This introduction presents the main motivations for the development of Description Logics (DLs) as a formalism for representing knowledge, as well as some important basic notions underlying all systems that have been created in the DL tradition. In addition, we provide the reader with an overview of the entire book and some guidelines for reading it. We first address the relationship between Description Logics and earlier semantic network and frame systems, which represent the original heritage of the field. We delve into some of the key problems encountered with the older efforts. Subsequently, we introduce the basic features of DL languages and related reasoning techniques. DL languages are then viewed as the core of knowledge representation systems, considering both the structure of a DL knowledge base and its associated reasoning services. The development of some implemented knowledge representation systems based on Description Logics and the first applications built with such systems are then reviewed. Finally, we address the relationship of Description Logics to other fields of Computer Science.We also discuss some extensions of the basic representation language machinery; these include features proposed for incorporation in the formalism that originally arose in implemented systems, and features proposed to cope with the needs of certain application domains.

https://assets.cambridge.org/97805218/76254/frontmatter/9780521876254_frontmatter.pdf

The Description Logic Handbook

'Satisfiability (SAT) related topics have attracted researchers from various disciplines: logic, applied areas such as planning, scheduling, operations research and combinatorial optimization, but also theoretical issues on the theme of complexity and much more, they all are connected through SAT. My personal interest in SAT stems from actual solving: The increase in power of modern SAT solvers over the past 15 years has been phenomenal. It has become the key enabling technology in automated verification of both computer hardware and software' - Edmund M. Clarke (FORE Systems University Professor of Computer Science and Professor of Electrical and Computer Engineering at Carnegie Mellon University). 'Bounded Model Checking (BMC) of computer hardware is now probably the most widely used model checking technique. The counterexamples that it finds are just satisfying instances of a Boolean formula obtained by unwinding to some fixed depth a sequential circuit and its specification in linear temporal logic. Extending model checking to software verification is a much more difficult problem on the frontier of current research. One promising approach for languages like C with finite word-length integers is to use the same idea as in BMC but with a decision procedure for the theory of bit-vectors instead of SAT. All decision procedures for bit-vectors that I am familiar with ultimately make use of a fast SAT solver to handle complex formulas' - Edmund M. Clarke (FORE Systems University Professor of Computer Science and Professor of Electrical and Computer Engineering at Carnegie Mellon University). 'Decision procedures for more complicated theories, like linear real and integer arithmetic, are also used in program verification. Most of them use powerful SAT solvers in an essential way. Clearly, efficient SAT solving is a key technology for 21st century computer science. I expect this collection of papers on all theoretical and practical aspects of SAT solving will be extremely useful to both students and researchers and will lead to many further advances in the field' - Edmund M. Clarke (FORE Systems University Professor of Computer Science and Professor of Electrical and Computer Engineering at Carnegie Mellon University).

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Handbook of Satisfiability

Benders decomposition uses a strategy of ``learning from one's mistakes.'' The aim of this paper is to extend this strategy to a much larger class of problems. The key is to generalize the linear programming dual used in the classical method to an ``inference dual.'' Solution of the inference dual takes the form of a logical deduction that yields Benders cuts. The dual is therefore very different from other generalized duals that have been proposed. The approach is illustrated by working out the details for propositional satisfiability and 0-1 programming problems. Computational tests are carried out for the latter, but the most promising contribution of logic-based Benders may be to provide a framework for combining optimization and constraint programming methods.

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Logic-Based Benders Decomposition

The paper studies new unit propagation based heuristics for Davis-Putnam-Loveland (DPL) procedure. These are the novel combinations of unit propagation and the usual "Maximum Occurrences in clauses of Minimum Size" heuristics. Based on the experimental evaluations of different alternatives a new simple unit propagation based heuristic is put forward. This compares favorably with the heuristics employed in the current state-of-the-art DPL implementations (C-SAT, Tableau, POSIT).

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Heuristics based on unit propagation for satisfiability problems

Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSpace. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the hight worst-case complexity of the problem, exhibit good performance with real-life problems.

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Practical reasoning for very expressive description logics

We describe an algorithm for the satisfiability problem of prepositional logic, which is significantly more efficient for this problem than is a general mixed-integer programming code. Our algorithm is a list processor using a tree-search method, and is based on Loveland's form of the algorithm of Davis and Putnam.

Solving propositional satisfiability problems

We show how the structure of proofs in a Horn clause knowledge base is completely described by certain of the extreme solutions to a suitable “dual” linear constraint set. The extreme points of this linear system are integer vectors, and give the count of the number of times that a given proposition is used in a proof of a “target” proposition. The “primal” to this dual provides the pointwise maximum vector which solves a set of dynamic programming recursions, and the latter recursions are derived from the Horn clause knowledge base. Variation in the facts or in the rules of the knowledge base corresponds to changes in only the criterion vector of the dual linear program. This linear programming approach to inference in expert systems also allows for the detection of “near proofs.” The latter are, by definition, proof structures which would become valid, if only exactly one more fact were known to be true. The first author, Robert G. Jeroslow, deceased August 31, 1988. INFORMS Journal on Computing, ISSN 1...

Dynamic Programming, Integral Polyhedra and Horn Clause Knowledge Base

An expert system applies the deduction rules in its knowledge base to a set of initial data to reach a conclusion. When the initial data are insufficient, the expert system may ask the user for additional information. This paper analyzes effectiveness and efficiency of question-asking strategies in expert systems with Horn clause knowledge bases. An effective strategy reaches a conclusion after asking as few questions as possible. An efficient strategy can be computed quickly. We prove that effective strategies are, unfortunately, not efficient. However, we present a somewhat less effective but very efficient strategy. It employs an algorithm which simultaneously performs deduction and question selection in log-linear time.

Question-asking strategies for Horn clause systems

Making inference efficient and intelligent is essential in developing expert systems. Inference in a rule-based expert system has intrinsic connection to quantitative approaches of optimization.
This thesis presents a linear programming representation for a subset of propositional logic, Horn clauses, which have simple forms but are widely used in expert systems. The inverse of a basis matrix of the associated linear program provides a comprehensive proof structure for inference. In particular, the basis matrix inverse tells how each assertion determines the others, and is itself determined by the others. This tabularized proof structure provides a convenient way of making inference transparent and flexible.
The linear program associated with a Horn clause system belongs to the class of Leontief flow problems. This thesis proves that the Leontief flow problem enjoys the same strong integrality property as the network flow problem. In particular, all extreme points of the polyhedron of a Leontief flow problem with integral data are integral.
A log-linear time algorithm is developed for a class of Leontief flow problems. This algorithm leads to an efficient procedure for selecting a question to ask the user when more information is needed.
For general propositional logic, a list processing procedure is developed and tested. This procedure combines the branch and bound method for integer programming with the symbolic inference process. Computational experiments show the improvement in inference efficiency.

Jinchang Wang

Papers

Solving propositional satisfiability problems

Dynamic Programming, Integral Polyhedra and Horn Clause Knowledge Base

Question-asking strategies for Horn clause systems

Rule-based expert systems and discrete optimization