0
votes
1answer
74 views

Are the structure of logical expression based on formative constructions like sequences or trees ?

Recently, I get confused when reading the book Principles of Mathematical Logic written by D. Hilbert. How to define the term 'logical expression'? I just envisage that it might be defined as anyone ...
14
votes
2answers
282 views

Is there a “tree-like” proof of compactness theorem in the case of uncountably many variables?

I like proofs using trees and König's lemma, since they are very visual. One of the applications of König's lemma you can show to students is proving compactness theorem for propositional calculus, ...
8
votes
2answers
207 views

Ordinal interpretation of Friedman's $n$?

I heard that Kruskal's tree theorem can be turned into a finite form that creates an extremely fast growing function because ordinals could be encoded into trees. On this wiki page it mentions that ...
0
votes
1answer
81 views

Natural order of rational trees?

What would be a natural order of rational trees? Rational trees arise naturally from free algebras if we view a term as a finite tree. For example the term f(a,g(b,c)) could be viewed as the ...
0
votes
1answer
417 views

How to make a parse tree for the following propositional logic formula?

I have a formula $\neg (( q \rightarrow \neg q) \vee p \vee ( \neg q \rightarrow ( r \wedge p)))$. As it contains 3 subformulas between the $\vee$'s, how can I put it into a parse tree. Would it be ...
1
vote
1answer
205 views

Depth distribution of normalized decision trees?

Lets work with the following inductive definition of a decision tree: 1) $\bot$, $\top$ are decision trees. 2) If $x_i$ is a variable and $T_0$, $T_1$ are decision trees then $(\lnot x_i \land T_0) ...
0
votes
1answer
142 views

Need help performing a tree method to test for satisfiability

For those who commented on my previous questions, sorry for the lack of information and explanation. Clearly I did not do a good job of explaining myself so I deleted the question and hope this one ...