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Decidability of SHIQ with Complex Role Inclusion Axioms
- Artificial Intelligence
, 2003
"... Motivated by medical terminology applications, we investigate the decidability of the well known expressive DL, extended with role inclusion axioms (RIAs) of the form R P . We show that this extension is undecidable even when RIAs are restricted to the forms R#S R or S #R # but that decidability can ..."
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Cited by 76 (13 self)
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Motivated by medical terminology applications, we investigate the decidability of the well known expressive DL, extended with role inclusion axioms (RIAs) of the form R P . We show that this extension is undecidable even when RIAs are restricted to the forms R#S R or S #R # but that decidability can be regained by further restricting RIAs to be acyclic. We present a tableau algorithm for this DL and report on its implementation, which behaves well in practise and provides important additional functionality in a medical terminology application.
RIQ and SROIQ are harder than SHOIQ
- In Proc. KR’08
, 2008
"... Abstract. We identify the complexity of (finite model) reasoning in the DL SROIQ to be N2ExpTime-complete. We also prove that (finite model) reasoning in the DL SR—a fragment of SROIQ without nominals, number restrictions, and inverse roles—is 2ExpTime-hard. 1 From SHIQ to SROIQ In this paper we stu ..."
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Cited by 60 (6 self)
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Abstract. We identify the complexity of (finite model) reasoning in the DL SROIQ to be N2ExpTime-complete. We also prove that (finite model) reasoning in the DL SR—a fragment of SROIQ without nominals, number restrictions, and inverse roles—is 2ExpTime-hard. 1 From SHIQ to SROIQ In this paper we study the complexity of reasoning in the DL SROIQ—the logic chosen as a candidate for OWL 2. 1 SROIQ has been introduced in [1] as an extension of SRIQ, which itself was introduced previously in [2] as an extension of RIQ [3]. These papers present tableau-based procedures for the respective DLs and prove their soundness, completeness and termination. In contrast to sub-languages of SHOIQ whose computational complexities are currently well understood [4], almost nothing was known, up until now, about the complexity of SROIQ, SRIQ and RIQ except for the hardness results inherited from their sub-lanbuages: SROIQ is NExpTime-hard as an extension of SHOIQ, SRIQ and RIQ are ExpTime-hard as extensions of SHIQ. The
Deciding regular grammar logics with converse through first-order logic
- JOURNAL OF LOGIC, LANGUAGE AND INFORMATION
, 2005
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A Principle for Incorporating Axioms into the First-Order Translation of Modal Formulae
- Automated Deduction—CADE-19, volume 2741 of Lecture Notes in Artificial Intelligence
, 2003
"... In this paper we present a translation principle, called the axiomatic translation, for reducing propositional modal logics with background theories, including triangular properties such as transitivity, Euclideanness and functionality, to decidable logics. The goal of the axiomatic translation ..."
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Cited by 20 (7 self)
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In this paper we present a translation principle, called the axiomatic translation, for reducing propositional modal logics with background theories, including triangular properties such as transitivity, Euclideanness and functionality, to decidable logics. The goal of the axiomatic translation principle is to find simplified theories, which capture the inference problems in the original theory, but in a way that is more amenable to automation and easier to deal with by existing theorem provers. The principle of the axiomatic translation is conceptually very simple and can be largely automated. Soundness is automatic under reasonable assumptions, and termination of ordered resolution is easily achieved, but the non-trivial part of the approach is proving completeness.
Restricted Role-Value-Maps in a Description Logic with Existential Restrictions and Terminological Cycles
- In Proc. DL’03, http://CEUR-WS.org/Vol-81
, 2003
"... In a previous paper we have investigated subsumption in the presence of terminological cycles for the description logic which allows conjunctions, existential restrictions, and the top concept, and have shown that the subsumption problem remains polynomial for all three types of semantics usua ..."
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Cited by 12 (1 self)
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In a previous paper we have investigated subsumption in the presence of terminological cycles for the description logic which allows conjunctions, existential restrictions, and the top concept, and have shown that the subsumption problem remains polynomial for all three types of semantics usually considered for cyclic definitions in description logics.
Constructing finite least Kripke models for positive logic programs in serial regular grammar logics
- Logic Journal of the IGPL
"... A serial context-free grammar logic is a normal multimodal logic L characterized by the seriality axioms and a set of inclusion axioms of the form ✷tϕ → ✷s1... ✷skϕ. Such an inclusion axiom corresponds to the grammar rule t → s1... sk. Thus the inclusion axioms of L capture a context-free grammar G( ..."
