Talk:Predicate functor logic

Sundry comments
A problem with expositing PFL is that Quine kept changing the notation until the 1982 final ed. of Methods of Logic. Kuhn (1983) and Bacon (1985) use notations that diverge from any that Quine employed. The primitives of Kuhn are Major and minor Inversion, and not Permutation. The alethic part of Bacon is the conditional and negation. Bacon has no primitive functor corresponding to Cropping'.

I would welcome additions to this article by anyone who feels comfortable with Bacon (1985). Mind you, that article is mostly in the Fitch natural deduction framework, and Wikipedia is weak on natural deduction, perhaps because it is now out of fashion. Has anyone written about PFL since Bacon (1985)?

Anybody care to comment about how PFL fits into the universal algebra family? Is it a Boolean algebra with monadic operators? If not, is it still a variety?Palnot (talk) 06:18, 21 January 2008 (UTC)

Interpretation of formulae
After reading this article, I'm still missing some basic pieces of information needed to make sense of PFL. I have the strong impression that the manner in which variables are eliminated is somewhat akin to what is done in stack-based programming languages such as Forth and PostScript — the S functor is looking very much like PS dup, the inv functor looking very much like PS exch, etc. — but I'm not sure how the formulae are supposed to be read.

What would be helpful is if this article could contain a section about interpretation of PFL formulae: how would it explicitly be defined that a formula is satisfied? 81.170.129.141 (talk) 08:54, 17 October 2012 (UTC)

Curry paradox is not specific to combinatory logic?
The article currently says "in 1959, combinatory logic was commonly deemed a failure for the following reasons:....Curry also discovered the Curry paradox, peculiar to combinatory logic...";

But https://en.wikipedia.org/wiki/Curry's_paradox#Lambda_calculus says that the Curry paradox is not "peculiar to combinatory logic" but in fact also applies to Lambda calculus, a PFL competitor. Should the reference to the Curry paradox be removed from this article? Bayle Shanks (talk) 19:17, 22 January 2016 (UTC)

Possible mistake in identity defn?
The definition given for the identity predicate functor is:


 * $$ IFx_1x_2...x_n \leftrightarrow Fx_1x_1...x_n \leftrightarrow Fx_2x_2...x_n.$$

I don't know PFL and haven't read the paper but this definition is surprising to me. Are you sure it isn't supposed to be:


 * $$ IFx_1x_2...x_n \leftrightarrow (Fx_1...x_n \leftrightarrow Fx_2...x_n).$$

The proposed definition i gave differs in that, first, in my proposal, the arity of F one less than the arity of IF, and second, in my proposal, the added parentheses show that IF is true whenever F is unchanged by replacing x_1 by x_2 or vice versa in the first argument.

Bayle Shanks (talk) 17:35, 23 January 2016 (UTC)