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On Tue, Oct 2, 2012 at 8:29 PM, And Rosta <and.rosta@hidden.email> wrote: > Jorge Llambías, On 02/10/2012 23:22: > >>> > > For me it's something like this: "A binding operator removes any free > > occurrences of its variable from its complement formulas." > > I don't understand "removes". And what is "its variable"? By removes I mean removes the freedom of. The binders are lV, rV, sV and xV. V is what I take to be the variable of the binder. The way I understand binding, those four are the only binders we have in Xorban so far. >"Its variable" > is the variable it is linked to by syntactic binding. (And changing to "A > binding operator removes from its complement formula any free occurrences of > the variable it syntactically-binds" doesn't make sense -- if it binds them, > then they're not free.) They are free before being bound. In "sa mlta xkra", "a" is free in formulas "mlta" and "xkra", but it is bound in the formula "sa mlta xkra". This is pretty much my understanding of free and bound variables: http://en.wikipedia.org/wiki/Free_variables_and_bound_variables. Binding operators act on functions of the variable they bind. A special case of functions of a variable is the constant function, one that does not vary with a variable, and that corresponds to the case where a binding operator acts on something that does not depend on the variable being bound by the operator. > > I think binders always do the same to their complements: they bind > > any free occurrence of their variable. Anything else strikes me as > > more complicated. > > To me that is bordering on gibberish, so I'm fairly sure we're not > understanding each other. > > I can't work out what's at the root of our communication failure. Would it > help if you provided a list of the syntactic rules you think are needed? For binding? All binders appear in this form: F := Ba F1 F2 Formulas F1 and F2 typically will have "a" as a free variable. Formula F does not have "a" as a free variable, because what B does is bind that variable. (The meaning of the resulting F will depend on the choice of B, but in any case it won't have a free "a".) The special cases where F1 and/or F2 don't have a free "a" are just special cases. > I should also add that if there are terminological difficulties, I am > happy to be flexible about terminology. For example, if "syntactic binding" > is confusing because it's hard to keep it distinct from "semantic binding", > I'm happy to adopt a different term, such as, say, "govern" rather than > "bind". I'm sure our problem is terminological, because nothing of what I'm saying sounds remotely controversial to me. co ma'a xrxe