybeans, and so forth.5) Sound sculpture: to make sculpture producing interesting sounds (sometimes noises like creak or clatter). Extensive genres: wood sculpture, metal construction, assemblage (junk arts), kinetic arts, and so on.6) Sound installation: to make a place where participants experience sounds generated by objects or equipment.7) Multimedia: in the broad sense, to mix visuals with music; noises like jingle, tap, and bang! in daily life, or natural environmental sounds like a pit-a-pat of falling rain, a whisper of leaves, or... (shrink)

Recently Lafont [6] showed the finite model property for the multiplicative additive fragment of linear logic (MALL) and for affine logic (LLW), i.e., linear logic with weakening. In this paper, we shall prove the finite model property for intuitionistic versions of those, i.e. intuitionistic MALL (which we call IMALL), and intuitionistic LLW (which we call ILLW). In addition, we shall show the finite model property for contractive linear logic (LLC), i.e., linear logic with contraction, and for its intuitionistic version (ILLC). (...) The finite model property for related substructural logics also follow by our method. In particular, we shall show that the property holds for all of FL and GL - -systems except FL c and GL - c of Ono [11], that will settle the open problems stated in Ono [12]. (shrink)

To investigate the cognitive processes underlying creative inspiration, we tested the extent to which viewing or copying prior examples impacted creative output in art. In Experiment 1, undergraduates made drawings under three conditions: copying an artist's drawing, then producing an original drawing; producing an original drawing without having seen another's work; and copying another artist's work, then reproducing that artist's style independently. We discovered that through copying unfamiliar abstract drawings, participants were able to produce creative drawings qualitatively different from the (...) model drawings. Process analyses suggested that participants' cognitive constraints became relaxed, and new perspectives were formed from copying another's artwork. Experiment 2 showed that exposure to styles of artwork considered unfamiliar facilitated creativity in drawing, while styles considered familiar did not do so. Experiment 3 showed that both copying and thoroughly viewing artwork executed using an unfamiliar style facilitated creativity in drawing, whereas merely thinking about alternative styles of artistic representation did not do so. These experiments revealed that deep encounters with unfamiliar artworks—whether through copying or prolonged observation—change people's cognitive representations of the act of drawing to produce novel artwork. (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)

In the performing arts, such as music and dance performances, people actively interact with each other and show their exciting performances. Some studies have proposed that this interaction is a social origin of the performing arts. Some have further investigated this phenomenon based on the synchronization and coordination theory. Though the majority of these studies have focused on the collaborative context, several genres of the performing arts, such as jazz sessions and breakdance battles, have a competitive context. Several studies have (...) suggested that, in this competitive context, performers actively interact with each other and construct some correspondence. Moreover, a few recent studies focusing on competitive conversations, such as debates, have shown that, compared to people's interactions in collaborative conversations, people in competitive contexts frequently coordinate their behaviors in complicated ways. However, the interaction and coordination among performers in these competitive contexts have not been sufficiently investigated. Therefore, we investigated the coordination of expert breakdancers in battle scenes and measured their rhythmic movements using a motion capture system. We calculated the relative phase of the rhythmic movements between two dancers to investigate their coordination. The results showed that the dancers' rhythmic movements tended to synchronize in an anti-phase fashion, which means that there were similarities as well as differences between the two dancers' rhythmic movements. Furthermore, this pattern of coordination changed dynamically as time elapsed, from an in-phase synchronization or leader-follower relationships to an anti-phase synchronization and then leader-follower relationships. (shrink)

The paper traces the development and the role of syntactic reduction in Edmund Husserl’s early writings on mathematics and logic, especially on arithmetic. The notion has its origin in Hermann Hankel’s principle of permanence that Husserl set out to clarify. In Husserl’s early texts the emphasis of the reductions was meant to guarantee the consistency of the extended algorithm. Around the turn of the century Husserl uses the same idea in his conception of definiteness of what he calls “mathematical manifolds.” (...) The paper argues that the notion anticipates the notion of reduction in term rewrite theory in computer science. The role of the reduction for Husserl is, however, primarily epistemological: its purpose is to impart clarity to formal mathematics. (shrink)

We introduce subsystems WLJ and SI of the intuitionistic propositional logic LJ, by weakening the intuitionistic implication. These systems are justifiable by purely constructive semantics. Then the intuitionistic implication with full strength is definable in the second order versions of these systems. We give a relationship between SI and a weak modal system WM. In Appendix the Kripke-type model theory for WM is given.

