# Formal Languages as Models for Biological Growth

• P. Tautu
Conference paper
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 11)

## Abstract

A formal system is a mathematical structure S= (V, F, A, R), where
1. (i).

V is a set of symbols, called alphabet, V={a1 |i=0, 1, 2,...}. The set of all finite words (strings) composed with the elements of V is denoted by V*. Assuming the existence of an empty word Λ, the set V+ of nonempty words over V is then defined as V* -{Λ}.

2. (ii).

FV* is a set of formulae, a language over V.

3. (iii).

AF is a set of initial situations, called axioms.

4. (iv).

R is a set of rules of deduction (the primitives). A rule ρ∈R is defined as a subset of the Cartesian product Fn × F, where Fn is itself a Cartesian product F×...×F having n≥1 factors whose elements are the ordered n-tuples of formulae. Let F=(x1,..., xn) be an ordered n-tuple of formulae. If there exists a peR and a formula y such that Foy is obtained, then it is said that y is an immediate consequence of the premises (x1,..., xn). The formulae in F are the arguments of rule ρ. The set R of deduction rules defines the relation of immediate deducibility ( see Gross and Lentin, 1970).

Lentin

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