# Fuzzy Logic - T-norms

#### clytaemnestra

##### New member
Hi, I've got the following tasks to solve:

1. calculate the following statement by using the Godel's t norm:
(ϕ ∧ ψ) ⇒ (ϕ ⇒ ψ)
Godel's t norm: tG (a, b) = min(a, b)

2. calculate the following statement by using the product t norm:
¬(ϕ ∨ ψ) ⇒ (¬ϕ ∧ ¬ψ)
product's t norm: tΠ(a, b) = a · b

3. calculate the following statement by using the Lukasziewisz's norm:
(ϕ ⇒ ψ) ⇒ (¬ϕ ∨ ψ),
Lukasziewisz's norm: tL(a, b) = max(0, a + b − 1)

Now, I checked the coursebook, Wiki and googled out some videos and materials - all of them describe it in some way, but none of them has specific instructions on how to plug it into a statement and solve it with it (for a dummy like me). Now, I don't want to come off az lazy - I'm of course willing to try to solve it on my own, before asking for help, but I couldn't find any materials on it. Thus I'd like to ask, if anyone has materials or any clue how to solve it? I'm not sure even how to start.

#### lex

##### Full Member
(I notice all 3 are tautologies under 'normal' predicate logic).

I see your problem, when you do searches on the internet.
Here are a few possibles:
http://math.uchicago.edu/~may/REU2014/REUPapers/Mendelssohn.pdf

(Table 2 may be of use in the following):
https://res.mdpi.com/d_attachment/philosophies/philosophies-06-00021/article_deploy/philosophies-06-00021.pdf

I think the book to get your hands on if you could is Hájek’s "Metamathematics of Fuzzy Logic". Chapter 2 may be helpful.
(Reviewed here: https://www.sfu.ca/~jeffpell/papers/ReviewHajek.pdf)

https://en.wikipedia.org/wiki/T-norm_fuzzy_logics

Sorry. Let me know if you get a good text.

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