"Law is also formal languages using logics"
In theory yes, but contracts are not math and even though the consequences of disputes are costly, there is enough subjectivity within legal language that arbitration and interpretation by third parities is often required. i.e., two parties can have differing opinions on the meaning of the language and there can be enough uncertainty that costly proceedings are justified. (I'm talking specifically about civil rather than criminal law, and excluding cases where an interpretation of evidence is required)
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