I am interested in old texts which uses rationale and logical arguments only to reach to conclusion or prove some axiom. Are there such text which can be rightfully called logical treatises, scientific papers. Does ancient Hindu literature contain such body of texts?
In any logical/mathematical sysem, we have certain Axioms, whose validity are taken for granted within that system.
For example, a mathematical system that tries to introduce the concept of real/complex numbers, the three Axioms - field, order and completeness Axioms - are taken for granted. That is they are not required to be proved (within that particular system). All the remaining propositions/theorems of that system are then proved using those Axioms.
The only Hindu scriptures which share this pattern to an extent are the Darshana Shastras (the 6 Philosophical scriptures - Samkhya, Nyaya etc).
In the Darshanas, we have the proofs/standards (known as Pramana) which serve the same purpose as does an Axiom in a mathematical system.
For example, for the Samkhya Philosophy, we have:
Drishtamanumanamaptavachanancha sarvapramanasiddhatvat |
Trividham pramanamishtam prameyasiddhih pramanAddhi ||
Pratyaksha (direct perception), anumAna (inferrence) and Apta Vakya (i.e words of the Rishis or scriptures) - these three standards are accepted in Samkhya. All other standards are accomplished/established by these three only. By using these three pramanas the propositions are established.
Samkhya Karika 4
So, just like all the theorems/propositions in a logical system, are established using the validity of the Axioms which are accepted in that system, in this Samkhya doctrine, all the propositions are similarly established using the three Pramanas which are accepted as valid in the doctrine.
In addition to the answer by @Rickross I recommend
Jonardon Ganeri: Philosophy in Classical India. The proper work of reason. Ganeri is familiar with mathematical logic. In his book, "Chapter III The rational basis of metaphysics" he attempts to reconstruct some of the Nyaya-Vaiseshika logical texts by a graph-theoretic approach. The chapter contains a detailed reference, not only to the original Indian sources.
More general concerning its philosophical scope is Roy W. Perrett: An Introduction to Indian Philosophy. Perrett has a chapter on "Reasoning" which also discusses Nyaya logic. Perret tries to handle Indian and Western philosophy on the same footing. His approach aims to "give proper weight to cultural diversity - indeed requires it - but eschews any kind of relativism that would prohibit cross-cultural criticism." Also Perrett's book gives many references.
In my opinion, both texts are quite challenging.