Foundations of logic programming
Foundations of logic programming
A theory of diagnosis from first principles
Artificial Intelligence
Model minimization—an alternative to circumscription
Journal of Automated Reasoning
Formal methods in artificial intelligence
Formal methods in artificial intelligence
Explanation and prediction: an architecture for default and abductive reasoning
Computational Intelligence
First-order logic and automated theorem proving
First-order logic and automated theorem proving
A fixpoint semantics for disjunctive logic programs
Journal of Logic Programming
Intensional updates: abduction via deduction
Logic programming
Foundations of disjunctive logic programming
Foundations of disjunctive logic programming
Selected papers from the third annual conference on Meik US 92
On the duality of abduction and model generation in a framework for model generation with equality
FGCS'921 Selected papers of the conference on Fifth generation computer systems
Computing circumscriptive databases, I: theory and algorithms
Information and Computation
The resolution calculus
A rational and efficient algorithm for view deletion in databases
ILPS '97 Proceedings of the 1997 international symposium on Logic programming
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic Logic: Context-Dependent Reasoning
On the semantics of updates in databases
PODS '83 Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems
Automated Deduction Techniques for Classification in Description Logic Systems
Journal of Automated Reasoning
Satchmo - The Compiling and Functional Variants
Journal of Automated Reasoning
Computation of Stable Models and Its Integration with Logical Query Processing
IEEE Transactions on Knowledge and Data Engineering
Checking Consistency of Database Constraints: a Logical Basis
VLDB '86 Proceedings of the 12th International Conference on Very Large Data Bases
JELIA '96 Proceedings of the European Workshop on Logics in Artificial Intelligence
Generalized Query Answering in Disjunctive Deductive Databases: Procedural and Non-Monotonic Aspects
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
Minimal Model Generation with Positive Unit Hyper-Resolution Tableaux
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
A Tableau Calculus for Minimal Model Reasoning
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
Simplifying and Generalizing Formulae in Tableaux. Pruning the Search Space and Building Models
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Tableaux for Diagnosis Applications
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
MGTP: A Model Generation Theorem Prover - Its Advanced Features and Applications
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Generating small Models of First Order Axioms
GWAI '81 Proceedings of the German Workshop on Artificial Intelligence
A Hyperresolution-Based Proof Procedure and its Implementation in Prolog
GWAI '87 Proceedings of the 11th German Workshop on Artificial Intelligence
Model Generation with Existentially Quantified Variables and Constraints
ALP '97-HOA '97 Proceedings of the 6th International Joint Conference on Algebraic and Logic Programming
Proving Finite Satisfiability of Deductive Databases
CSL '87 Proceedings of the 1st Workshop on Computer Science Logic
Using Resolution for Deciding Solvable Classes and Building Finite Models
Baltic Computer Science, Selected Papers
SATCHMO: A Theorem Prover Implemented in Prolog
Proceedings of the 9th International Conference on Automated Deduction
An Improved Method for Adding Equality to Free Variable Semantic Tableaux
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Embedding Negation as Failure into a Model Generation Theorem Prover
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Efficient Model Generation through Compilation
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Non-Horn Magic Sets to Incorporate Top-down Inference into Bottom-up Theorem Proving
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
KI '97 Proceedings of the 21st Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Semantics for disjunctive logic programs
Semantics for disjunctive logic programs
SEM: a system for enumerating models
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Duality for Goal-Driven Query Processing in Disjunctive Deductive Databases
Journal of Automated Reasoning
I-SATCHMO: An Improvement of SATCHMO
Journal of Automated Reasoning
Ordered Semantic Hyper Tableaux
Journal of Automated Reasoning
Computational Space Efficiency and Minimal Model Generation for Guarded Formulae
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
R-UNSEARCHMO: A Refinement on UNSEARCHMO
PRICAI '02 Proceedings of the 7th Pacific Rim International Conference on Artificial Intelligence: Trends in Artificial Intelligence
A relevance restriction strategy for automated deduction
Artificial Intelligence
I-SATCHMORE: an improvement of A-SATCHMORE
Journal of Computer Science and Technology
SATCHMOREBID: SATCHMO(RE) with BIDirectional relevancy
New Generation Computing
Model building with ordered resolution: extracting models from saturated clause sets
Journal of Symbolic Computation - Special issue: First order theorem proving
Database Repairs and Analytic Tableaux
Annals of Mathematics and Artificial Intelligence
A Logical Framework for Querying and Repairing Inconsistent Databases
IEEE Transactions on Knowledge and Data Engineering
Eliminating redundant search space on backtracking for forward chaining theorem proving
Journal of Computer Science and Technology
Representing and Building Models for Decidable Subclasses of Equational Clausal Logic
Journal of Automated Reasoning
Completeness of hyper-resolution via the semantics of disjunctive logic programs
Information Processing Letters
An incremental algorithm for generating all minimal models
Artificial Intelligence
The axiomatic translation principle for modal logic
ACM Transactions on Computational Logic (TOCL)
Notions of Sameness by Default and their Application to Anaphora, Vagueness, and Uncertain Reasoning
Journal of Logic, Language and Information
An Improvement of Herbrand's theorem and its application to model generation theorem proving
Journal of Computer Science and Technology
UNSEARCHMO: eliminating redundant search space on backtracking for forward chaining theorem proving
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
An incremental algorithm for generating all minimal models
Artificial Intelligence
Tableaux for Projection Computation and Knowledge Compilation
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Completeness of hyper-resolution via the semantics of disjunctive logic programs
Information Processing Letters
Anaphora resolution as equality by default
DAARC'07 Proceedings of the 6th discourse anaphora and anaphor resolution conference on Anaphora: analysis, algorithms and applications
A Tableau Calculus for Minimal Modal Model Generation
Electronic Notes in Theoretical Computer Science (ENTCS)
Blocking and other enhancements for bottom-up model generation methods
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
First-Order reasoning for attempto controlled english
CNL'10 Proceedings of the Second international conference on Controlled Natural Language
Aluminum: principled scenario exploration through minimality
Proceedings of the 2013 International Conference on Software Engineering
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Minimal Herbrand models of sets of first-order clauses are useful in several areas of computer science, for example, 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 first-order clauses. The approach builds upon ipositive unit hyperresolution (iPUHR) itableaux, 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 depth-first relying on a icomplement splitting expansion rule and on a form of backtracking involving constraints. A Prolog implementation, named MM-SATCHMO, of this procedure is given, and its performance on benchmark suites is reported. The second minimal model generation procedure performs a breadth-first, constrained expansion of PUHR (complement) tableaux. Both procedures are optimal in the sense that each minimal model is constructed only once, and the construction of nonminimal models is interrupted as soon as possible. They are complete in the following sense: The depth-first minimal model generation procedure computes all minimal Herbrand models of the considered clauses provided these models are all finite. The breadth-first minimal model generation procedure computes all finite minimal Herbrand models of the set of clauses under consideration. The proposed procedures are compared with related work in terms of both principles and performance on benchmark problems.