Certain conjunctive query answering in first-order logic

2012 ◽  
Vol 37 (2) ◽  
pp. 1-35 ◽  
Author(s):  
Jef Wijsen
Keyword(s):  
Order Logic ◽  
Query Answering ◽  
First Order Logic ◽  
Conjunctive Query ◽  
First Order

scholarly journals Counting Query Answers over a DL-Lite Knowledge Base

2020 ◽  
Author(s):  
Diego Calvanese ◽  
Julien Corman ◽  
Davide Lanti ◽  
Simon Razniewski
Keyword(s):  
Knowledge Base ◽  
Data Access ◽  
Upper Bounds ◽  
Order Logic ◽  
Query Answering ◽  
First Order Logic ◽  
Management Systems ◽  
Query Rewriting ◽  
Data Complexity ◽  
First Order

Counting answers to a query is an operation supported by virtually all database management systems. In this paper we focus on counting answers over a Knowledge Base (KB), which may be viewed as a database enriched with background knowledge about the domain under consideration. In particular, we place our work in the context of Ontology-Mediated Query Answering/Ontology-based Data Access (OMQA/OBDA), where the language used for the ontology is a member of the DL-Lite family and the data is a (usually virtual) set of assertions. We study the data complexity of query answering, for different members of the DL-Lite family that include number restrictions, and for variants of conjunctive queries with counting that differ with respect to their shape (connected, branching, rooted). We improve upon existing results by providing PTIME and coNP lower bounds, and upper bounds in PTIME and LOGSPACE. For the LOGSPACE case, we have devised a novel query rewriting technique into first-order logic with counting.

scholarly journals Satisfiability Checking and Query Answering for Large Ontologies

10.29007/n1sv ◽  
2018 ◽  
Author(s):  
Christoph Weidenbach ◽  
Patrick Wischnewski
Keyword(s):  
State Of The Art ◽  
The State ◽  
Order Logic ◽  
Query Answering ◽  
First Order Logic ◽  
First Order ◽  
Satisfiability Checking ◽  
Superposition Calculus

In this paper we develop a sound, complete and terminating superposition calculusplus a query answering calculus for the BSH-Y2 fragment of theBernays-Schoenfinkel Horn class of first-order logic.BSH-Y2 can be used to represent expressive ontologies.In addition to checking consistency, our calculus supports query answeringfor queries with arbitrary quantifier alternations.Experiments on BSH-Y2 (fragments) of several large ontologies show that ourapproach advances the state of the art.

scholarly journals Deterministic planning in incompletely known domains with local effects

2021 ◽  
Author(s):  
Vitaliy Batusov
Keyword(s):  
Knowledge Base ◽  
Order Logic ◽  
Query Answering ◽  
First Order Logic ◽  
Situation Calculus ◽  
Local Effects ◽  
First Order ◽  
Conformant Planning ◽  
Recent Advances ◽  
Planning Algorithm

Conformant planning has been traditionally studied in the form of classical planning extended with a mechanism for expressing unknown facts and/or disjunctive knowledge. Despite a sizable body of research, most approaches do not attempt to move beyond essentially propositional planning. We address this shortcoming by defining conformant planning in terms of the situation calculus semantics and use recent advances in the fields of first-order knowledge base progression and query answering to develop a sound and complete conformant planning algorithm capable of handling knowledge defined in an expressive fragment of first-order logic. We implement a prototype planner and evaluate its performance on several existing domains.

scholarly journals Deterministic planning in incompletely known domains with local effects

2021 ◽  
Author(s):  
Vitaliy Batusov
Keyword(s):  
Knowledge Base ◽  
Order Logic ◽  
Query Answering ◽  
First Order Logic ◽  
Situation Calculus ◽  
Local Effects ◽  
First Order ◽  
Conformant Planning ◽  
Recent Advances ◽  
Planning Algorithm

Conformant planning has been traditionally studied in the form of classical planning extended with a mechanism for expressing unknown facts and/or disjunctive knowledge. Despite a sizable body of research, most approaches do not attempt to move beyond essentially propositional planning. We address this shortcoming by defining conformant planning in terms of the situation calculus semantics and use recent advances in the fields of first-order knowledge base progression and query answering to develop a sound and complete conformant planning algorithm capable of handling knowledge defined in an expressive fragment of first-order logic. We implement a prototype planner and evaluate its performance on several existing domains.

