Truth Table of Buddism/Four fold logic?

Catuṣkoṭi or tretralemma is mostly made up by intellectuals who commented on what they thought was the dhamma, and they tried to push their sloppy reasoning as the dhamma too, like Nagarjuna, so it is mostly in Mahayana. None of that stuff is strongly buddhist. The intellectual works like the Upanishads use it too, with their neti neti, and the jains also, to support exactly the same claim like Nagarjuna, ie ''you can't talk about reality'', ie the absolute truth cannot be said with conventional language. Buddhist intellectuals are not really rigorous logicians, even more so when compared to today logicians.

Plenty of people have tried to formalize the tretralemma like here https://arxiv.org/pdf/1405.7744.pdf

Hence the interpretation of this modified catus.kot.i is: If somebody denies all these alternatives, then he/she intends to mean by abbreviation using the representatives that he/she declares that the ultimate truth or the reality can- not be described by any formula of any propositional calculus in which A is a generic formula. Particularly any propositional calculus for which A is a sentence letter doesn’t work to describe the reality.

https://plato.stanford.edu/entries/contradiction/#LNCBudTet

In the sutras, the tetralemma is just rejecting a claim and also rejecting the negation of the claim. This is from the claim being ill-defined, completely out of topic. But intellectuals prefer to view it has a deep thing about reality.

First, Catuskoti explicitly rejects propositions of the type "p and not p" as being true. Therefore, it is wrong to say that contradictions are held valid in buddhism. They are not.

Secondly, 4-fold rejection is posited from an ultimate standpoint and not the conventional standpoint (two-truths theory). From an ultimate standpoint, the differences are also fabricated between phenomenon and therefore are not ultimately real. In this manner it is said that contradictions are true- because both are mere appearances from the ultimate standpoint. But from the conventional standpoint, they are both not true at the same time and this contradictions in conventional domain are not held valid.

Remarks:

1. The finding of contradictions is posited within the conventional domain of the two-truths theory. Such contradictions are not logical contradictions. They are rather contradictions from a point of view or a theory (for example, dual logic) which takes for granted essentialist reasoning. Within Buddhism, which refutes essentialism, such contradictions are not contradictions because there is no one fixed logic, no ultimate building block to which everything could be reduced.

2. To understand how these so called contradictions are possible, it is suffice to mention here that the context sets the tone/them for the sort of statements posited and that the scope of such statements is within that context or like contexts only.

3. The idea if a truth table for catuskoti is to ask another system to mold itself and distort in order to speak according to the language of some other theory. Instead, it should help to understand that the buddhist logic, is not mathematical in its language (which of course does not make it any less incorrect or wrong). Buddhist logicians havent used formal logic but that does not make it any less rigorous. It will be suggested to read texts that explicitly deal with Buddhist logic to clear this misconception. It is is not being said that comparisons are not possible or should not be done. Just that for comparisons require one to thoroughly know the two systems being compared.

4. D S Ruegg has a brilliant essay that critically refutes the idea of looking at BUddhist logic through categories of thinking that are alien to the system and offers a much better perspective on Catuskoti. [ref. The uses of the four positions of the Catuskoti and the problem of the description of reality in Mahayana Buddhism].

OP: One thing that I find Buddhism fascinating is the "true contradictions", which says that there are statements that can be both true and false.

You can find such statements in Pali-canon not because the Dhamma falls into one of those logical statements but because the blessed one mentioned & rejected all those possibilities in related to Dhamma.

'After death a Tathagata exists,' 'After death a Tathagata does not exist,' 'After death a Tathagata both exists & does not exist,' 'After death a Tathagata neither exists nor does not exist'

"These positions that are undeclared, set aside, discarded by the Blessed One

Cited from: Cula-Malunkyovada Sutta (MN 63)

Another interesting statement can be found in Bāhiya Sutta (Ud 1.10)

Bāhiya, there is no you in connection with that. When there is no you in connection with that, there is no you there. When there is no you there, you are neither here nor yonder nor between the two. This, just this, is the end of stress."

OP: I was googling and found Dialetheism and Catuṣkoṭi on Wikipedia, but I have not found a truth table that represents this idea.

You couldn't find such a truth table because there is no such truth table in Buddhism. Truth tables can only be applied to something which can be explained by reasoning and logic. But Dhamma cannot. The Dhamma taught by the blessed one is very subtle and deep. It's very hard to understand for majority of the people bounded by craving and live in their own world made up by five aggregates of clinging. Only a wise man can understand this Dhamma. Nibbana is the ultimate goal of Buddhists. To tell you that it is an atakkāvacara Dhamma I've quoted a passage below.

What is Nibbana is a question that a Buddhist or non- Buddhist may prefer to ask at the outset. This is not a question of today or yesterday. Clever answers may be given and Nibbana may be explained in glowing terms, but no amount of theorizing will bring us nearer to it, for it is beyond words, logic and reasoning (atakkavacam). It is easier and safer to speak of what Nibbana is not, for it is impossible to express it in words.

Note: This is how I understood. I may be wrong but not Dhamma.