Access the full text.
Sign up today, get DeepDyve free for 14 days.
(1972)
Building in equational theories
H. Bürckert (1994)
A Resolution Principle for Constrained LogicsArtif. Intell., 66
Alan Frisch, R. Scherl (1991)
A Constraint Logic Approach to Modal Deduction
Alan Frisch (1989)
A General Framework for Sorted Deduction: Fundamental Results on Hybrid Reasoning
G. Robinson, L. Wos (1983)
Paramodulation and Theorem-Proving in First-Order Theories with Equality
(1973)
Symbolic Logic and Theorem Proving
Christoph Weidenbach (1992)
A New Sorted Logic
A. Cohn (1992)
A Many Sorted Logic with Possibly Empty Sorts
C. Beierle, Ulrich Hedtstück, Udo Pletat, P. Schmitt, J. Siekmann (1992)
An Order-Sorted Logic for Knowledge Representation SystemsArtif. Intell., 55
H. Aït-Kaci, R. Nasr (1986)
LOGIN: A Logic Programming Language with Built-In InheritanceJ. Log. Program., 3
M. Stickel (1985)
Automated deduction by theory resolutionJournal of Automated Reasoning, 1
A. Laux (1995)
Constraints and modalities in terminological knowledge representation systems
A.M. Frisch, R.B. Scherl (1991)
Principles of Knowledge Representation and Reasoning: Proceedings of the 2nd International Conference
H. Bürckert (1991)
A Resolution Principle for a Logic with Restricted Quantifiers, 568
H. Bürckert, B. Hollunder, W. Nutt, J. Siekmann (1990)
Concept Logics
Arnold Oberschelp (1962)
Untersuchungen zur mehrsortigen QuantorenlogikMathematische Annalen, 145
A. Schmidt (1938)
Über deduktive Theorien mit mehreren Sorten von GrunddingenMathematische Annalen, 115
Christoph Walther (1988)
Many-sorted unificationJ. ACM, 35
J. Jaffar, J. Lassez (1987)
Constraint logic programming
G. Smolka (1988)
A feature logic with subsorts
M. Genesereth, N. Nilsson (1987)
Logical foundations of artificial intelligence
(1988)
Definite relations over constraint languages, LILOG Report
Alan Frisch (1991)
The Substitutional Framework for Sorted Deduction: Fundamental Results on Hybrid ReasoningArtif. Intell., 49
M. Schmidt-Schauβ (1989)
Computational Aspects of an Order-Sorted Logic with Term Declarations
C. Weidenbach, H.-J. Ohlbach (1990)
Proceedings of the 9th European Conference on Artificial Intelligence
A. Colmerauer (1984)
Equations and Inequations on Finite and Infinite Trees
(1988)
Ein Schema far constraint-basierte relationale Wissensbaseu
(1990)
Keisler, Model Theol
H. Aït-Kaci (1986)
An Algebraic Semantics Approach to the Effective Resolution of Type EquationsTheor. Comput. Sci., 45
J. Robinson (1965)
A Machine-Oriented Logic Based on the Resolution PrincipleJ. ACM, 12
A. Schmidt (1951)
Die Zulässigkeit der Behandlung mehrsortiger Theorien mittels der üblichen einsortigen PrädikatenlogikMathematische Annalen, 123
F. Donini, M. Lenzerini, D. Nardi, Andrea Schaerf (1991)
A hybrid system integrating Datalog and concept languages
Christoph Weidenbach (1993)
Extending the Resolution Method with Sorts
R. Brachman, James Schmolze (1985)
An Overview of the KL-ONE Knowledge Representation SystemCogn. Sci., 9
Christoph Weidenbach, Hans Ohlbach (1990)
A Resolution Calculus with Dynamic Sort Structures and Partial Functions
(1930)
Recherches sur la th6orie de la d6monstration
Christoph Walther (1982)
A Many-Sorted Calculus Based on Resolution and Paramodulation
M. Höhfeld, G. Smolka (1988)
Definite relations over constraint languages
H. Bürckert, B. Hollunder, A. Laux (1994)
Concept Logics with Function Symbols
Alan Frisch, R. Scherl (1991)
A General Framework for Modal Deduction
Quantification in first-order logic always involves all elements of the universe. However, it is often more natural to just quantify over those elements of the universe which satisfy a certain condition. Constrained logics therefore provide restricted quantifiers ∀X:R F and ∃X:R F whereX is a set of variables, and which can be read as “F holds for all elements satisfying the restrictionR” and “F holds if there exists an element which satisfiesR”. In order to test satisfiability of a set of such formulas by means of an appropriately extended resolution principle, one needs a procedure which transforms them into a set of clauses with constraints. Such a procedure essentially differs from the classical transformation of first-oder formulas into a set of clauses, in particular since quantification over the empty set may occur and since the needed Skolemization procedure has to take the restrictions of restricted quantifiers into account. In the first part of this article we present a procedure that transforms formulas with restricted quantifiers into a set of clauses with constraints while preserving satisfiability. The thus obtained clauses are of the formC ‖R whereC is an ordinary clause andR is a restriction, and can be read as “C holds ifR holds”. These clauses can now be tested on unsatisfiability via the existingconstrained resolution principle. In the second part we generalize the constrained resolution principle in such a way that it allows for further optimization, and we introduce a combination of unification and constraint solving that can be employed to instantiate this kind of optimization.
Annals of Mathematics and Artificial Intelligence – Springer Journals
Published: Aug 13, 2005
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.