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Apr
23
revised Satisfiability proof of formulas with pure literals
added 1 character in body
Apr
23
comment Satisfiability proof of formulas with pure literals
Hi thx for your reply. Yes, I understand the principle, but I have problems in formulating a precise (structural) induction proof.
Apr
23
comment Satisfiability proof of formulas with pure literals
Thx for the comment, I've edited my question and included the case for $\psi := \varphi \land \ell$. Is this going in the right direction?
Apr
23
revised Satisfiability proof of formulas with pure literals
added 290 characters in body
Apr
22
revised Satisfiability proof of formulas with pure literals
edited title
Apr
22
revised Satisfiability proof of formulas with pure literals
edited body
Apr
22
revised Satisfiability proof of formulas with pure literals
added 2 characters in body
Apr
22
asked Satisfiability proof of formulas with pure literals
Apr
22
comment Validity of a first-order formula
yay! Can I ask you yet another question, just to be sure: If I replace $r$ in $\varphi$ by $\doteq$ (equality), so now I am considering also the theory of equality and its axioms, then the formula becomes valid. So, each instance of $r(x,y)$ gets replaced by $x \doteq y$. My assumption is that, then the formula is valid. because $x$ and $y$ are equal and according to the predicate substitution axioms of equality theory $p(x)$ and $p(y)$ always evaluates to the same truth value. Is this kind of the right (formal) argument?
Apr
22
comment Validity of a first-order formula
Thank you for your reply. So, I choose $\mathbb N_0$ as my Domain. $I(x) = 0$, $I(y)=1$. Moreover the meaning of predicate $p$ is "is even". The meaning of the predicate $r(x,y)$ is $y$ is greater than $x$, and I am done?
Apr
22
asked Validity of a first-order formula
Jan
29
accepted Get rid of an existential quantifier
Jan
29
awarded  Editor
Jan
29
comment Get rid of an existential quantifier
yeah thank you. i've edited my question
Jan
29
revised Get rid of an existential quantifier
edited body
Jan
29
asked Get rid of an existential quantifier
Jan
23
awarded  Student
Jan
23
accepted Number of triangles in a graph
Jan
23
awarded  Supporter
Jan
23
asked Number of triangles in a graph