D4Ly
asked on
True and False Worlds for Predicate Logic formulas
NOTE: 'for all' and 'for some' will be denoted with A and E respectively. Also, 'implies' will be denoted as -->, 'OR' will be \/ and 'AND' will be /\.
a) Ax Ey Q(x,y)
b) Ex Ey (R(x) \/ V(y))
c) Ey Ax (T(x) --> R(x,y))
What are the worlds for which these predicate formulas are true and false?
a) Ax Ey Q(x,y)
b) Ex Ey (R(x) \/ V(y))
c) Ey Ax (T(x) --> R(x,y))
What are the worlds for which these predicate formulas are true and false?
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ASKER
yes this is hw...though it doesn't matter. I figured it all out.
Thanks a lot though NetExpert...you're answers are leading to the sufficient one I need.
Thanks a lot though NetExpert...you're answers are leading to the sufficient one I need.
ASKER
worLds, not words.
Worlds
- Requires to provide domains for all variables and interpretations for all predicates
ie.
Ax P(x)
World_1:
Domain for x {1,2,3} and an interpretation for P:
1 | T
2 | T
3 | T
so
Ax P(x) = T {if all x in the Domain, the interpretation of P is T, or else F}
ie2.
ExP(x)
World = {T if there is an x in the Domain so that P is T, or else F}
Worlds
- Requires to provide domains for all variables and interpretations for all predicates
ie.
Ax P(x)
World_1:
Domain for x {1,2,3} and an interpretation for P:
1 | T
2 | T
3 | T
so
Ax P(x) = T {if all x in the Domain, the interpretation of P is T, or else F}
ie2.
ExP(x)
World = {T if there is an x in the Domain so that P is T, or else F}
What do you mean by words?
What are Q, R, V and T?