Definition: Axioms

Let \(L\subseteq (\Sigma^*,\cdot) \) be a formal language with strings $s\in L$ formed according to a syntax and let inside a domain of discourse $U,$ a semantics $I(U,L)$ and $[[]]_I$ be given.

Axioms of $L$ are a non-emtpy, finite number of interpretable strings $a_1, \ldots, a_n\in L$ such that $$[[a_i]]_I=1,\quad i=1,\ldots,n.$$

Less formally, axioms are selected strings in the formal language $L$, which can be interpreted as "true" statements about $U.$

Chapters: 1 2
Definitions: 3 4

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