MHB Predicate Logic: Semantics and Validity

AI Thread Summary
The discussion centers on the interpretation of a predicate logic formula given a specific domain and set of conditions. The user questions why the interpretation of (∀x)[Bx ⊃ (Lxx ⊃ Lxa)] is considered false, despite believing that (Lxx ⊃ Lxa) evaluates to true if Lxa is true. The false case presented, Ba ⊃ (Laa ⊃ Laa), is also debated regarding its truth value. Ultimately, the formula is confirmed to be true in the provided interpretation, indicating a misunderstanding of the conditions leading to the false interpretation. The conversation highlights the complexities of evaluating predicate logic semantics and validity.
joyofbitz
Messages
1
Reaction score
0
Hello,

Given the domain as:

D = {a,b}; ~Ba & Bb & Laa & ~Lab & Lba & ~Lbb

Why is the interpretation false? (∀x)[Bx ⊃ (Lxx ⊃ Lxa)]

I am having trouble understanding why that is the case because (Lxx ⊃ Lxa) evaluates to true in any case as long as Lxa is true in all cases, so the overall interpration should be true in all cases.

The false case that is given is: Ba ⊃ (Laa ⊃ Laa), but isn't this case true as well?
 
Physics news on Phys.org
You are right: the formula (∀x)[Bx ⊃ (Lxx ⊃ Lxa)] is true in the given interpretation.
 

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
View full post »

Similar threads

I Syntactic vs semantic logical consequence (entailment)
Replies
5
Views
2K
Predicate logic - true or false formulae
Replies
1
Views
2K
Logic: Logical Status of Statement Forms
Replies
7
Views
9K
Axiomatization of quantum mechanics and physics in general ?
5
Replies
210
Views
18K
Can someone explain what Bertrand Russell is saying on Aristotle's logic?
Replies
7
Views
9K
I Bayes again - how to interpret in vitro genotoxicity data
Replies
8
Views
2K
MHB Why can we show that an other polynomial is irreducible?
Replies
2
Views
2K
Solve FORTRAN 77 Programming Problem: Date Validation & Conversion
Replies
5
Views
3K
Is Mathematics a Belief System?
Replies
22
Views
4K
MHB What is Professor Leonard's advice for students taking calculus?
Replies
2
Views
11K

Hot Threads

Recent Insights

Back
Top