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  "body": "\n## Summary\n\nA well-formed formula, or simply formula, is a string of symbols built by the grammar of a formal language.\nIn first-order logic, formulas are built from atomic formulas with [[connectives|QS0XVAN9BG]] and quantifiers.\nFormulas are the objects that proofs manipulate and that [[structures|983GZBQYT4]] make true or false.\nOnly well-formed strings have a meaning, so the definition is the first step of every formal logic.\n\n## Explanations\n\n### L1 human\n\nNot every string of symbols makes sense: $\\forall x \\, (x \u003c y)$ does, but $\\forall \\land x \u003c$ does not.\nThe rules for formulas are like grammar rules for sentences.\nThey start with simple claims such as $x = y$ or $x \u003c y$, and allow you to combine claims with \"not\", \"and\", \"for all\" and so on.\nA formula with free variables, such as $x \u003c y$, is true or false only once values for $x$ and $y$ are given.\n",
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