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Cited by 10 (6 self)
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A serial context-free grammar logic is a normal multimodal logic L characterized by the seriality axioms and a set of inclusion axioms of the form ✷tϕ → ✷s1... ✷skϕ. Such an inclusion axiom corresponds to the grammar rule t → s1... sk. Thus the inclusion axioms of L capture a context-free grammar G(L). If for every modal index t, the set of words derivable from t using G(L) is a regular language, then L is a serial regular grammar logic. In this paper, we present an algorithm that, given a positive multimodal logic program P and a set of finite automata specifying a serial regular grammar logic L, constructs a finite least L-model of P. (A model M is less than or equal to model M ′ if for every positive formula ϕ, if M | = ϕ then M ′ | = ϕ.) A least L-model M of P has the property that for every positive formula ϕ, P | = ϕ iff M | = ϕ. The algorithm runs in exponential time and returns a model with size 2 O(n3). We give examples of P and L, for both of the case when L is fixed or P is fixed, such that every finite least L-model of P must have size 2 Ω(n). We also prove that if G is a context-free grammar and L is the serial grammar logic corresponding to G then there exists a finite least L-model of ✷sp iff the set of words derivable from s using G is a regular language. 1
Description logics for ontologies
- In Proceedings of the International Conference on Conceptual Structures (ICCS
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Analytic cut-free tableaux for regular modal logics of agent beliefs
- Proceedings of CLIMA VIII, vol. 5056 of LNAI
, 2008
"... Abstract. We present a sound and complete tableau calculus for a class BReg of extended regular modal logics which contains useful epistemic logics for reasoning about agent beliefs. Our calculus is cut-free and has the analytic superformula property so it gives a decision procedure. Applying sound ..."
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Cited by 8 (7 self)
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Abstract. We present a sound and complete tableau calculus for a class BReg of extended regular modal logics which contains useful epistemic logics for reasoning about agent beliefs. Our calculus is cut-free and has the analytic superformula property so it gives a decision procedure. Applying sound global caching to the calculus, we obtain the first optimal (EXPTime) tableau decision procedure for BReg. We demonstrate the usefulness of BReg logics and our tableau calculus using the wise men puzzle and its modified version, which requires axiom (5) for single agents. 1
An extension of complex role inclusion axioms in the description logic SROIQ
- In Proceedings of IJCAR
, 2010
"... Abstract. We propose an extension of the syntactic restriction for complex role inclusion axioms in the description logic SROIQ. Like the original restriction in SROIQ, our restrictions can be checked in polynomial time and they guarantee regularity for the sets of role chains implying roles, and th ..."
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Cited by 8 (0 self)
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Abstract. We propose an extension of the syntactic restriction for complex role inclusion axioms in the description logic SROIQ. Like the original restriction in SROIQ, our restrictions can be checked in polynomial time and they guarantee regularity for the sets of role chains implying roles, and thereby decidability for the main reasoning problems. But unlike the original restrictions, our syntactic restrictions can represent any regular compositional properties on roles. In par-ticular, many practically relevant complex role inclusion axioms, such as those describing various parthood relations, can be expressed in our extension, but could not be expressed in the original SROIQ. 1
A Reduction from DLP to PDL
- Journal of Logic and Computation
, 2005
"... We present a reduction from a new logic extending van der Meyden’s dynamic logic of permission (DLP) into propositional dynamic logic (PDL), providing a 2EXPTIME decision procedure and showing that all the machinery for PDL can be reused for reasoning about dynamic policies. As a sideeffect, we esta ..."
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Cited by 7 (0 self)
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We present a reduction from a new logic extending van der Meyden’s dynamic logic of permission (DLP) into propositional dynamic logic (PDL), providing a 2EXPTIME decision procedure and showing that all the machinery for PDL can be reused for reasoning about dynamic policies. As a sideeffect, we establish that DLP is EXPTIME-complete. The logic we introduce extends the logic DLP so that the policy set can be updated depending on its current value and such an update corresponds to add/delete transitions in the model, showing similarities with van Benthem’s sabotage modal logic. Key-words: dynamic logic of permissions, logic of programs, deletion of states/transitions, computational complexity. 1