We treat a class of multi-person bargaining mechanisms based on games in coalitional form. For this class of games we identify properties of non-cooperative solution concepts, which are necessary and sufficient for the equilibrium outcomes to coincide with the core of the underlying coalitional form game. We view this result as a non-cooperative axiomatization of the core. In contrast to most of the literature on multi-person bargaining we avoid a precise specification of the rules of the game. Alternatively, we impose (...) properties of such games, which give rise to a large class of mechanisms, all of which are relevant for our axiomatization. (shrink)

For a robot to cohabit with people, it should be able to learn people’s nonverbal social behavior from experience. In this paper, we propose a novel machine learning method for recognizing gestures used in interaction and communication. Our method enables robots to learn gestures incrementally during human–robot interaction in an unsupervised manner. It allows the user to leave the number and types of gestures undefined prior to the learning. The proposed method (HB-SOINN) is based on a self-organizing incremental neural network (...) and the hidden Markov model. We have added an interactive learning mechanism to HB-SOINN to prevent a single cluster from running into a failure as a result of polysemy of being assigned more than one meaning. For example, a sentence: “Keep on going left slowly” has three meanings such as, “Keep on (1)”, “going left (2)”, “slowly (3)”. We experimentally tested the clustering performance of the proposed method against data obtained from measuring gestures using a motion capture device. The results show that the classification performance of HB-SOINN exceeds that of conventional clustering approaches. In addition, we have found that the interactive learning function improves the learning performance of HB-SOINN. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.4 (2003) 73-84 [Access article in PDF] Music-Picture:One Form of Synthetic Art Education"Music-picture (a picture drawn through musical perception)" has been widely accepted by art educators in Japan. The purpose of this essay is to propose the making of music-pictures as art education and to put it on afirm theoretical base. I first investigate three gestalt rules: adjacency, continuance, and resemblance, all of which (...) are applicable to the senses of both seeing and hearing. Next I present research on color hearing as one version ofsynaesthesia, which is the comprehensive faculty that binds the five senses in various ways. The well-organized music-picture program by Kaoru Sasaki 1 is introduced as an example. 2 The synthetic art-educational value of music-picture will become clearer through these examinations. The Interrelations between Visual Arts and Music It is exciting that the visual arts meet music in an art class, even if these subjects are entirely different in regard to media, expressive form, the category of perception, and mastery of techniques. Put simply, Picasso's works are visible, whereas Stravinsky's pieces are invisible. Nevertheless, both powerfully convey imaginative and often narrative messages. Relying on intuition alone, I firmly believe both are interchangeable.My research on common methods of organizing both recorded music and painting was my first observation of the mutual relationship between music and visual arts. 3 But what I considered then would not be applied to art class directly because the research was based on my practical experience. It did not have any educational goals. Now I recognize that instructive approaches are necessary to lay the foundation for art classes dealing with interaction between two distinct modalities.In Japan, the Ministry of Education and Science provides the government curriculum guidelines nearly every ten years. It contains descriptions on two subjects: The visual arts and music taught in these classes are at an elementary school level and a junior high school level, both located within a compulsory education system. The new version has been in force since April 2002 (the new school term starts in April in Japan). Objectives in the two educational fields are similar and ideas of what art and music education ought to be are almost the same. The aim common to both in the government curriculum guidelines: "Through expression and appreciation, we [End Page 73] cultivate students' sentiments" invites the linking of music and the visual arts across the curriculum.Many art educators in Japan are interested in this sort of idea and have actually put it into practice. 4 They are engaged in interrelating or even unifying music and the visual arts. Additionally I know other teachers who have designed and proposed many ideas toward this crossover. Listed below are general ideas that seek to combine visual arts with music in an art class.1) Music-picture: to make a pictorial description of impressions received from music.2) Sound map: to make a map of sounds heard at a given location. Each sound is visualized by simple marks like - - -, <<<, ~~~, ooo, and xxx.3) Graphic notation: to write a score which directs the details, whole form, and progression of music by graphics instead of staff notation. Using onomatopoeias or instructions by words are common. It can be improvised, based on intuitively translating visual impacts into sounds.4) Sound toy: to make an original musical instrument of familiar easil obtained materials. For instance, a corrugated cardboard ukulele whose strings are rubber bands, a pair of maracas made of empty cans and soybeans, and so forth.5) Sound sculpture: to make sculpture producing interesting sounds (sometimes noises like creak or clatter). Extensive genres: wood sculpture, metal construction, assemblage (junk arts), kinetic arts, and so on.6) Sound installation: to make a place where participants experience sounds generated by objects or equipment.7) Multimedia: in the broad sense, to mix visuals with music; noises like jingle, tap, and bang! in daily life, or natural environmental sounds like a pit-a-pat of falling rain, a whisper of leaves, or... (shrink)

