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1d
comment Propositional Logic: Proof involving only the symbols $\{\rightarrow,F \}$
"D∨H∨Y" From your translation it's clear that you meant ((D∨H)∨Y). You didn't make this clear until you did the translation.
2d
comment Propositional Logic: Proof involving only the symbols $\{\rightarrow,F \}$
"I think they called Lyndon Axioms.." On p. 218 of J. A. Kalman's Automated Reasoning With Otter he indicates that these three axioms appear in a 1939 paper of Wajsberg (the axioms are in Polish notation, but this is not material here).
Apr
19
comment How to demystify the axioms of propositional logic?
I've tried to give an intuitive explanation (in my answer below) as to how CCNpNqCqp tells us everything else about C, and everything about N too.
Apr
19
answered How to demystify the axioms of propositional logic?
Apr
15
comment Can't get Logical Error
(∼p)∨q)∧(∼q)=(∼p) is not a law. Let p=0, and q=1. Then the left hand side evaluates to 0, but the right evaluates to 1. ((∼p)∨q)∧p=q is also not a law. Let q=1, and p=0.
Apr
15
comment If there are Predicates before Predicate Calculus, why is it called such?
Propositional calculus doesn't require a reference to "True" or "False".
Apr
11
comment Why is the negation of $A \Rightarrow B$ not $A \Rightarrow \lnot B$?
"A⇒B says that knowing A alone is enough to know B." Yikes! What if detachment isn't a rule of inference? How does knowing "A" end up as enough to know B in such a case? Also, even if we have detachment as a rule of inference, if Epq is true also, then it seems fair to say that knowing "p" alone is enough to know "q" also. However, Epq is definitely different from Cpq. Alright, I guess if detachment is a rule of inference, and it is not presumed that knowing B is enough to know A, then A $\rightarrow$ B says that knowing A is enough to know B.
Apr
11
comment Why is the negation of $A \Rightarrow B$ not $A \Rightarrow \lnot B$?
"The OP is obviously not using whatever kind of logic it is you mentioned." Syntactically speaking the logic he is using probably is the same as Lukasiewicz 3-valued logic in that the formation rules are the same. You've tried to explain things here semantically, but the issue here is purely syntactical in terms of formation rules (and in truth semantics doesn't always explain much ... not all tautologies have the same power). To get the negation of something, we first have to have the entire wff. Then we negate it. (A$\rightarrow$$\lnot$B) doesn't negate the conditional, it negates "B".
Apr
11
answered Why is the negation of $A \Rightarrow B$ not $A \Rightarrow \lnot B$?
Apr
11
comment Why is the negation of $A \Rightarrow B$ not $A \Rightarrow \lnot B$?
This doesn't explain things. Suppose that (1) is False, as say it is in Lukasiewicz 3-valued logic. It still holds that NCab and CaNb differ.
Apr
8
comment Is there a single logic symbol for “implies the negation of”?
And thus in reverse Polish notation, D == NC
Apr
7
comment Prove validity of argument
Have you tried assuming any of the subwffs of 1. or 2. seeing what you can derive, and then using conditional introduction?
Apr
6
comment Prove validity of argument
Statement 1. is a conjunction. What rules of inference can you use on a conjunction? Statement 2. is a disjunction. What rules of inference can you use on a disjunction? Also, can any sub-wff (sub well-formed formula) of 1. or 2. imply the conclusion by itself?
Apr
6
comment Prove validity of argument
What is your list of rules of inference?
Mar
25
comment Completness and Set of Result of One Set ?!?
@CarlMummert Also, are you sure about that? The normal deductive system just has tautologies in the object language. The set in question here has statements which evaluate to true and statements which evaluate to false.
Mar
25
comment Completness and Set of Result of One Set ?!?
@CarlMummert Well, the normal deductive system isn't complete according to the definition referenced by the author in the comments, because no contingent proposition is provable, nor is it's negation provable. We can pick any propositional variable as $\phi$ there If the variable was provable, then by assigning it a truth value of "false" we could prove a false statement, and classical logic would be unsound. Similarly, if the negation of the variable was provable, then by assigning the variable a truth value of "true" we could prove a false statement, and classical logic would be unsound.
Mar
25
comment Completness and Set of Result of One Set ?!?
@LoveMathContest If you can't prove anything, then the logical results of the set is empty. The empty set is enumerable since it corresponds to the ordinal 0.
Mar
25
revised Completness and Set of Result of One Set ?!?
added 43 characters in body
Mar
25
answered Completness and Set of Result of One Set ?!?
Mar
22
answered Can I use two inferred clauses to get the empty set?