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10 lines
696 B
10 lines
696 B
Variables in $\mathcal{T}_{LIA}$ are of integer sort ($\mathbb{Z}$).
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The functions of $\mathcal{T}_{LIA}$ are $+$ and $-$ and the predicates are
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$=, \neq, <, >, \leq,$ and $\geq$. The axioms withing $\mathcal{T}_{LIA}$
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define the meaning for these functions and predicates.
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Therefore, for the theory of Linear Integer Arithmetic $\mathcal{T}_{LIA}$ we have:
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\begin{itemize}
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\item $\Sigma = \{ ... ..., -3,-2,-1,0,1,2,3...,=,+,-,\neq, <, >, \leq,\geq\} $
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\item $\mathcal{A}$ defines the usual meaning to all symbols. (Constant number symbols are mapped to the corresponding value in $\mathbb{Z}$, $+$ is interpreted as the function $0+0\rightarrow 0$, $0+1\rightarrow 1$, etc.).
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\end{itemize}
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