Chapter 30. Reasoning with Quantified Boolean Formulas

2021 ◽  
Author(s):  
Enrico Giunchiglia ◽  
Paolo Marin ◽  
Massimo Narizzano
Keyword(s):  
Computer Aided Design ◽  
Automated Planning ◽  
Conjunctive Normal Form ◽  
Knowledge Representation And Reasoning ◽  
Research Issue ◽  
Important Research ◽  
Variable Elimination ◽  
Quantified Boolean Formulas ◽  
Boolean Formulas ◽  
Aided Design

The implementation of effective reasoning tools for deciding the satisfiability of Quantified Boolean Formulas(QBFs) is an important research issue in Artificial Intelligence and Computer Science. Indeed, QBF solvers have already been proposed for many reasoning tasks in knowledge representation and reasoning, in automated planning and in formal methods for computer aided design. Even more, since QBF reasoning is the prototypical PSPACE problem, the reduction of many other decision problems in PSPACE are readily available. For these reasons, in the last few years several decision procedures for QBFs have been proposed and implemented, mostly based either on search or on variable elimination, or on a combination of the two. In this chapter, after a brief recap of the basic terminology and notation about QBFs, we briefly review various applications of QBF reasoning that have been recently proposed, and then we focus on the description of the main approaches which are at the basis of currently available solvers for prenex QBFs in conjunctive normal form (CNF). Other approaches and extensions to non prenex, non CNF QBFs are briefly reviewed at the end of the chapter.

Fixed-Parameter Tractability of Dependency QBF with Structural Parameters

2020 ◽  
Author(s):  
Robert Ganian ◽  
Tomáš Peitl ◽  
Friedrich Slivovsky ◽  
Stefan Szeider
Keyword(s):  
Structural Parameters ◽  
Knowledge Representation And Reasoning ◽  
Fixed Parameter Tractability ◽  
Complete Problem ◽  
Quantified Boolean Formulas ◽  
Fixed Parameter ◽  
Boolean Formulas ◽  
Hard Problems ◽  
Evaluation Problem ◽  
Primal Graph

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. DQBF evaluation is a canonical NEXPTIME-complete problem, a complexity class containing many prominent problems that arise in Knowledge Representation and Reasoning. One approach for solving such hard problems is to identify and exploit structural properties captured by numerical parameters such that bounding these parameters gives rise to an efficient algorithm. This idea is captured by the notion of fixed-parameter tractability (FPT). We initiate the study of DQBF through the lens of fixed-parameter tractability and show that the evaluation problem becomes FPT under two natural parameterizations: the treewidth of the primal graph of the DQBF instance combined with a restriction on the interactions between the dependency sets, and also the treedepth of the primal graph augmented by edges representing dependency sets.

Computer-Aided Design of the Mine Hoist Spindle Based on Case-Based Reasoning

2011 ◽  
Vol 204-210 ◽  
pp. 1880-1883
Author(s):  
Shuang Chen ◽  
Jun Wang
Keyword(s):  
Artificial Intelligence ◽  
Computer Aided Design ◽  
Research Direction ◽  
Case Based Reasoning ◽  
Important Research ◽  
Computer Aided ◽  
Aided Design ◽  
Mine Hoist ◽  
Important Research Direction ◽  
Case Based

CBR(Case-based reasoning)is an important research direction of artificial intelligence field,which start a new way for it. The mine hoist spindle is the most critical equipment to hoisting equipment.It is the main part of the machine which relates to the upgrading of equipment life.With the platform of Visual C++,we analysised the design methods of the mine hoist spindle based on CBR in this experiment.It will combine computer-aided design technology with artificial intelligence factors.

scholarly journals Clause/Term Resolution and Learning in the Evaluation of Quantified Boolean Formulas

2006 ◽  
Vol 26 ◽  
pp. 371-416 ◽  
Author(s):  
E. Giunchiglia ◽  
M. Narizzano ◽  
A. Tacchella
Keyword(s):  
Normal Form ◽  
Automated Reasoning ◽  
Comparative Evaluation ◽  
State Of The Art ◽  
Conjunctive Normal Form ◽  
Disjunctive Normal Form ◽  
Propositional Satisfiability ◽  
Quantified Boolean Formulas ◽  
Boolean Formulas ◽  
Input Formula

Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as a set of clauses. Deduction starts by inferring new clauses by resolution, and goes on until the empty clause is generated or satisfiability of the set of clauses is proven, e.g., because no new clauses can be generated. In this paper, we restrict our attention to the problem of evaluating Quantified Boolean Formulas (QBFs). In this setting, the above outlined deduction process is known to be sound and complete if given a formula in CNF and if a form of resolution, called ``Q-resolution'', is used. We introduce Q-resolution on terms, to be used for formulas in disjunctive normal form. We show that the computation performed by most of the available procedures for QBFs --based on the Davis-Logemann-Loveland procedure (DLL) for propositional satisfiability-- corresponds to a tree in which Q-resolution on terms and clauses alternate. This poses the theoretical bases for the introduction of learning, corresponding to recording Q-resolution formulas associated with the nodes of the tree. We discuss the problems related to the introduction of learning in DLL based procedures, and present solutions extending state-of-the-art proposals coming from the literature on propositional satisfiability. Finally, we show that our DLL based solver extended with learning, performs significantly better on benchmarks used in the 2003 QBF solvers comparative evaluation.

CAD Of Anticorrosive Protection Of Steel Structures

2019 ◽  
pp. 18-23
Keyword(s):  
Protective Coating ◽  
Computer Aided Design ◽  
Steel Structures ◽  
Cost Effective ◽  
Operating Conditions ◽  
Computational Tool ◽  
Protection Method ◽  
Cost Effective Method ◽  
The Cost ◽  
Aided Design

The choice of cost-effective method of anticorrosive protection of steel structures is an urgent and time consuming task, considering the significant number of protection ways, differing from each other in the complex of technological, physical, chemical and economic characteristics. To reduce the complexity of solving this problem, the author proposes a computational tool that can be considered as a subsystem of computer-aided design and used at the stage of variant and detailed design of steel structures. As a criterion of the effectiveness of the anti-corrosion protection method, the cost of the protective coating during the service life is accepted. The analysis of existing methods of steel protection against corrosion is performed, the possibility of their use for the protection of the most common steel structures is established, as well as the estimated period of effective operation of the coating. The developed computational tool makes it possible to choose the best method of protection of steel structures against corrosion, taking into account the operating conditions of the protected structure and the possibility of using a protective coating.

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