Susumu Hayashi

An arithmetical hierarchy of the law of excluded middle and related principles

The topic of this paper is relative constructivism. We are concerned with classifying nonconstructive principles from the constructive viewpoint. We compare, up to provability in intuitionistic arithmetic, subclassical principles like Markovs principle, (a function-free version of) weak Konigs lemma, Posts theorem, excluded middle for simply existential and simply universal statements, and many others. Our motivations are rooted in the experience of one of the authors with an extended program extraction and of another author with bound extraction from classical proofs.

Umbilical vein-artery differences of plasma amino acids in the last trimester of human pregnancy.

The plasma levels of 20 free amino acids in the umbilical veins and umbilical arteries of 8 premature (29--36 weeks gestation) and 16 mature (38--42 weeks gestation) newborn infants were measured at delivery. In premature newborn infants, most of the 20 amino acids were significantly higher in the umbilical vein than in the umbilical artery. Only glutamic acid was significantly lower in the umbilical vein than in the umbilical artery. In mature newborn infants, 7 (Ala, Lys, Leu, Val, Ile, Phe and His) of the 20 plasma amino acids were significantly higher and 4 (Glu, Gly, Ser and Orn) were significantly lower in the umbilical vein than in the umbilical artery. These results indicate that the relative contribution of individual amino acids to the placental supply of nitrogen to the human fetus discernibly changes with increasing fetal age during the last trimester of gestation.

Adjunction of semifunctors: categorical structures in nonextensional lambda calculus

Abstract Some connections between λ-calculus and category theory have been known. Among them, it has been shown by Lambek that cartesian closed categories (ccc for short) can be identified with extensional typed λ-calculus (cf. Lambek (1980), and Lambek and Scott (1986)). In this paper we introduce the notion of adjunction of semifunctors (for simplicity, we refer to this as ‘semiadjunction’) and, by the aid of this notion, we define the notion of semi cartesian closed category (semi-ccc for short). Some categorical or algebraic systems aimed to represent λ-calculus will turn out to be special cases of semi-ccc. Another intersting connection between ccc and λ-calculus is Scotts embedding of λ-theory into a ccc (cf. Scott (1980)). (This will be referred to as Scott embedding.) We will show that any semiadjunction is embeddable in an adjunction (of functors) and Scott embedding is a special case.

Games with 1-backtracking

We associate with any game G another game, which is a variant of it, and which we call bck(G). Winning strategies for bck(G) have a lower recursive degree than winning strategies for G: if a player has a winning strategy of recursive degree 1 over G, then it has a recursive winning strategy over bck(G), and vice versa. Through bck(G) we can express in algorithmic form, as a recursive winning strategy, many (but not all) common proofs of non-constructive Mathematics, namely exactly the theorems of the sub-classical logic Limit Computable Mathematics (Hayashi (2006) [6], Hayashi and Nakata (2001) [7])

Application of cephalosporins to obstetrics and gynecology: transfer of cefazolin and cephalothin to uterine tissue.

Antibiotics should be administered so as to maintain effective therapeutic levels in target organs. In routine clinical treatment, however, doses of antibiotics are determined on the basis of their achievable concentrations in blood. To determine the optimum doses of antibiotics against obstetric and gynecologic infections, the authors gave a single intravenous dose of 2 gm of cefazolin or cephalothin to 51 patients before hysterectomy and measured the levels of the antibiotics in uterine tissues and compared them with corresponding serum levels. The maximum tissue levels of cefazolin were generally about 6 to 7 times higher than those of cephalothin: In tthe perimetrium, levels were 154 microgram/gm for cefazolin and 24.1 microgram/gm for cephalothin; in the myometrium, 109.5 microgram/gm for cefazolin, and 15.5 microgram/gm for cephalothin; and in the endometrium, 98.9 microgram/gm for cefazolin and 10.4 microgram/gm for cephalothin. In the tissues, however, cephalothin reached peak levels more rapidly than cefazolin. Comparisons of the tissue levels and MIC of cefazolin and cephalothin revealed that cefazolin was maintained at over 12.5 microgram/gm for at least 150 minutes in the perimetrium, myometrium, and endometrium, whereas cephalothin was maintained at these levels for 40 to 50 minutes only in the perimetrium and myometrium. The ratio of tissue levels to serum levels was 40-70 to 100 for cefazolin and about 30 or less to 100 for cephalothin.

Test Driven Development of UML Models with SMART Modeling System

We are developing a methodology for Test-Driven Development of Models (TDDM) based on an experimental UML 2.0 modeling tool SMART. Our experience shows that TDDM is quite useful for agile model developments. SMART provides guidance on how to build models based on compiler errors of testcases, something similar to what Quick Fix of Eclipse does. It also provides such guidance from failures of testcases, which seems difficult in the case of TDD of programs.

A NEW FORMALIZATION OF FEFERMAN’S SYSTEM OF FUNCTIONS AND CLASSES AND ITS RELATION TO FREGE STRUCTURE

A new axiomatization of Feferman’s systems of functions and classes1,2 is given. The new axiomatization has a finite number of class constructors resembling the proposition constructors of Frege structure by Aczel.3 Aczel wrote “It appears that from the technical point of view the two approaches (Feferman’s system and Frege structure) run parallel to each other in the sense that any technical result for one approach can be reconstructed for the other”.3 By the aid of the new axiomatization, Aczel’s observation becomes so evident. It is now straightforward to give a mutual interpretation between our formulation and a first order theory of Frege structure, which improve results by Beeson in Ref. 4.

Testing Proofs by Examples

We will present the project of proof animation, which started last April. The motivations, aims, and problems of the proof animation will be presented. We will also make a demo of ProofWorks, a small prototype tool for proof animation

Semantics of a graphical model for representing hypotheses and a system supporting the management of hypotheses

Constructing hypotheses is a principal work for academic researchers to constitute knowledge. Hypotheses often contain uncertainty, might conflict with each others, and might be revised by discovery of new witnesses. Therefore researchers are heavily loaded with the management of hypotheses. In order to support such activities we propose a graphical model for representing hypotheses, under the recent situation that materials for academic researches are distributed in digital manners, e.g. digital libraries and WWW. We also propose how to construct and manage hypothesis graphs based on our model. It is well-known that graphs are suitable to represent knowledge and many works treating knowledge as graphs have been presented. Previous researches proposed methods how to construct and manage hypotheses automatically, while our present work is aimed at supporting researchers so that they can construct and manage graphs based on semantics with uncertainty. In this paper, we define the syntax and the semantics of hypothesis graphs in our model and present methods to support researchers in the construction and management of hypothesis graphs with a system implemented the methods.

Two Extensions of PX system (extended abstract)

Abstract Two extensions of PX system will be discussed. The extensions are ctPX (catch/throw PX) and mvPX (multiple values PX). ctPX is a PX system extended with Nakanos catch/throw logic. ctPX enables to extract LISP programs with catch/throw mechanism form natural proofs. mvPX is a PX system which uses multiple values rather than lists to keep a finite sequences of data. Programs extracted by ctPX are more efficient than the ones by the original PX.