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)

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)

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)

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)

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 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)

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 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 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.

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game . Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game , by a simple and natural interpretation . Jervell proposed another type of a combinatorial game, by abstracting (...) Gentzen's proof-reductions and showed that his game is independent of PA. We show that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φω = ϵ0) in the Veblen hierarchy of ordinals. (shrink)

This paper presents a new correctness criterion for marked Danos-Reginer graphs (D-R graphs, for short) of Multiplicative Cyclic Linear Logic MCLL and Abrusci's non-commutative Linear Logic MNLL. As a corollary we obtain an affirmative answer to the open question whether a known quadratic-time algorithm for the correctness checking of proof nets for MCLL and MNLL can be improved to linear-time.

This paper presents a new correctness criterion for marked Danos-Reginer graphs of Multiplicative Cyclic Linear Logic MCLL and Abrusci's non-commutative Linear Logic MNLL. As a corollary we obtain an affirmative answer to the open question whether a known quadratic-time algorithm for the correctness checking of proof nets for MCLL and MNLL can be improved to linear-time.

Persons with visual impairments (hereafter PVI) detect and discover obstacles and road conditions by touching with a white cane when walking on the streets. In one training session, an Orientation and Mobility specialist (hereafter SPT) guided a PVI by grasping and moving the cane that the PVI was holding. We conducted a multimodal analysis of two instruction sequences, one a "proving and achieving" demonstration (Sacks in Lectures on conversation, Blackwell, 1992) and the other a "learnable" (Zemel and Koschmann, in Discourse (...) Stud 16:163–183, 2014) demonstration. The achieving demonstration proved the assessment of the PVI's performance. In the "learnable" demonstration, the PVI was able to receive and perform the most critical part of the "learnable" of the long contact touch without the aid of talk. Sharing a single cane touch is an efficient way for both the guiding SPT and the guided PVI to jointly experience and understand the environmental features. The SPT did not need to verbally confirm that the guided touch was accountable to the PVI and seemed confident that intersubjectivity with the PVI had been established. A unique form of being with others and achieving intersubjectivity in society was identified. In traditional learning instruction, it has been assumed that the learnable is presented and communicated visually and audibly. However, through guided touch learnable is presented and conveyed effectively in the cases of this paper. It seems that the sense of touch has been considered to be just for the occasion, but this is an example of something that is not just for the occasion but is consequential, that is, usable for further occasions. The data is in Japanese. (shrink)

Methodological nationalism in sociological theory is unfit for the current globalized era, and should be discarded. In light of this contention, the present article discusses Max Weber’s view of language as a way to relativize the frame of the national society. While a “linguistic turn” in sociology since the 1960s has assumed that the sharing of language—linguistic community—stands as an intersubjective foundation for understanding of meaning, Weber saw linguistic community as constructed. From Weber’s rationalist, subjectivist, individualist viewpoint, linguistic community was (...) a result of social actions, not a prior entity as assumed by German metaphysical organicism (and historicist holism). Indeed, Central Europe in Weber’s era was a battlefield of linguistic nationalism(s); in contrast to the national societies of the Cold War period, national borders were unstable and ultimately the multiethnic empires of the region were dismantled after World War I into ethnolinguistic nation-states. Experience of this contemporary reality brought Weber to the core of the relationship between language and politics: A language community is an imaginary one demarcated not by language itself but by conscious opposition against outsiders, with monolingual contexts within borders created artificially by homogenizing policies like linguistic standardization and national education—the first modernity of language. In this way, Weber felt, language can be a means to domination. (shrink)

Sister chromatid separation in anaphase is an important event in the cell's transmission of genetic information to a descendent. It has been investigated from different aspects: cell cycle regulation, spindle and chromosome dynamics within the three‐dimensional cell architecture, transmission fidelity control and cellular signaling. Integrated studies directed toward unified understanding are possible using multidisciplinary methods with model organisms. Ubiquitin‐dependent proteolysis, protein dephosphorylation, an unknown function by the TPR repeat proteins, chromosome transport by microtubule‐based motors and DNA topological change by DNA (...) topoisomerase II are all necessary for progression from metaphase to anaphase. Chromosome condensation, mitotic kinetochore function and spindle formation require a large number of proteins, which are prerequisites for successful sister chromatid separation. Factors that help to retain sister chromatid connection after replication and prevent premature separation remain to be determined. Although sister chromatid separation occurs in anaphase, gene functions in other cell cycle stages also ensure the progression of correct chromatid separation. (shrink)

「主体から主体を越えて主体の底」へ行こうとした西田哲学と共に、「悲哀の底」の「底なき底」においたとうとする論考。.

The aim of this article is to explore how a self-referential social system, although it is not a human being, can be said to “observe.” For this purpose, the article reformulates Niklas Luhmann’s theory of social systems as sociological phenomenology, or the de-consciousness philosophized phenomenology, because a social system has the same structure of intentionality as consciousness: Just as consciousness is always consciousness of something, communication is always communication of something. In correlation to this communicative intentionality, communicated environments come and (...) go as social phenomena. A social system is not a thing, but an autonomously observing subject. Hence, this systems theory takes on the role of a second-order observer: It observes how social systems as first-order observers observe self-referentially because phenomena given to the natural attitude of the first-order observer constitute multiple social realities in daily life. Therefore, the theory of self-referential social systems is not objectivism, but a variation of mundane subjectivist phenomenology. (shrink)

The aim of this article is to explore how a self-referential social system, although it is not a human being, can be said to “observe.” For this purpose, the article reformulates Niklas Luhmann’s theory of social systems as sociological phenomenology, or the de-consciousness philosophized phenomenology, because a social system has the same structure of intentionality as consciousness: Just as consciousness is always consciousness of something, communication is always communication of something. In correlation to this communicative intentionality, communicated environments come and (...) go as social phenomena. A social system is not a thing, but an autonomously observing subject. Hence, this systems theory takes on the role of a second-order observer: It observes how social systems as first-order observers observe self-referentially because phenomena given to the natural attitude of the first-order observer constitute multiple social realities in daily life. Therefore, the theory of self-referential social systems is not objectivism, but a variation of mundane subjectivist phenomenology. (shrink)

The aim of this article is to explore how a self-referential social system, although it is not a human being, can be said to “observe.” For this purpose, the article reformulates Niklas Luhmann’s theory of social systems as sociological phenomenology, or the de-consciousness philosophized phenomenology, because a social system has the same structure of intentionality as consciousness: Just as consciousness is always consciousness of something, communication is always communication of something. In correlation to this communicative intentionality, communicated environments come and (...) go as social phenomena. A social system is not a thing, but an autonomously observing subject. Hence, this systems theory takes on the role of a second-order observer: It observes how social systems as first-order observers observe self-referentially because phenomena given to the natural attitude of the first-order observer constitute multiple social realities in daily life. Therefore, the theory of self-referential social systems is not objectivism, but a variation of mundane subjectivist phenomenology. (shrink)