Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Decision Procedure for Herbrand Formulae without Skolemization   This paper describes a decision procedure for disjunctions of conjunctions of
anti-prenex normal forms of pure first-order logic (FOLDNFs) that do not
contain $\vee$ within the scope of quantifiers. The disjuncts of these FOLDNFs
are equivalent to prenex normal forms whose quantifier-free parts are
conjunctions of atomic and negated atomic formulae (= Herbrand formulae). In
contrast to the usual algorithms for Herbrand formulae, neither skolemization
nor unification algorithms with function symbols are applied. Instead, a
procedure is described that rests on nothing but equivalence transformations
within pure first-order logic (FOL). This procedure involves the application of
a calculus for negative normal forms (the NNF-calculus) with $A \dashv\vdash A
\wedge A$ (= $\wedge$I) as the sole rule that increases the complexity of given
FOLDNFs. The described algorithm illustrates how, in the case of Herbrand
formulae, decision problems can be solved through a systematic search for
proofs that reduce the number of applications of the rule $\wedge$I to a
minimum in the NNF-calculus. In the case of Herbrand formulae, it is even
possible to entirely abstain from applying $\wedge$I. Finally, it is shown how
the described procedure can be used within an optimized general search for
proofs of contradiction and what kind of questions arise for a
$\wedge$I-minimal proof strategy in the case of a general search for proofs of
contradiction.

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The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg