Is there a word in English which expresses the idea of 'logicate' (which is not an English word)?

I am trying to translate the Greek word λογιξομαι, logitsomai,which is usually translated 'account' or 'reckon' which I do not think quite catch the meaning.

In English, we have words for numerical logic, for example 'calculate' and 'enumerate'; and we also have words for thought processes like 'reason', 'reckon' or 'estimate', some of which are financially appropriate, such as 'account'. 'Reckon' to me, is one of these - 'reckoning the books' used to mean reckoning up the double entry account ledgers at the end of a financial period.

But I cannot find a word which carries the idea of pure, intuitive logic.

'Reason' has connotations of disingenuity, a matter of a reason behind the reason. It is not intuitive logic. It reasons, often with an underlying motive.

But λογιξομαι, logitsomai, represents, to me, a logical view that is not cognitive, but intuitive. It views something conceptual, and immediately 'sees' what is right about it, logically.

The best I can come up with, after a long time considering it, is 'logicate' which is available in English it seems to me; but it is not an English word.

[Edit after post : I am translating a biblical word but this is a matter of translation into colloquial English, not theology. One of the main places is "Abraham believed God - and there was XXXXX to him, unto righteousness". From the very open structure of the wording (it is intransitive and so-called "deponent") it is clear that something is seen, logically, and it is attributed (a close word to λογιξομαι, logitsomai) to Abraham.

Deduce/deduction

But λογιξομαι, logitsomai, represents, to me, a logical view that is not cognitive, but intuitive. It views something conceptual, and immediately 'sees' what is right about it, logically.

My first idea would be to deduce (noun: deduction).

Deduce
verb

Arrive at (a fact or a conclusion) by reasoning; draw as a logical conclusion.
‘little can be safely deduced from these figures’

Edit

I only read your comment after I had answered.

Again, I would say that deduce is cognitive process, not intuition.

I agree with your comment by itself (logic is a cognitive process), but then your question is wrongly conflating "logic" and "intuition" to mean the same thing, which is not the case. Logic is not intuitive. If you logically come to a conclusion, that means you have used cognitive processes.

This is further confirmed by the dictionary definition of logic:

Reasoning conducted or assessed according to strict principles of validity.

This clashes with the dictionary definition of intuition:

The ability to understand something instinctively, without the need for conscious reasoning.

One possible exception - In an informal setting, "logical" is often used as a synonym for "obvious", which can make it seem like an equivalent to "intuitive". But it is important to observe that this informal meaning is not listed in the dictionary:

Logical
adjective

1. Of or according to the rules of logic or formal argument.
   ‘a logical impossibility’

1.1. Characterized by or capable of clear, sound reasoning.
‘her logical mind’

1.2. Expected or sensible under the circumstances.
‘the polar expedition is a logical extension of his Arctic travels’

You cannot use "intuitive" in any of the example sentences without changing its meaning. "intuitive" and "logical" are not interchangeable, as they do not mean the same thing.

Reason is correct too.

But I cannot find a word which carries the idea of pure, intuitive logic. 'Reason' has connotations of disingenuity, a matter of a reason behind the reason. It is not intuitive logic. It reasons, often with an underlying motive.

You're conflating two different meanings of the word "reason". These two meanings are completely separate from each other.

Reference link here

1. As a noun, it can refer to "a justification"

Reason
noun

A cause, explanation, or justification for an action or event.
‘she asked him to return, but didn't give a reason’
‘I resigned for personal reasons’

In other words, this meaning relates to the bolded word in your statement:

a matter of a reason behind the reason

2. Both as a (mass) noun and a verb, it can refer to "rational thought, deduction"

Reason
mass noun

The power of the mind to think, understand, and form judgements logically.
‘there is a close connection between reason and emotion’

Reason
verb

Think, understand, and form judgements logically.
‘humans do not reason entirely from facts’

In other words, this meaning relates to the bolded word in your statement:

a matter of a reason behind the reason

These two meanings of "reason" are not connected. You can use one without necessarily implying the other.

However, if you want to disambiguate (because the context does not already make it clear which meaning you're referring to), then you can use reasoning.

Since the verb "to reason" exclusively refers to "rational thought" and not "a justification", and "reasoning" is derived from the verb, that means there is no ambiguity here.

Abraham believed God - and there was certainty to him, unto righteousness.

Edit:

Truth; resides in the certainty to comprehend that two plus two make four. If that is granted, all else follows... 1984

Original Quote:

"Freedom is the freedom to say that two plus two make four. If that is granted, all else follows".

Edit: [Additional thoughts, retort (maybe)]

I would just like to add the following context. Thanks.

Consider the regal tones of reason in the light of certainty:

Reason is the power to judge as certainty is the freedom to believe.

Reason is to find deceit as certainty is to know truth.

Reason is to harbour doubt as certainty is to embrace conviction.

Through reason you may find certainty.

But faith in God cannot be reasoned!

You need to get away from the idea of "logic". Though logos is a valuable and important word, the English descendant logic has nothing to do with emotion or intuition (just ask Mr Spock). It's a near-synonym of reason, and your use of the term in the question is (with due respect) misleading.

I think you may need to get away from literal translation and find something in English with a similar connotation. A semi-financial term like "It was credited to him as righteousness" might do, but I think prove is best. I appreciate that it is non-exact, but in your example Abraham's belief was precisely proof of his righteousness, and the etymology, of passing a test, is also helpful.

This does not fit the translation phrase you presented, but in terms of an "intuitive truth", you can use the word postulate:

2a :to assume or claim as true, existent, or necessary :depend upon or start from the postulate of
  b :to assume as a postulate or axiom (as in logic or mathematics)
_{Merriam-Webster}

I was thinking about the notion of first principles when giving this answer. The idea is that there is a such a thing as a true statement that people are willing to accept as fact without proof.

A first principle is a basic, foundational, self-evident proposition or assumption that cannot be deduced from any other proposition or assumption. In philosophy, first principles are taught by Aristotelians and a nuanced version of first principles are referred to as postulates by Kantians.
_Wikipedia

However, another word to consider for your sample sentence is sincerity.

The quality of being free from pretense, deceit, or hypocrisy.
'the sincerity of his beliefs is unquestionable'
_{Oxford Living Dictionaries}

The word has as a close synonym truthfulness, which is close your notion of an inherent logical truth. So, in your sentence:

Abraham believed God - and there was sincerity to him, unto righteousness