The Expressivity of Constraint Query Languages with Boolean Algebra Linear Cardinality Constraints

2005 ◽  
pp. 167-182 ◽  
Author(s):  
Peter Revesz
Keyword(s):  
Boolean Algebra ◽  
Query Languages ◽  
Cardinality Constraints

scholarly journals Extending the Description Logic ALC with More Expressive Cardinality Constraints on Concepts

10.29007/f3hh ◽  
2018 ◽  
Author(s):  
Franz Baader ◽  
Andreas Ecke
Keyword(s):  
Boolean Algebra ◽  
Description Logic ◽  
Knowledge Bases ◽  
The Other ◽  
Cardinality Constraints ◽  
New Formalism ◽  
Statistical Knowledge ◽  
General Constraints ◽  
Consistency Problem ◽  
The One

We extend the terminological formalism of the well-known description logic ALC from concept inclusions (CIs) to more general constraints formulated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA). In QFBAPA one can formulate Boolean combinations of inclusion constraints and numerical constraints on the cardinalities of sets.Our new formalism extends, on the one hand, so-called cardinality restrictions on concepts, which have been introduced two decades ago, and on the other hand the recently introduced statistical knowledge bases. Though considerably more expressive, our formalism has the same complexity (NExpTime) as cardinality restrictions on concepts. We will also introduce a restricted version of our formalism for which the complexity is ExpTime. This yields the until now unknown exact complexity of the consistency problem for statistical knowledge bases.

scholarly journals Description Logics That Count, and What They Can and Cannot Count

10.29007/ltzn ◽  
2020 ◽  
Author(s):  
Franz Baader ◽  
Filippo De Bortoli
Keyword(s):  
Boolean Algebra ◽  
Natural Number ◽  
Predicate Logic ◽  
Description Logics ◽  
Expressive Power ◽  
Cardinality Constraints ◽  
Presburger Arithmetic ◽  
First Order ◽  
First Order Predicate Logic

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 restriction 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 this way, using appropriate bisimulation characterizations and 0--1 laws as tools for distinguishing 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. Here we dispense with these restrictions to make 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.

Classification of means and methods of the Web semantic retrieval

2017 ◽  
pp. 030-050
Author(s):  
J.V. Rogushina ◽  
Keyword(s):  
Search Engines ◽  
Domain Knowledge ◽  
Information Needs ◽  
Web Search ◽  
User Interaction ◽  
Query Languages ◽  
Semantic Search ◽  
Semantic Retrieval ◽  
The Web

Problems associated with the improve ment of information retrieval for open environment are considered and the need for it’s semantization is grounded. Thecurrent state and prospects of development of semantic search engines that are focused on the Web information resources processing are analysed, the criteria for the classification of such systems are reviewed. In this analysis the significant attention is paid to the semantic search use of ontologies that contain knowledge about the subject area and the search users. The sources of ontological knowledge and methods of their processing for the improvement of the search procedures are considered. Examples of semantic search systems that use structured query languages (eg, SPARQL), lists of keywords and queries in natural language are proposed. Such criteria for the classification of semantic search engines like architecture, coupling, transparency, user context, modification requests, ontology structure, etc. are considered. Different ways of support of semantic and otology based modification of user queries that improve the completeness and accuracy of the search are analyzed. On base of analysis of the properties of existing semantic search engines in terms of these criteria, the areas for further improvement of these systems are selected: the development of metasearch systems, semantic modification of user requests, the determination of an user-acceptable transparency level of the search procedures, flexibility of domain knowledge management tools, increasing productivity and scalability. In addition, the development of means of semantic Web search needs in use of some external knowledge base which contains knowledge about the domain of user information needs, and in providing the users with the ability to independent selection of knowledge that is used in the search process. There is necessary to take into account the history of user interaction with the retrieval system and the search context for personalization of the query results and their ordering in accordance with the user information needs. All these aspects were taken into account in the design and implementation of semantic search engine "MAIPS" that is based on an ontological model of users and resources cooperation into the Web.

Synthesis of Antennas on the Base of the Boolean Algebra Transformations and the Atomic Functions Theory

2005 ◽  
Vol 64 (9) ◽  
pp. 699-712
Author(s):  
Victor Filippovich Kravchenko ◽  
Miklhail Alekseevich Basarab
Keyword(s):  
Boolean Algebra

Temporalizing Rewritable Query Languages Over Knowledge Bases

2015 ◽  
Author(s):  
Stefan Borgwardt ◽  
Marcel Lippmann ◽  
Veronika Thost
Keyword(s):  
Knowledge Bases ◽  
Query Languages

An Outline of a Theory of Propositional Vagueness

2018 ◽  
Author(s):  
Andrew Bacon
Keyword(s):  
Boolean Algebra ◽  
Total Evidence ◽  
Coarse Grained ◽  
Atomic Boolean Algebra

This chapter presents a series questions in the philosophy of vagueness that will constitute the primary subjects of this book. The stance this book takes on these questions is outlined, and some preliminary ramifications are explored. These include the idea that (i) propositional vagueness is more fundamental than linguistic vagueness; (ii) propositions are not themselves sentence-like; they are coarse grained, and form a complete atomic Boolean algebra; (iii) vague propositions are, moreover, not simply linguistic constructions either such as sets of world-precisification pairs; and (iv) propositional vagueness is to be understood by its role in thought. Specific theses relating to the last idea include the thesis that one’s total evidence can be vague, and that there are vague propositions occupying every evidential role, that disagreements about the vague ultimately boil down to disagreements in the precise, and that one should not care intrinsically about vague matters.

scholarly journals Assessing the Risk of Democratic Reversal in the United States: A Reply to Kurt Weyland

2021 ◽  
pp. 1-6
Author(s):  
Matias López ◽  
Juan Pablo Luna
Keyword(s):  
United States ◽  
Comparative Analysis ◽  
Boolean Algebra ◽  
Qualitative Comparative Analysis ◽  
The United States ◽  
American Democracy ◽  
Institutional Dynamics ◽  
The Public ◽  
Original Analysis ◽  
The Impact

ABSTRACT By replying to Kurt Weyland’s (2020) comparative study of populism, we revisit optimistic perspectives on the health of American democracy in light of existing evidence. Relying on a set-theoretical approach, Weyland concludes that populists succeed in subverting democracy only when institutional weakness and conjunctural misfortune are observed jointly in a polity, thereby conferring on the United States immunity to democratic reversal. We challenge this conclusion on two grounds. First, we argue that the focus on institutional dynamics neglects the impact of the structural conditions in which institutions are embedded, such as inequality, racial cleavages, and changing political attitudes among the public. Second, we claim that endogeneity, coding errors, and the (mis)use of Boolean algebra raise questions about the accuracy of the analysis and its conclusions. Although we are skeptical of crisp-set Qualitative Comparative Analysis as an adequate modeling choice, we replicate the original analysis and find that the paths toward democratic backsliding and continuity are both potentially compatible with the United States.

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