Algorithmic language

Z Lem
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Language of algorithmic logic or, briefly, algorithmic language is an extension of the language of first-order logic. As usual, in order to define an algirithmic language one has to define two sets:

  • the alhabet [math]\mathcal{A}[/math], i.e. the set of atomic symbols,
  • the set of well formed expressions, a subset of [math]\mathcal{A}*[/math].

In fact, we shall consider a family of algorithmic languages that share some common structure. Any alphabet has these subsets:

  • the set [math]V[/math] of variables,
  • the set [math]\Phi[/math] of functors,
  • the set of [math]P[/math] predicates (i.e. of relational symbols),
  • the set of [math]L[/math] logical connectives
  • the set of [math]S[/math] program connectives
  • the set of auxiliary symbols, such as parentheses, semicolon, etc.