• Publications
  • Influence
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 intuitionisticExpand
An arithmetical hierarchy of the law of excluded middle and related principles
TLDR
This paper compares, up to provability in intuitionistic arithmetic, subclassical principles like Markov's principle, (a function-free version of) weak Konig's lemma, Post's theorem, excluded middle for simply existential and simply universal statements, and many others. Expand
Consistent and Coherent Learning with δ-Delay
A consistent learner is required to correctly and completely reflect in its actual hypothesis all data received so far. Though this demand sounds quite plausible, it may lead to the unsolvability ofExpand
Normal Proofs and Their Grammar
TLDR
Grammars reflect the structure of normal inhabitants in such a way that, when non-terminals are ignored, a derivation tree of the grammars yielding a-termM can be identified with B?hm tree ofM. Expand
VC Dimensions of Principal Component Analysis
TLDR
In the course of the upper bound proof, this work provides a simple proof of Warren's bound of the number of sign sequences of real polynomials and discusses the distribution of eigenvalues of a data covariance matrix. Expand
Limiting Partial Combinatory Algebras towards Infinitary Lambda-Calculi and Classical Logic
  • Y. Akama
  • Mathematics, Computer Science
  • CSL
  • 10 September 2001
TLDR
This work will construct from every partial combinatory algebra A a PCA a-lim(A) s.t. transfinite times to interpret infinitary λ-calculi and discuss limit structures for A in terms of Barendregt's range property. Expand
A Study of Abramsky's Linear Chemical Abstract Machine
TLDR
It is shown that one step computation of LCHAM is equivalent to that of the linear λ-calculus, and the principal typing theorem of L CHAM is proved, which implies the decidability of type checking. Expand
On Mints' Reduction for ccc-Calculus
  • Y. Akama
  • Mathematics, Computer Science
  • TLCA
  • 16 March 1993
TLDR
A divide- and-conquer lemma is presented to infer the SN+CR (Strongly Normalization and Church-Rosser) property of a reduction system from that property of its subsystems, and some relations of the two restricted expansions against traditional reductions are obtained. Expand
A Lambda-to-CL Translation for Strong Normalization
  • Y. Akama
  • Mathematics, Computer Science
  • TLCA
  • 2 April 1997
TLDR
This translation provides a simpler SN proof of Godel's λ-calculus by the ordinal number assignment method andconstructs a homomorphism from a conditionally partial combinatory algebra which arises over SN κ-terms to a partial combinators algebra which arose over SN CL-terms. Expand
VC dimension of ellipsoids
We will establish that the VC dimension of the class of d-dimensional ellipsoids is (d^2+3d)/2, and that maximum likelihood estimate with N-component d-dimensional Gaussian mixture models induces aExpand
...
1
2
3
4
5
...