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What is the practical importance of the propositional fragment?

  • A.It is the only logic for which sound inference exists
  • B.It requires no semantics to be given for its symbols
  • C.Bounded problems can be encoded and solved by very fast tools
  • D.Every first order problem reduces to it without any loss

Answer: C

Hardware verification, planning to a fixed horizon and scheduling are routinely encoded into propositional satisfiability and solved by tools handling millions of clauses. The reduction from first order requires bounding the domain and loses generality. Sound inference exists for richer logics, and semantics is required. That a weaker logic with extraordinary tools often beats a stronger one with weaker tools is a consideration expressiveness comparisons alone would miss entirely.

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