On QBF Proofs and Preprocessing

QBFs (quantified boolean formulas), which are a superset of propositional formulas, provide a canonical representation for PSPACE problems. To overcome the inherent complexity of QBF, significant effort has been invested in developing QBF solvers as well as the underlying proof systems. At the same time, formula preprocessing is crucial for the application of QBF solvers. This paper focuses on a missing link in currently-available technology: How to obtain a certificate (e.g. proof) for a formula that had been preprocessed before it was given to a solver? The paper targets a suite of commonly-used preprocessing techniques and shows how to reconstruct certificates for them. On the negative side, the paper discusses certain limitations of the currently-used proof systems in the light of preprocessing. The presented techniques were implemented and evaluated in the state-of-the-art QBF preprocessor bloqqer.Comment: LPAR 201

QRAT+: Generalizing QRAT by a More Powerful QBF Redundancy Property

The QRAT (quantified resolution asymmetric tautology) proof system simulates virtually all inference rules applied in state of the art quantified Boolean formula (QBF) reasoning tools. It consists of rules to rewrite a QBF by adding and deleting clauses and universal literals that have a certain redundancy property. To check for this redundancy property in QRAT, propositional unit propagation (UP) is applied to the quantifier free, i.e., propositional part of the QBF. We generalize the redundancy property in the QRAT system by QBF specific UP (QUP). QUP extends UP by the universal reduction operation to eliminate universal literals from clauses. We apply QUP to an abstraction of the QBF where certain universal quantifiers are converted into existential ones. This way, we obtain a generalization of QRAT we call QRAT+. The redundancy property in QRAT+ based on QUP is more powerful than the one in QRAT based on UP. We report on proof theoretical improvements and experimental results to illustrate the benefits of QRAT+ for QBF preprocessing.Comment: preprint of a paper to be published at IJCAR 2018, LNCS, Springer, including appendi

Incremental QBF Solving

We consider the problem of incrementally solving a sequence of quantified Boolean formulae (QBF). Incremental solving aims at using information learned from one formula in the process of solving the next formulae in the sequence. Based on a general overview of the problem and related challenges, we present an approach to incremental QBF solving which is application-independent and hence applicable to QBF encodings of arbitrary problems. We implemented this approach in our incremental search-based QBF solver DepQBF and report on implementation details. Experimental results illustrate the potential benefits of incremental solving in QBF-based workflows.Comment: revision (camera-ready, to appear in the proceedings of CP 2014, LNCS, Springer

Shortening QBF Proofs with Dependency Schemes

We provide the first proof complexity results for QBF dependency calculi. By showing that the reflexive resolution path dependency scheme admits exponentially shorter Q-resolution proofs on a known family of instances, we answer a question first posed by Slivovsky and Szeider in 2014 [30]. Further, we conceive a method of QBF solving in which dependency recomputation is utilised as a form of inprocessing. Formalising this notion, we introduce a new calculus in which a dependency scheme is applied dynamically. We demonstrate the further potential of this approach beyond that of the existing static system with an exponential separation

“Brave men” and “emotional women”: A literature review on gendered norms towards patients with pain

Abstract Background More women than men report chronic pain but despite the large body of research on sex differences there is a lack of knowledge on the influence of social and cultural gender. As gender norms can lead to gender bias in health care it is important to raise awareness about them. The purpose of this study was to illustrate gendered norms about men and women with chronic pain in scientific journals, and to analyze how societal norms are reproduced in health care. Methods A literature search of the databases PsycINFO, CINAHL and PubMed was conducted, January 2000 to April 2015, with the search term chronic pain combined with femininity, masculinity, gender bias, gender stereotypes and gender roles. A total of 77 articles met the inclusion criteria and were analyzed qualitatively. The integrative approach enabled a review of articles from both social and medical sciences, and to include qualitative and quantitative research. The material was sorted into theoretical categories and further coded into substantive categories. Results The included articles showed a variety of gendered norms about men’s and women’s experience and expression of pain, their identity, lifestyle and coping style. Women were described as emotional and hysterical, constantly dealing with mistrust from health care. Men were pictured as brave, stoic and struggling with their sense of masculinity. Prevailing societal norms are consolidated in health care, positioning the masculine man as the ideal patient. Conclusions Gender stereotypes are reproduced in healthcare, which can lead to gender bias in the treatment of patients with pain. The findings were used to develop a tool, “the pain cube”, aimed to improve health care providers’ consciousness about gendered norms. Key messages Men and women with chronic pain are depicted in a stereotypical way in scientific articles. Increased awareness about gendered norms can support health care professionals in providing equitable care. </jats:sec