Talk:Propositional formula

message: These are treated as the same in the article, but only idempotency is actually discussed.  Contrast e.g., http://www.tpub.com/neets/book13/54h.htm Cerberus (talk) 02:34, 7 September 2011 (UTC)
thread_title:  Absorption vs. Idempotency 

message: Regarding the "Connective seniority (symbol rank)" section: https://en.wikipedia.org/wiki/Propositional_formula#Connective_seniority_(symbol_rank)
This section  appears to contradict (significantly) the book, "Foundations Of Computation" by Critchlow and Eck (2nd ed, 2011). Pg 3 of that book, which deals with the relative precedences (are precedences the same things as "ranks" / "seniorities" ?), states (but with my additional clarifications in square brackets):
"Parentheses can be used in compound expressions to indicate the order in which the operators are to be evaluated. In the absence of parentheses, the order of evaluation is determined by precedence rules. For the logical operators defined above [i.e., conjunction, disjunction and negation], the rules are that ¬ [i.e., negation] has higher precedence than ∧ [conjunction], and ∧ has precedence over ∨ [disjunction]. This means that in the absence of parentheses, any ¬ operators are evaluated first, followed by any ∧ operators, followed by any ∨ operators."
And then pg 5 adds more operators to the above, stating:
"When these operators [material conditional/implication, biconditional and exclusive or] are used in expressions, in the absence of parentheses to indicate order of evaluation, we use the following precedence rules: The exclusive or operator, ⊕, has the same precedence as ∨ [disjunction]. The [material] conditional operator,
→, has lower precedence than ∧, ∨, ¬, and ⊕, and is therefore evaluated after them. Finally, the biconditional operator, ↔, has the lowest precedence and is therefore evaluated last."
In summary, Critchlow and Eck (2nd ed, 2011) give the relative precedences of the logical operators, from highest to lowest, as follows:
    ¬  (negation)
    ∧  (conjunction)
    ∨  (disjunction), ⊕ (exclusive or)      (equal precedence)
    →  (material conditional)
    ↔  (biconditional)
Why does the article give SUCH different rankings?
86.175.18.7 (talk) 14:13, 5 October 2018 (UTC)
replies: text: To me, both rankings seem to be almost the same, except that they are presented in orders reverse to each other, (and that and/or are ranked differently). - Jochen Burghardt (talk) 16:42, 6 October 2018 (UTC)

text: Jochen, thanks, they do seem more similar as reverses of each other. But they still remain different, and when did "almost the same" become good enough in maths? Use of these different rankings will lead to a given propositional formula evaluating to true for one ranking and false for the other. In arithmetic algebra, we don't have expressions such as (2 * 3 + 4) having one value (6 + 4) in one ranking (or according to one author) and another value (2 * 7) in a different ranking (or according to some other author). So one ranking must surely be "wrong", or at least highly unconventional. (Or is logic just one of those areas in which different practitioners define things differently??) 86.175.18.7 (talk) 13:45, 7 October 2018 (UTC)
thread_title:  The section "Connective seniority (symbol rank)" appears to contradict (significantly) pgs 3 and 5 of the book, "Foundations Of Computation" by Critchlow and Eck (2nd ed, 2011) 

message: A propositional formula is a truth function with arguments propositional variables or propositional constants (simple propositions). Simple propositions/propositional constants have the same status from the point of view of truth values as the propositional variables. The second sentence, re the the truth values of all variables being given/known and determining an unique truth value, indicates this status. The (known) truth values of simple propositions as well as those of the proper propositional variables are replaced in the truth function/propositional formula giving the final truth value, similarly to numerical constants a, b being substituted in an (usual/numeric) algebraic function/formula/expression f(x, y) giving the final numerical value.--178.138.193.100 (talk) 20:53, 13 June 2021 (UTC)
replies: text: A propositional formula, like any expression, can be used to define a function. However, this requires to fix the parameters and their order. For example, f(x,y) = (x ∧ ¬y) is different from f(y,x) = (x ∧ ¬y), although the both use the same formula, viz. x ∧ ¬y. - Jochen Burghardt (talk) 09:31, 15 June 2021 (UTC)
thread_title:  Truth function 

message: Simple propositions like "It rains tomorrow/in the next hours." can have a variabile truth value, not known at the present moment. Thus simple propositions can also be propositional variables like p, q. They have the same notation, with small letters.--178.138.195.100 (talk) 21:18, 13 June 2021 (UTC)
thread_title:  Variable truth value of simple propositions/propositional constants 

message: The article mentions the so-called "engineering connectives", but without enough details. In what branches of engineering are they called engineering connectives?--178.138.193.100 (talk) 21:26, 13 June 2021 (UTC)
replies: text: There is lot of nonsense in the sections mentioning "engineering"; you probably spotted some of them. I guess "engineering connectives" is supposed to mean terminology for logical connectives used in digital electronics. - Jochen Burghardt (talk) 15:36, 15 June 2021 (UTC)
thread_title:  Engineering connectives 

message: Some of them them group AND before OR, others the other way round. And then one example goes from "a & a → b"  to "a & (a → b)" despite the ordering giving IMPLICATION a higher rank than AND. Manny123 (talk) 20:32, 7 December 2021 (UTC)
thread_title:  Examples in section "Connective seniority (symbol rank)" contradict each other and the given ordering