![]() ![]() ![]() ![]() We study dependency quantified Boolean formulas (DQBF), an extension of QBF in which dependencies of existential variables are listed explicitly rather than being implicit in the order of quantifiers. We note that NEXPTIMEcomplete problems are provably intractable, while no such proofs for problems in the Polynomial or Boolean Hierarchies are known (Papadimitriou 1994). 2004), and other problems that are central to knowledge representation and reasoning. 2013), consistency checking for certain description logics (Tobies 1999 Tobies 2001 Lutz 2001), checking the existence of secure plans (Eiter et al. As one of the canonical NEXPTIME-complete problems, DQBF can be used to succinctly encode problems for which no efficient encodings into QBF are likely to exist, such as synthesis of safe controllers (Bloem, Könighofer, and Seidl 2014), distributed synthesis for specifications in linear temporal logic (Chatterjee et al. The price of this additional syntactic tool is the NEXPTIMEcompleteness of DQBF evaluation (Peterson, Reif, and Azhar 2001), and as such DQBF evaluation is believed to be significantly more difficult than SAT and QBF evaluation, which are NP-and PSPACE-complete, respectively. Under consideration for acceptance in TPLP. On the practical side, we present a translation-based QASP solver that converts quantified logic programs into QBFs and then executes a QBF solver, and we evaluate experimentally the approach on conformant and conditional planning benchmarks. ![]() We define the language of quantified logic programs and use it to represent the solutions to different variants of conformant and conditional planning. For solving planning problems, we use Quantified Answer Set Programming (QASP), an extension of ASP with existential and universal quantifiers over atoms that is analogous to Quantified Boolean Formulas (QBFs). We represent planning problems using a simple formalism where logic programs describe the transition function between states, the initial states and the goal states. More precisely, we consider the problems of conformant and conditional planning with sensing actions and assumptions. We present a general approach to planning with incomplete information in Answer Set Programming (ASP). ![]()
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