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Modal Logic and the Two-Variable Fragment [chapter]

Carsten Lutz, Ulrike Sattler, Frank Wolter
2001 Lecture Notes in Computer Science  
then L-satisfiability is ExpTimecomplete but F O 2 satisfiability is NExpTime-complete.  ...  We introduce a modal language L which is obtained from standard modal logic by adding the Boolean operators on accessibility relations, the identity relation, and the converse of relations.  ...  In this case, the complexity-gap is even wider: Over N, < , weak temporal logic is NP-complete [25] while F O 2 is NExpTime-complete [7, 15] .  ... 
doi:10.1007/3-540-44802-0_18 fatcat:bc73bdist5f6tjs2k7dyzwdp5u

Deciding ALBO with Tableau

Renate A. Schmidt, Dmitry Tishkovsky
2007 International Workshop on Description Logics  
ALBO is a very expressive description logic which is NExpTime complete and subsumes Boolean modal logic and the two-variable fragment of rstorder logic.  ...  In particular, we dene a sound and complete tableau calculus for the description logic ALBO and show that it provides a basis for decision procedures for this logic and numerous other description logics  ...  Introduction The description logic ALBO is an extension of the description logic ALB introduced in [7] with singleton concepts, called nominals in modal logic.  ... 
dblp:conf/dlog/SchmidtT07 fatcat:33kl27jykzdo5acl36wlmwzwj4

The Fluted Fragment with Transitivity

Ian Pratt-Hartmann, Lidia Tendera, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
On the other hand we show that the satisfiability problem is undecidable already for the two-variable fragment of the logic in the presence of three transitive relations.  ...  We show that the logic enjoys the finite model property when only one transitive relation is available.  ...  Indeed, the satisfiability problem for FO 2 , the two-variable fragment of first-order logic, is known to be NExpTime-complete [5] , whence the corresponding problem for FL 2 is certainly in NExpTime.  ... 
doi:10.4230/lipics.mfcs.2019.18 dblp:conf/mfcs/Pratt-HartmannT19 fatcat:3nrwwbvwxvgothi6vgmd5qmh2q

On the decidability and complexity of integrating ontologies and rules

R ROSATI
2005 Journal of Web Semantics  
As a consequence, we are able to show that such a framework of r-hybrid KBs comprises many systems proposed for combining rules and Description Logics. Then, we study reasoning in r-hybrid KBs.  ...  Such a framework is very general, in the sense that: (i) the construction is parametric with respect to the logic used to specify the structural component; (ii) the rule component is very expressive, since  ...  In words, I ⊂ A I if the extension of the predicates of A in I is strictly larger than in I .  ... 
doi:10.1016/j.websem.2005.05.002 fatcat:w5mk6euzbjfwhcmjqdwa3zk4py

Using Tableau to Decide Expressive Description Logics with Role Negation [chapter]

Renate A. Schmidt, Dmitry Tishkovsky
2007 Lecture Notes in Computer Science  
ALBO is a very expressive description logic which subsumes Boolean modal logic and the two-variable fragment of rst-order logic and reasoning in it is NExpTime-complete.  ...  In particular, we dene a sound and complete tableau calculus for the description logic ALBO and show that it provides a basis for decision procedures for this logic and numerous other description logics  ...  In [5] it is shown that satisability in the two-variable rst-order fragment with equality is NExpTime-complete.  ... 
doi:10.1007/978-3-540-76298-0_32 fatcat:fqh2afbiejgidj3tk4nvjwttka

Using tableau to decide description logics with full role negation and identity

Renate A. Schmidt, Dmitry Tishkovsky
2014 ACM Transactions on Computational Logic  
In this paper we define a sound and complete tableau calculus for the ALBOid that provides a basis for decision procedures for this logic and all its sublogics.  ...  This paper presents a tableau approach for deciding expressive description logics with full role negation and role identity.  ...  The tableau decision procedures found in the description logic literature, and implemented in existing tableau-based description logic systems, can handle a large class of description logics, but cannot  ... 
doi:10.1145/2559947 fatcat:6vkog6nx3jbhle24p57nq46agu

Satisfiability for two-variable logic with two successor relations on finite linear orders [article]

Diego Figueira
2013 arXiv   pre-print
We show that the problem is decidable in NEXPTIME.  ...  We study the finitary satisfiability problem for first order logic with two variables and two binary relations, corresponding to the induced successor relations of two finite linear orders.  ...  In this setting, linear orders have special connections with temporal logics, but it is also applicable in other scenarios, like in databases or description logics.  ... 
arXiv:1204.2495v3 fatcat:hvc3msmleff4dbcmthkvfhttnq

Logics with counting and equivalence

Ian Pratt-Hartmann
2014 Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14  
We show that the satisfiability and finite satisfiability problems for this logic are both NEXPTIME-complete.  ...  ) problem is NEXPTIME-complete [3, 12] ; C 2 lacks the finite model property, and its satisfiability and finite satisfiability problems are both NEXPTIME-complete [4, 13, 14] ; L 2 1E retains the finite  ...  The situation is illustrated in Fig. 3 . Recall that, if B is any configuration, then B contains exactly one element satisfying s.  ... 
doi:10.1145/2603088.2603117 dblp:conf/csl/Pratt-Hartmann14 fatcat:xu777jgukbeo3iqzqy55a6clx4

