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Verfeinerungsmonoide, Vaught Monoide und Boolesche AlgebrenDobbertin, Hans, January 1983 (has links)
Thesis (Doctoral)--Universität Hannover, 1983.
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On s-filtered [sigma-filtered] Boolean algebrasGeschke, Stefan. January 1999 (has links)
Berlin, Freie University, Diss., 2000. / Dateiformat: zip, Dateien im PDF-Format.
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Dicomplemented lattices a contextual generalization of Boolean algebras /Kwuida, Léonard. Unknown Date (has links) (PDF)
Techn. University, Diss., 2004--Dresden.
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Discrete-time modelling of gene networks by Zhegalkin PolynomialsFaisal, Saadia January 2008 (has links)
Zugl.: Hamburg, Techn. Univ., Diss., 2008
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Discrete-time modelling of gene networks by Zhegalkin Polynomials /Faisal, Saadia. January 2009 (has links)
Zugl.: Hamburg, Techn. University, Diss., 2008.
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Locally boolean domains and universal models for infinitary sequential languagesLöw, Tobias. Unknown Date (has links)
Techn. University, Diss., 2006--Darmstadt.
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On the Complexity of Boolean UnificationBaader, Franz 19 May 2022 (has links)
Unification modulo the theory of Boolean algebras has been investigated by several autors. Nevertheless, the exact complexity of the decision problem for unification with constants and general unification was not known. In this research note, we show that the decision problem is complete for unification with constants and PSPACE-complete for general unification. In contrast, the decision problem for elementary unification (where the terms to be unified contain only symbols of the signature of Boolean algebras) is 'only' NP-complete.
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A New Combination Procedure for the Word Problem that Generalizes Fusion Decidability Results in Modal LogicsBaader, Franz, Ghilardi, Silvio, Tinelli, Cesare 30 May 2022 (has links)
Previous results for combining decision procedures for the word problem in the non-disjoint case do not apply to equational theories induced by modal logics - which are not disjoint for sharing the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other types of equational theories. In this paper, we present a new approach for combining decision procedures for the word problem in the non-disjoint case that applies to equational theories induced by modal logics, but is not restricted to them. The known fusion decidability results for modal logics are instances of our approach. However, even for equational theories induced by modal logics our results are more general since they are not restricted to so-called normal modal logics. / This report has also appeared as Report No. 03-03, Department of Computer Science, The University of Iowa.
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On the Complexity and Expressiveness of Description Logics with CountingBaader, Franz, De Bortoli, Filippo 20 June 2022 (has links)
Simple counting quantifiers that can be used to compare the number of role successors of an individual or the cardinality of a concept with a fixed natural number have been employed in Description Logics (DLs) for more than two decades under the respective names of number restrictions and cardinality restrictions on concepts. Recently, we have considerably extended the expressivity of such quantifiers by allowing to impose set and cardinality constraints formulated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA) on sets of role successors and concepts, respectively. We were able to prove that this extension does not increase the complexity of reasoning. In the present paper, we investigate the expressive power of the DLs obtained in this way, using appropriate bisimulation characterizations and 0–1 laws as tools to differentiate between the expressiveness of different logics. In particular, we show that, in contrast to most classical DLs, these logics are no longer expressible in first-order predicate logic (FOL), and we characterize their first-order fragments. In most of our previous work on DLs with QFBAPA-based set and cardinality constraints we have employed finiteness restrictions on interpretations to ensure that the obtained sets are finite, as required by the standard semantics for QFBAPA. Here we dispense with these restrictions to ease the comparison with classical DLs, where one usually considers arbitrary models rather than finite ones, easier. It turns out that doing so does not change the complexity of reasoning.
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Concept Descriptions with Set Constraints and Cardinality ConstraintsBaader, Franz 20 June 2022 (has links)
We introduce a new description logic that extends the well-known logic ALCQ by allowing the statement of constraints on role successors that are more general than the qualified number restrictions of ALCQ. To formulate these constraints, we use the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA), in which one can express Boolean combinations of set constraints and numerical constraints on the cardinalities of sets. Though our new logic is considerably more expressive than ALCQ, we are able to show that the complexity of reasoning in it is the same as in ALCQ, both without and with TBoxes. / The first version of this report was put online on April 6, 2017. The current version, containing more information on related
work, was put online on July 13, 2017.
This is an extended version of a paper published in the proceedings of FroCoS 2017.
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