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BNF for FOL Sentences

  • S := <sentence>

  • <sentence> := <atomicsentence>
                          | <sentence> <connective> <sentence>
                          | <quantifier> <variable> ,... <sentence>
                          | ¬ <sentence>
                          | ( <sentence> )

  • <atomicsentence> := <predicate> ( <term> , ... )

  • <term> := <function> ( <term> , ... )
                  | <constant>
                  | <variable>

  • <connective> := ∧ | v | → | ↔

  • <quantifier> := ∃ | ∀

  • <constant> := “c" | “x1" | “john" | ...

  • <variable> := "a" | "x" | "s" | ...

  • <predicate> := “before" | “hasColor" | “raining" | ...

  • <function> := “mother" | “leftLegOf" | ...


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