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On Mon, Oct 8, 2012 at 3:05 PM, And Rosta <and.rosta@hidden.email> wrote: > Jorge Llambías, On 08/10/2012 16:54: > > > The point of the formal grammar is to select which concatenations of > > phonological words have meaning. > > No concatenations of phonological words have meaning directly. Let me try again: The function of the syntax part of the formal grammar is to separate the concatenations of word classes that have meaning from those that don't. To separate concatenations with meaning such as "LA CCA CCA" from others without meaning such as "LA LA LA", and also to determine that "LA CCA CCA CCA" consists of two sentences "(LA CCA CCA) (CCA)", and not anything else. > But to speak instead of the grammar: the syntactic component will generate > all possible sentential syntactic structures; the lexical and inflectional > components will map each sentential syntactic structure to a corresponding > phonological structure (concatenation of phonological words). I have trouble seeing how that is different from what I'm saying. > > [...] > >> Doing something similar for Core Xorban, for the non-binding tree, > >> we'd want something like: complement := argument-terminal | phrase > >> phrase := head complement* [where the number of complements varies > >> according to the identity of the Head]. > > > > What you would want then is: > > > > phrase := head-0 | head-1 complement | head-2 complement complement | > > head-3 complement complement complement | ... complement := > > argument-terminal | phrase > > > > which is either an infinite grammar or one with some fixed maximum > > of complements per head. > > > > That's basically what Xorban is, where (ignoring > > illocutionary-operators for now) head-0, head-3, head-4, etc are all > > empty, since Xorban only has head-1 and head-2. Head-1 is what we > > call unary operators, and head-2 are the binary operators, and > > "argument-terminal" are the atomic formulas. > > I think Xorban has to be the infinite one, on the assumption that there is > no upper limit to the adicity of predicates. The adicity of predicates does not enter into the syntax, because all predicates of any adicity in Xorban have exactly the same syntax. A finite number of rules can generate an infinite number of sentences, but if you want predicates of each adicity to have a different syntax, you need an infinite number of rules (although you could have a rule schema to generate the infinite rules). We don't need to mention the adicity of a predicate in order to formulate the binding rules, do we? > Simple-formulas are not atomic. > Rather, they must consist of a predicate with a number of argument-terminal > complements, these argument-terminals being argument-places; all 'terminal' > (or 'complementless') nodes other than interjections are argument-terminals. > The reason for this conclusion is that binders bind not a formula but an > argument-terminal; ergo argument-terminals are separate nodes. By "atomic formula" I mean a formula that doesn't have another formula inside. They do consist of a stem and a desinence, and the desinence determines the adicity of the predicate, so in that sense they are not atomic. > >> And for binding, we'd want: Binding := binder bindee* But I can't > >> see how to capture the fact that a binder is a head and its bindees > >> are contained within its complement. > > > > Why can't you just say that binders are (certain) heads (namely l-, > > r-, s- and x- in Xorban so far), > > and jek too Yes, kind of. "jek" does bind its variable (in a slightly weird way), but then creates a new variable with the same name so that the resulting formula still has that variable unbound. > > and the bindees are any variables in the binder's desinence that are > > free in the complements? > > Are you thinking that a single variable appears multiple times in the > tree, expressed phonologically at each place it appears, and always with a > phonological form of the same type? If so, then binders would have three > complements, one of the complements being the variable, and predicates' > complements would be variables. I guess by "free in the complement" you must > mean "not bound by a binder that is within the complement" Exactly. >(for otherwise it > makes no sense to say that the bindee is free in the complement! The bindee > is by definition bound!) It starts free in the complement, and then it is bound by the binder, yes, so that it is bound in the resulting formula, the one containing the binder. > I'd been thinking that there were no variables in syntax and that instead > a binding relation between binder and argument-terminal is expressed > inflectionally. I think my version is simpler and more syntactically > orthodox. I'm not sure I see the distinction. > But anyway, to answer your question: your reformulation doesn't get us > away from having to state the basic fact that bindees occur within the > complement of their binder. Is that missing from my formulation? Yes, I'm taking that as a given. > To be clear: the syntactic rules of core Xorban are extremely simple; it's > just that BNF is not suited to stating them. I don't know if the syntactic > rules of termtree-augmented Xorban are equally simple, because I haven't yet > had time to sit down and work out what they are. They are still quite simple, and they are meant to be straightforwardly reducible to core Xorban. co ma'a xrxe .