Abstract
For a Quantified Boolean Formula \(({\it QBF })\) Φ=Qφ, an assignment is a function \(\cal M\) that maps each existentially quantified variable of Φ to a Boolean function, where φ is a propositional formula and Q is a linear ordering of quantifiers on the variables of Φ. An assignment \(\cal M\) is said to be proper, if for each existentially quantified variable y i , the associated Boolean function f i does not depend upon the universally quantified variables whose quantifiers in Q succeed the quantifier of y i . An assignment \(\cal M\) is said to be a model for Φ, if it is proper and the formula \(\phi^{\cal M}\) is a tautology, where \(\phi^{\cal M}\) is the formula obtained from φ by substituting f i for each existentially quantified variable y i . We show that any true quantified Horn formula has a Boolean model consisting of monotone monomials and constant functions only; conversely, if a QBF has such a model then it contains a clause–subformula in \({\it QHORN }\cap {\it SAT }\).
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Kleine Büning, H., Subramani, K., Zhao, X. (2004). On Boolean Models for Quantified Boolean Horn Formulas. In: Giunchiglia, E., Tacchella, A. (eds) Theory and Applications of Satisfiability Testing. SAT 2003. Lecture Notes in Computer Science, vol 2919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24605-3_8
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DOI: https://doi.org/10.1007/978-3-540-24605-3_8
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