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Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation
 Journal of Automated Reasoning
, 2000
"... . Minimal Herbrand models of sets of firstorder clauses are useful in several areas of computer science, e.g. automated theorem proving, program verification, logic programming, databases, and artificial intelligence. In most cases, the conventional model generation algorithms are inappropriate bec ..."
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. Minimal Herbrand models of sets of firstorder clauses are useful in several areas of computer science, e.g. automated theorem proving, program verification, logic programming, databases, and artificial intelligence. In most cases, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes an approach for generating the minimal Herbrand models of sets of firstorder clauses. The approach builds upon positive unit hyperresolution (PUHR) tableaux, that are in general smaller than conventional tableaux. PUHR tableaux formalize the approach initially introduced with the theorem prover SATCHMO. Two minimal model generation procedures are described. The first one expands PUHR tableaux depthfirst relying on a complement splitting expansion rule and on a form of backtracking involving constraints. A Prolog implementation, named MMSATCHMO, of this procedure is given and its performance on ben...
Positive Unit HyperResolution Tableaux for Minimal Model Generation
, 1997
"... Minimal Herbrand models for clausal theories are useful in several areas of computer science, e.g. automated theorem proving, program verification, logic programming, databases, and artificial intelligence. In most cases, the conventional model generation algorithms are inappropriate because they ge ..."
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Minimal Herbrand models for clausal theories are useful in several areas of computer science, e.g. automated theorem proving, program verification, logic programming, databases, and artificial intelligence. In most cases, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes a novel approach for generating the minimal Herbrand models of sets of clauses. The approach builds upon positive unit hyperresolution (PUHR) tableaux, that are in general smaller than conventional tableaux. PUHR tableaux formalize the approach initially introduced with the theorem prover SATCHMO. Two minimal model generation procedures are described. The first one expands PUHR tableaux depthfirst relying on a complement splitting expansion rule and on a form of backtracking involving constraints. A Prolog implementation, named MMSATCHMO, of this procedure is described. The second minimal model generation pr...
Optimization and Relaxation in Logic Languages
 Department of Computer Science, SUNYBuffalo
, 1997
"... Acknowledgements I wish to thank: 1. my advisor, Bharat Jayaraman, to whom this dissertation owes its existence in an uncountable number of ways, 2. Surya Mantha of Xerox Corporation, for input at various crucial stages, 3. Xerox Corporation, for generously providing funds that supported most of thi ..."
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Acknowledgements I wish to thank: 1. my advisor, Bharat Jayaraman, to whom this dissertation owes its existence in an uncountable number of ways, 2. Surya Mantha of Xerox Corporation, for input at various crucial stages, 3. Xerox Corporation, for generously providing funds that supported most of this work, 4. the rest of my committee, namely, Prof. Alan L. Selman and Prof. Kenneth W. Regan, for their interest in my welfare, 5. the secretaries in the department of computer science, for, among other things, shielding me from administrivial vagaries of the University, 6. my friends, for believing in, supporting, and encouraging me through thick andthin. I shall refrain from enumerating names here for fear of making the list longer than the rest of my dissertation.
Learning Effective And Robust Knowledge For Semantic Query Optimization
, 1997
"... xi 1 Introduction 1 1.1 Semantic Query Optimization : : : : : : : : : : : : : : : : : : : : : : 3 1.2 High Utility Semantic Knowledge for SQO : : : : : : : : : : : : : : : 6 1.3 Learning Effective and Robust Rules : : : : : : : : : : : : : : : : : : 8 1.4 Closely Related Work : : : : : : : : : : : ..."
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xi 1 Introduction 1 1.1 Semantic Query Optimization : : : : : : : : : : : : : : : : : : : : : : 3 1.2 High Utility Semantic Knowledge for SQO : : : : : : : : : : : : : : : 6 1.3 Learning Effective and Robust Rules : : : : : : : : : : : : : : : : : : 8 1.4 Closely Related Work : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 1.5 Summary of Contributions : : : : : : : : : : : : : : : : : : : : : : : : 12 1.6 Organization of the Dissertation : : : : : : : : : : : : : : : : : : : : : 13 2 Robustness of Knowledge 15 2.1 Consistency of Rules and Database Changes : : : : : : : : : : : : : : 15 2.2 Definitions of Robustness : : : : : : : : : : : : : : : : : : : : : : : : : 18 2.3 Estimating Robustness : : : : : : : : : : : : : : : : : : : : : : : : : : 19 2.4 Templates for Estimating Robustness : : : : : : : : : : : : : : : : : : 26 2.5 Empirical Demonstration : : : : : : : : : : : : : : : : : : : : : : : : : 27 2.6 Related Uncertainty Measures : : : : : : : : : : : : : : : : : : : ...
Preference Logic Programming: Optimization as Inference
, 1994
"... Preference Logic Programming (PLP) is an extension of Constraint Logic Programming (CLP) for declaratively specifying optimization problems. In the PLP framework, the definite clauses of a CLP program are augmented by two new kinds of clauses: optimization clauses and arbiter clauses. Optimization ..."
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Preference Logic Programming (PLP) is an extension of Constraint Logic Programming (CLP) for declaratively specifying optimization problems. In the PLP framework, the definite clauses of a CLP program are augmented by two new kinds of clauses: optimization clauses and arbiter clauses. Optimization clauses specify which predicates are to be optimized and arbiter clauses specify the criteria to be used for optimization. Together, these three kinds of clauses form a preferential theory, for which a possible worlds semantics was first given by Mantha et al. This paper shows how modal concepts can be used to capture the notion of optimization: Essentially, each world in the possibleworlds semantics for a preference logic program is a model of the program, and an ordering over these worlds is enforced by the arbiter clauses in the program. We introduce the notion of preferential consequence as truth in the optimal worlds. We propose an operational semantics that is an extension of SLD deri...