Sentential form

ACS Symposium Series Ameriean Chemieal Soeiety Washington, DC, 1977. 

This is a chemical grammar, the productions corresponding to reactions. The language is the set of all 1-alkanols, 1-alkyImagnesium bromides and 1-bromoalkanes. 

Although the productions are not of all of the regular form X a or X aY it is easily rewritten to conform to this format. The language is thus a regular language and a finite state machine for recognizing members of the language is easily constructed. Note that a derivation of a sentence corresponds directly to its synthesis. Derivation of ethyl bromide proceeds as  

Theorem. The set of all wellformed acyclic structures comprises a deterministic context free language. 

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In theory of formal grammars, the word-order freedom usually means a certain level of robustness against permutations of sentential forms [15]. To simplify the formulae with permutation elements, a permutation symbol is introduced as follows. Let s = S1S2 Smi where every Si S (i 1,..., m ). Then define... 

Now if we consider further the relationship between derivation of a sentence and its synthesis, especially the relationship between the intermediate sentential forms and the precursor structures in the syntheses we are led to the following theorem. 

Geometry is also special in that most examples we wish to reason about consist of a few objects, with a limited number of relationships. Thus it is feasible to use a simpler sentential calculus form of logic which cannot reason with variables. 

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