Abstract
The validity problem for full first-order logic is only semi-decidable. However, there are many interesting problems that, when expressed in clause normal form, have a finite Herbrand universe. They fall into a decidable subclass of first-order logic. Traditionally, such problems have been tackled using conventional first-order techniques. Some implementations, e.g. DCTP [SL01], are decision procedures for this class of problems. An alternative approach, justified by Herbrand’s theorem, is to generate the ground instances of such a problem and use a propositional decision system to determine the satisfiability of the resulting propositional problem. The applicability of the grounding approach has led to these problems being called “effectively propositional” (EPR) problems. The TPTP problem library [SS98] v2.4.1 contains 574 EPR problems. Many of these are group theory problems (101 problems) and CNF translations of formulae in propositional multi-modal logic (206 problems).
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Schulz, S., Sutcliffe, G. (2002). System Description: GrAnDe 1.0. In: Voronkov, A. (eds) Automated Deduction—CADE-18. CADE 2002. Lecture Notes in Computer Science(), vol 2392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45620-1_23
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DOI: https://doi.org/10.1007/3-540-45620-1_23
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