Resolution-Based Reasoning for Ontologies [chapter]

Boris Motik
2009 Handbook on Ontologies  
We overview the algorithms for reasoning with description logic (DL) ontologies based on resolution.  ...  Furthermore, we present a resolution-based algorithm that reduces a DL knowledge base into a disjunctive datalog program, while preserving the set of entailed facts.  ...  Preliminaries The Description Logic ALCHI Description logics have been introduced in detail in Chapter 1, but, to make this chapter self-contained, we present the definition of the DL ALCHI .  ... 
doi:10.1007/978-3-540-92673-3_24 dblp:series/ihis/Motik09 fatcat:nac7x6jwbvfalfrucfrs32zmsi

Effective Query Rewriting with Ontologies over DBoxes (Extended Abstract)

Inanç Seylan, Enrico Franconi, Jos de Bruijn
2009 International Workshop on Description Logics  
We consider query answering on Description Logic (DL) ontologies with DBoxes, where a DBox is a set of assertions on individuals involving atomic concepts and roles called DBox predicates.  ...  We present a procedure for computing interpolants in the DL ALC with general TBoxes.  ...  Deciding implicit definability reduces to checking query containment under Description Logic constraints [18] .  ... 
dblp:conf/dlog/SeylanFB09 fatcat:xqu5cwdxundjzlu6ien63eqwnq

A Tableaux Decision Procedure for SHOIQ

Ian Horrocks, Ulrike Sattler
2005 International Joint Conference on Artificial Intelligence  
This paper presents a tableaux decision procedure for SHOIQ, the DL underlying OWL DL. To the best of our knowledge, this is the first goal-directed decision procedure for SHOIQ.  ...  Introduction Description Logics (DLs) are a family of logic based knowledge representation formalisms.  ...  We can now finish the description of the tableau algorithm: A completion graph is complete if it contains a clash, or when none of the rules is applicable.  ... 
dblp:conf/ijcai/HorrocksS05 fatcat:ek7ezhegzncczhuaunv5qrglhm

Effective Query Rewriting with Ontologies over DBoxes

Inanç Seylan, Enrico Franconi, Jos de Bruijn
2009 International Joint Conference on Artificial Intelligence  
We consider query answering on Description Logic (DL) ontologies with DBoxes, where a DBox is a set of assertions on individuals involving atomic concepts and roles called DBox predicates.  ...  We present a procedure for computing interpolants in the DL ALC with general TBoxes.  ...  The work presented in this paper has been partially funded by the European project ONTORULE.  ... 
dblp:conf/ijcai/SeylanFB09 fatcat:5aobnxjry5el7j3as74jr64u2a

Knowledge Representation and Ontologies [chapter]

Stephan Grimm
2009 Scientific Data Mining and Knowledge Discovery  
Moreover, if C 0 is satisfiable, then the tableaux will generate a set of ABoxes containing a complete and clash-free ABox. D.  ...  has a clash if {C(x), ¬C(x)} ⊆ A, and is clash-free otherwise. A clash represents an obvious contradiction. Hence, it is immediate so see that an ABox containing a clash is unsatisfiable. D.  ...  Hardness proofs using tilings Tiling problems are a very useful tool for showing complexity results in description logics, modal logics, and fragments of FOL.  ... 
doi:10.1007/978-3-642-02788-8_6 fatcat:2qlaeg7fazadnfwow3fupmukqu

Combining Rules and Ontologies into Clopen Knowledge Bases

Labinot Bajraktari, Magdalena Ortiz, Mantas Šimkus
2018 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We argue that the guarded negation fragment of first-order logic(GNFO)—a very expressive fragment that subsumes many prominent ontology languages like Description Logics (DLs) and the guarded fragment—is  ...  We have implemented the approach for separable CKBs containing ontologies in the DL ALCH, and present in this paper some promising empirical results for real-life data.  ...  Keeping in mind that satisfiability in GNFO is 2EXPTIME-complete, this equivalence yields the NEXPTIME 2EXPTIME upper bound.  ... 
doi:10.1609/aaai.v32i1.11565 fatcat:zy2ntqtjavdwxmq642cxhi2e2m

Synthesis for Multi-weighted Games with Branching-Time Winning Conditions [chapter]

Isabella Kaufmann, Kim Guldstrand Larsen, Jiří Srba
2020 Lecture Notes in Computer Science  
We show that both the model checking problem as well as the synthesis problem are decidable and that the model checking problem is EXPTIME-complete, while the synthesis problem is in 2-EXPTIME and is NEXPTIME-hard  ...  The objectives are given in a recursive modal logic with semantics defined over a multi-weighted extension of a Kripke structure where each transition is annotated with multiple nonnegative weights representing  ...  A run in K is a sequence of states and transitions ρ = s 0 c0 − → s 1 c1 − → s 2 c2 − → . . . RML and the Model Checking Problem We can now define our logic.  ... 
doi:10.1007/978-3-030-51831-8_3 fatcat:vbeodushzvgixhyzcbjthlxuae
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