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Issues of Decidability for Description Logics in the Framework of Resolution
 In Automated Deduction in Classical and NonClassical Logics
, 1998
"... . We describe two methods on the basis of which efficient resolution decision procedures can be developed for a range of description logics. The first method uses an ordering restriction and applies to the description logic ALB, which extends ALC with the top role, full role negation, role intersect ..."
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Cited by 40 (19 self)
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. We describe two methods on the basis of which efficient resolution decision procedures can be developed for a range of description logics. The first method uses an ordering restriction and applies to the description logic ALB, which extends ALC with the top role, full role negation, role intersection, role disjunction, role converse, domain restriction, range restriction, and role hierarchies. The second method is based solely on a selection restriction and applies to reducts of ALB without the top role and role negation. The latter method can be viewed as a polynomial simulation of familiar tableauxbased decision procedures. It can also be employed for automated model generation. 1 Introduction Since the work of Kallick [13] resolutionbased decision procedures for subclasses of firstorder logic have drawn continuous attention [5,7,12]. There are two research areas where decidability issues also play a prominent role: extended modal logics and description logics [6,9,14]. Althoug...
Modular proof systems for partial functions with Evans equality
 Information and Computation
, 2006
"... The paper presents a modular superposition calculus for the combination of firstorder theories involving both total and partial functions. The modularity of the calculus is a consequence of the fact that all the inferences are pure – only involving clauses over the alphabet of either one, but not bo ..."
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Cited by 24 (16 self)
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The paper presents a modular superposition calculus for the combination of firstorder theories involving both total and partial functions. The modularity of the calculus is a consequence of the fact that all the inferences are pure – only involving clauses over the alphabet of either one, but not both, of the theories – when refuting goals represented by sets of pure formulae. The calculus is shown to be complete provided that functions that are not in the intersection of the component signatures are declared as partial. This result also means that if the unsatisfiability of a goal modulo the combined theory does not depend on the totality of the functions in the extensions, the inconsistency will be effectively found. Moreover, we consider a constraint superposition calculus for the case of hierarchical theories and show that it has a related modularity property. Finally we identify cases where the partial models can always be made total so that modular superposition is also complete with respect to the standard (total function) semantics of the theories. 1
A ResolutionBased Decision Procedure for Extensions of K4
 ADVANCES IN MODAL LOGIC
, 1998
"... This paper presents a resolution decision procedure for transitive propositional modal logics. The procedure combines the relational translation method with an ordered chaining calculus designed to avoid unnecessary inferences with transitive relations. We show the logics K4, KD4 and S4 can be trans ..."
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Cited by 19 (8 self)
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This paper presents a resolution decision procedure for transitive propositional modal logics. The procedure combines the relational translation method with an ordered chaining calculus designed to avoid unnecessary inferences with transitive relations. We show the logics K4, KD4 and S4 can be transformed into a bounded class of wellstructured clauses closed under ordered resolution and negative chaining.
Computational modal logic
 Handbook of Modal Logic
, 2006
"... 2 Syntax, semantics, and reasoning problems of modal logics........................... 3 3 Translationbased methods........................................... 6 3.1 Local satisfiability in multi modal Kn................................... 6 3.2 Global satisfiability, nonlogical axioms, transitive ..."
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Cited by 19 (4 self)
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2 Syntax, semantics, and reasoning problems of modal logics........................... 3 3 Translationbased methods........................................... 6 3.1 Local satisfiability in multi modal Kn................................... 6 3.2 Global satisfiability, nonlogical axioms, transitive modalities, and K4n................. 20
Herbrand’s theorem for prenex Gödel logic and its consequences for theorem proving
 IN LOGIC FOR PROGRAMMING AND AUTOMATED REASONING LPAR’2001, 201–216. LNAI 2250
, 2001
"... Herbrand’s Theorem £¥ ¤ ¦ for, i.e., Gödel logic enriched by the projection § operator is proved. As a consequence we obtain a “chain normal form” and a translation of £ ¤ ¦ prenex into (order) clause logic, referring to the classical theory of dense total orders with endpoints. A chaining calc ..."
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Cited by 16 (11 self)
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Herbrand’s Theorem £¥ ¤ ¦ for, i.e., Gödel logic enriched by the projection § operator is proved. As a consequence we obtain a “chain normal form” and a translation of £ ¤ ¦ prenex into (order) clause logic, referring to the classical theory of dense total orders with endpoints. A chaining calculus provides a basis for efficient theorem proving.
On Automating the Calculus of Relations
 In: Proc. IJCAR. Vol. 5195. LNCS
, 2008
"... Abstract. Relation algebras provide abstract equational axioms for the calculus of binary relations. They name an established area of mathematics with various applications in computer science. We prove more than hundred theorems of relation algebras with offtheshelf automated theorem provers. This ..."
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Cited by 15 (3 self)
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Abstract. Relation algebras provide abstract equational axioms for the calculus of binary relations. They name an established area of mathematics with various applications in computer science. We prove more than hundred theorems of relation algebras with offtheshelf automated theorem provers. This yields a basic calculus from which more advance applications can be explored. Here, we present two examples from the formal methods literature. Our experiments not only further underline the feasibility of automated deduction in complex algebraic structures and provide theorem proving benchmarks, they also pave the way for lifting established formal methods such as B or Z to a new level of automation. 1
Deciding Expressive Description Logics in the Framework of Resolution
"... We present a decision procedure for the description logic SHIQ based on the basic superposition calculus, and show that it runs in exponential time for unary coding of numbers. To derive our algorithm, we extend basic superposition with a decomposition inference rule, which transforms conclusions of ..."
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We present a decision procedure for the description logic SHIQ based on the basic superposition calculus, and show that it runs in exponential time for unary coding of numbers. To derive our algorithm, we extend basic superposition with a decomposition inference rule, which transforms conclusions of certain inferences into equivalent, but simpler clauses. This rule can be used for general firstorder theorem proving with any resolutionbased calculus compatible with the standard notion of redundancy.
Automated theorem proving by resolution in nonclassical logics
 Annals of Mathematics and Artificial Intelligence
, 2007
"... This paper is an overview of a variety of results, all centered around a common theme, namely embedding of nonclassical logics into first order logic and resolution theorem proving. We present several classes of nonclassical logics, many of which are of great practical relevance in knowledge repre ..."
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Cited by 9 (6 self)
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This paper is an overview of a variety of results, all centered around a common theme, namely embedding of nonclassical logics into first order logic and resolution theorem proving. We present several classes of nonclassical logics, many of which are of great practical relevance in knowledge representation, which can be translated into tractable and relatively simple fragments of classical logic. In this context, we show that refinements of resolution can often be used successfully for automated theorem proving, and in many interesting cases yield optimal decision procedures. 1
Automated verification of refinement laws
 Annals of Mathematics and Artificial Intelligence, Special Issue on Firstorder Theorem Proving
, 2008
"... AMAI manuscript No. (will be inserted by the editor) ..."
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Cited by 8 (5 self)
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AMAI manuscript No. (will be inserted by the editor)