My research achievements are concerned with
five independent subjects
for
mathematical investigations on proofs and computations
(I)(V) chronologically,
the last one is the origin
of my research proposal.

(I) ProofTheory and Combinatorial Independence (cf.[10,11])

We established relationships between unprovable combinatorial
problems (in the sense of Gödel)
and proofreductions for arithmetic and secondorder logics
(a la GentzenTakeuti).

(II) Full Completeness Theorems

(IIi) MLL Full Completeness Theorems (cf.[9,8])

We obtained various forms of Full Completeness Theorems (these
theorems had emerged surprisingly in the 1990's in the framework of Girard's linear logic (LL)) by using the concrete mathematical structures of topological vector spaces
and Pontryagin duality.

(IIii) MALL Full Completeness in Hypercoherences (cf.[6])

We solved affirmatively an open full completeness theorem
(since the beginnings of full completeness)
for a larger fragment (MALL)
by using Ehrhard's hypercoherent spaces to retain Joyal's
categorical property of softness.

(III) MALL ProofNets (cf.[7])

We analyzed a
graph theoretical characterization
of proofs by making a correspondence to the theory of categories (morphisms as proofs).

(IV) Categorical Semantics for Polarized Linear Logic (cf.[
5,4,3])

We developed a construction of polarity for linear logic
in categorical model, as well as algebraic phase spaces,
by using adjunction between contravariant
positive and negative categories.

(V) Computational Structure of RNAi (cf.[1,2])

As innovative applications of computational logic
to biological phenomena, we elucidated the computational power of
RNA interference by means of Minsky register machines
and showed its sustainability
by means of Markov Multitype branching processes.