- #1
disgradius
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My current understanding of schemata and structures in monadic logic is that, for example, if there are two predicate letters F and G that there would be (2*2)^the size of the universe of discourse possible structures as each object in that universe of discourse could take on any of the 4 possible truth assignments (TT, TF, FT, FF) from F and G.
I'm having some issues understanding how it's possible to find the number of pure monadic schemata possible independent of the size of the universe of discourse as it seems that the number possible would depend on the number of structures possible which in turns requires a size for the universe of discourse. My thinking is that there would be 2^# of structures possible for potential schemata till equivalence since we can combine them like truth assignments can be combined to form those schemata without quantifiers found in simpler truth functional logic.
Sorry if this is really confusing, in a nutshell what I'm asking is:
how can I find the number of pure monadic predicate letters that can be created from a given number of monadic predicate letters? Do I have to know the size of the universe of discourse and if not how would I go about doing this?
Apologies if this should go in the hw&coursework section, wasn't really sure if I needed a specific problem to post there.
Thanks!
I'm having some issues understanding how it's possible to find the number of pure monadic schemata possible independent of the size of the universe of discourse as it seems that the number possible would depend on the number of structures possible which in turns requires a size for the universe of discourse. My thinking is that there would be 2^# of structures possible for potential schemata till equivalence since we can combine them like truth assignments can be combined to form those schemata without quantifiers found in simpler truth functional logic.
Sorry if this is really confusing, in a nutshell what I'm asking is:
how can I find the number of pure monadic predicate letters that can be created from a given number of monadic predicate letters? Do I have to know the size of the universe of discourse and if not how would I go about doing this?
Apologies if this should go in the hw&coursework section, wasn't really sure if I needed a specific problem to post there.
Thanks!