scholarly journals Making Cross Products and Guarded Ontology Languages Compatible

2017 ◽  
Author(s):  
Pierre Bourhis ◽  
Michael Morak ◽  
Andreas Pieris
Keyword(s):  
Description Logics ◽  
Order Logic ◽  
Query Answering ◽  
First Order Logic ◽  
First Order ◽  
Ontology Languages ◽  
Guarded Fragment

Cross products form a useful modelling tool that allows us to express natural statements such as "elephants are bigger than mice", or, more generally, to define relations that connect every instance in a relation with every instance in another relation. Despite their usefulness, cross products cannot be expressed using existing guarded ontology languages, such as description logics (DLs) and guarded existential rules. The question that comes up is whether cross products are compatible with guarded ontology languages, and, if not, whether there is a way of making them compatible. This has been already studied for DLs, while for guarded existential rules remains unanswered. Our goal is to give an answer to the above question. To this end, we focus on the guarded fragment of first-order logic (which serves as a unifying framework that subsumes many of the aforementioned ontology languages) extended with cross products, and we investigate the standard tasks of satisfiability and query answering. Interestingly, we isolate relevant fragments that are compatible with cross products.

First-Order Logic Reasoning Support for the Semantic Web

2009 ◽  
Vol 19 (12) ◽  
pp. 3091-3099 ◽  
Author(s):  
Gui-Hong XU ◽  
Jian ZHANG
Keyword(s):  
Semantic Web ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Logic Reasoning

Boolean-valued structures

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Model Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Rules ◽  
Mathematical Concepts ◽  
Semantic Framework ◽  
First Order ◽  
Standard Models ◽  
Boolean Valued Model ◽  
Semantic Values

Chapters 6-12 are driven by questions about the ability to pin down mathematical entities and to articulate mathematical concepts. This chapter is driven by similar questions about the ability to pin down the semantic frameworks of language. It transpires that there are not just non-standard models, but non-standard ways of doing model theory itself. In more detail: whilst we normally outline a two-valued semantics which makes sentences True or False in a model, the inference rules for first-order logic are compatible with a four-valued semantics; or a semantics with countably many values; or what-have-you. The appropriate level of generality here is that of a Boolean-valued model, which we introduce. And the plurality of possible semantic values gives rise to perhaps the ‘deepest’ level of indeterminacy questions: How can humans pin down the semantic framework for their languages? We consider three different ways for inferentialists to respond to this question.

scholarly journals Extensions in graph normal form

2020 ◽  
Author(s):  
Michał Walicki
Keyword(s):  
Normal Form ◽  
Fixed Points ◽  
Propositional Logic ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Special Cases

Abstract Graph normal form, introduced earlier for propositional logic, is shown to be a normal form also for first-order logic. It allows to view syntax of theories as digraphs, while their semantics as kernels of these digraphs. Graphs are particularly well suited for studying circularity, and we provide some general means for verifying that circular or apparently circular extensions are conservative. Traditional syntactic means of ensuring conservativity, like definitional extensions or positive occurrences guaranteeing exsitence of fixed points, emerge as special cases.

Relational Chase Procedures Interpreted as Resolution with Paramodulation1

1991 ◽  
Vol 15 (2) ◽  
pp. 123-138
Author(s):  
Joachim Biskup ◽  
Bernhard Convent
Keyword(s):  
Alternative Interpretation ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Problem ◽  
First Order ◽  
Inference Problems ◽  
The One ◽  
The Relationship ◽  
Theoretical Foundations ◽  
Insight Into

In this paper the relationship between dependency theory and first-order logic is explored in order to show how relational chase procedures (i.e., algorithms to decide inference problems for dependencies) can be interpreted as clever implementations of well known refutation procedures of first-order logic with resolution and paramodulation. On the one hand this alternative interpretation provides a deeper insight into the theoretical foundations of chase procedures, whereas on the other hand it makes available an already well established theory with a great amount of known results and techniques to be used for further investigations of the inference problem for dependencies. Our presentation is a detailed and careful elaboration of an idea formerly outlined by Grant and Jacobs which up to now seems to be disregarded by the database community although it definitely deserves more attention.

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