# help me define the connectives for 3 value logic

so basically i have a project about 3 valued logic ie truth=1 false = 0, unknown = 1/2

in a previous project I had to come up with formulae for 2 valued logic as follows:

negation
t(~p) = 1-t(p)

Conjunction
T(p^q) = min[t(p), t(q)]

Disjunction
T(p V q) = max[t(p), t(q)]

Conditional
~p -> q  === ~p V q => t(p->q) = t[~pVq]
=> max[t(~p), t(q)]
=> max[1-t(p), t(q)]

biconditional
p<->q === (p->q)^(q->p) => t(p->q) = t[(p->q)^(q->p)]
=> min[t(p->q), t(q->p)
=> min[max[1-t(p), t(q)], max[1-t(q), t(p)]]


using this information I have to define the connectives for 3 valued logic. and I dont really know how to do that. this is due tomorrow, please help!!! :(

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This section of a Wikipedia article should at least get you started. –  Brian M. Scott Jun 8 '12 at 7:57
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## 2 Answers

Unless you need more connectives for your project, you already have a set of connectives for a 3-valued logic. Do you see that both the formulas for conditional and equivalence always yield outputs in {0, 1/2, 1}? If so, since you have connectives which behave just the like the classical operations on {0, 1}, then you know that the formulas you have give you operations on {0, 1/2, 1}. Do you need more possible connectives for conjunction, disjunction, implication, or equivalence for another 3-valued logic?

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i guess your right, no i do not. i think my teacher just wanted us to state the set of connectives I already had. so i thought maybe I needed more. thanks! –  anthony Jun 8 '12 at 17:41
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I would suggest looking at Petr Hajek's Basic Logic (many-valued logic). There are several ways to define the connectives. One of famous possibilities is Łukasiewicz's Logic.

See SEP and Wikipedia for more information on other many-valued logics.

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