We introduce a simple inference system based on two primitive relations between terms, namely, inclusion and exclusion relations. We present a normalization theorem, and then provide a characterization of the structure of normal proofs. Based on this, inferences in a syllogistic fragment of natural language are reconstructed within our system. We also show that our system can be embedded into a fragment of propositional minimal logic.

We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall show that Takeuti-Arai's cut-elimination procedure of $(\Pi^{1}_{1}-CA) + BI$ and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game. As a direct corollary the independence result of the Hydra Game follows.

Short interspersed repetitive elements, or SINEs, are tRNA-derived retroposons that are dispersed throughout eukaryotic genomes and can be present in well over 104 total copies. The enormous volume of SINE amplifications per organism makes them important evolutionary agents for shaping the diversity of genomes, and the irreversible, independent nature of their insertion allows them to be used for diagnosing common ancestry among host taxa with extreme confidence. As such, they represent a powerful new tool for systematic biology that can be (...) strategically integrated with other conventional phylogenetic characters, most notably morphology and DNA sequences. This review covers the basic aspects of SINE evolution that are especially relevant to their use as systematic characters and describes the practical methods of characterizing SINEs for cladogram construction. It also discusses the limits of their systematic utility, clarifies some recently published misunderstandings, and illustrates the effective application of SINEs for vertebrate phylogenetics with results from selected case studies. BioEssays 22:148–160, 2000. ©2000 John Wiley & Sons, Inc. (shrink)

The thesis according to which the meaning of a mathematical sentence is given by its proof was held by both Wittgenstein and the intuitionists, following Heyting and Dummett. In this paper, we clarify the meaning of this thesis for Wittgenstein, showing how his position differs from that of the intuitionists. We show how the thesis originates in his thoughts, from the middle period, about proofs by induction, and we sketch his answers to a number of objections, including the idea that, (...) given the particular meaning he gives to this thesis, he cannot account for mathematical conjectures. We conclude by showing how his views find a favourable echo today in the paradigm of “proposition-as-type” and extensions of the Curry-Howard isomorphism from which this paradigm originates. (shrink)

It is well known that the modal logic S5 can be embedded in the classical predicate logic by interpreting the modal operator in terms of a quantifier. Wajsberg [10] proved this fact in a syntactic way. Mints [7] extended this result to the quantified version of S5; using a purely proof-theoretic method he showed that the quantified S5 corresponds to the classical predicate logic with one-sorted variable. In this paper we extend Mints' result to the basic modal logic S4; we (...) investigate the correspondence between the quantified versions of S4 (with and without the Barcan formula) and the classical predicate logic (with one-sorted variable). We present a purely proof-theoretic proof-transformation method, reducing an LK-proof of an interpreted formula to a modal proof. (shrink)

It is well known that the modal logic S5 can be embedded in the classical predicate logic by interpreting the modal operator in terms of a quantifier. Wajsberg proved this fact in a syntactic way. Mints extended this result to the quantified version of S5; using a purely proof-theoretic method he showed that the quantified S5 corresponds to the classical predicate logic with one-sorted variable. In this paper we extend Mints’ result to the basic modal logic S4; we investigate the (...) correspondence between the quantified versions of S4 and the classical predicate logic. We present a purely proof-theoretic proof-transformation method, reducing an LK-proof of an interpreted formula to a modal proof. (shrink)

A complete list of Finsler, Scott and Boffa sets whose transitive closures contain 1, 2 and 3 elements is given. An algorithm for deciding the identity of hereditarily finite Scott sets is presented. Anti-well-founded sets, i. e., non-well-founded sets whose all maximal ∈-paths are circular, are studied. For example they form transitive inner models of ZFC minus foundation and empty set, and they include uncountably many hereditarily finite awf sets. A complete list of Finsler and Boffa awf sets with 2 (...) and 3 elements in their transitive closure is given. Next the existence of infinite descending ∈-sequences in Aczel universes is shown. Finally a theorem of Ballard and Hrbáček concerning nonstandard Boffa universes of sets is considerably extended. (shrink)