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16 lines
858 B
16 lines
858 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 = \Z \union \{+,-\} \union \{=, \neq, <, \leq,>,\geq\} $
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\item $\mathcal{A}$ defines the usual meaning to all symbols:
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\begin{itemize}
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\item Constant symbols are mapped to the corresponding value in $\Z$.
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\item $+$ is interpreted as the function $0+0 \rightarrow 0, 0+1 \rightarrow 1, \ldots$. $-$ follows it analogous interpretation.
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\item The predicate symbols are interpreted as their respective comparison operator.
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\end{itemize}
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\end{itemize}
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