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 Superposition with First-class Booleans and Inprocessing Clausification

2021 ◽  
pp. 378-395
Author(s):  
Visa Nummelin ◽  
Alexander Bentkamp ◽  
Sophie Tourret ◽  
Petar Vukmirović
Keyword(s):  
State Of The Art ◽  
Higher Order ◽  
The State ◽  
Order Logic ◽  
Theorem Prover ◽  
First Order Logic ◽  
Higher Order Logic ◽  
First Order ◽  
Superposition Calculus

AbstractWe present a complete superposition calculus for first-order logic with an interpreted Boolean type. Our motivation is to lay the foundation for refutationally complete calculi in more expressive logics with Booleans, such as higher-order logic, and to make superposition work efficiently on problems that would be obfuscated when using clausification as preprocessing. Working directly on formulas, our calculus avoids the costly axiomatic encoding of the theory of Booleans into first-order logic and offers various ways to interleave clausification with other derivation steps. We evaluate our calculus using the Zipperposition theorem prover, and observe that, with no tuning of parameters, our approach is on a par with the state-of-the-art approach.

scholarly journals A Clausal Normal Form Translation for FOOL

10.29007/ltkk ◽  
2018 ◽  
Author(s):  
Evgenii Kotelnikov ◽  
Laura Kovács ◽  
Martin Suda ◽  
Andrei Voronkov
Keyword(s):  
Normal Form ◽  
Programming Languages ◽  
Program Analysis ◽  
State Of The Art ◽  
Order Logic ◽  
Theorem Prover ◽  
First Order Logic ◽  
First Order ◽  
Theorem Provers ◽  
Superposition Calculus

Automated theorem provers for first-order logic usually operate on sets of first-order clauses. It is well-known that the translation of a formula in full first-order logic to a clausal normal form (CNF) can crucially affect performance of a theorem prover. In our recent work we introduced a modification of first-order logic extended by the first class boolean sort and syntactical constructs that mirror features of programming languages. We called this logic FOOL. Formulas in FOOL can be translated to ordinary first-order formulas and checked by first-order theorem provers. While this translation is straightforward, it does not result in a CNF that can be efficiently handled by state-of-the-art theorem provers which use superposition calculus. In this paper we present a new CNF translation algorithm for FOOL that is friendly and efficient for superposition-based first-order provers. We implemented the algorithm in the Vampire theorem prover and evaluated it on a large number of problems coming from formalisation of mathematics and program analysis. Our experimental results show an increase of performance of the prover with our CNF translation compared to the naive translation.

scholarly journals Towards closed world reasoning in dynamic open worlds

2010 ◽  
Vol 10 (4-6) ◽  
pp. 547-563 ◽  
Author(s):  
MARTIN SLOTA ◽  
JOÃO LEITE
Keyword(s):  
Semantic Web ◽  
State Of The Art ◽  
Knowledge Bases ◽  
Order Logic ◽  
First Order Logic ◽  
Static Case ◽  
First Order ◽  
Closed World ◽  
Hybrid Knowledge ◽  
First Time

AbstractThe need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics forhybrid knowledge basescomposed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve.In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties.To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.

Principles and practice in verifying rule-based systems

1992 ◽  
Vol 7 (2) ◽  
pp. 115-141 ◽  
Author(s):  
Alun D. Preece ◽  
Rajjan Shinghal ◽  
Aïda Batarekh
Keyword(s):  
Expert System ◽  
Knowledge Base ◽  
State Of The Art ◽  
Knowledge Bases ◽  
Order Logic ◽  
First Order Logic ◽  
Rule Based ◽  
First Order ◽  
Rule Bases ◽  
System Knowledge

AbstractThis paper surveys the verification of expert system knowledge bases by detecting anomalies. Such anomalies are highly indicative of errors in the knowledge base. The paper is in two parts. The first part describes four types of anomaly: redundancy, ambivalence, circularity, and deficiency. We consider rule bases which are based on first-order logic, and explain the anomalies in terms of the syntax and semantics of logic. The second part presents a review of five programs which have been built to detect various subsets of the anomalies. The four anomalies provide a framework for comparing the capabilities of the five tools, and we highlight the strengths and weaknesses of each approach. This paper therefore provides not only a set of underlying principles for performing knowledge base verification through anomaly detection, but also a survey of the state-of-the-art in building practical tools for carrying out such verification. The reader of this paper is expected to be familiar with first-order logic.

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 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 Model-Finding for Externally Verifying FOL Ontologies: A Study of Spatial Ontologies

2020 ◽  
Author(s):  
Shirly Stephen ◽  
Torsten Hahmann
Keyword(s):  
Systematic Study ◽  
State Of The Art ◽  
Order Logic ◽  
First Order Logic ◽  
Problem Size ◽  
Effective Measure ◽  
First Order ◽  
Highly Effective ◽  
Model Finding ◽  
Synthetic Datasets

Use and reuse of an ontology requires prior ontology verification which encompasses, at least, proving that the ontology is internally consistent and consistent with representative datasets. First-order logic (FOL) model finders are among the only available tools to aid us in this undertaking, but proving consistency of FOL ontologies is theoretically intractable while also rarely succeeding in practice, with FOL model finders scaling even worse than FOL theorem provers. This issue is further exacerbated when verifying FOL ontologies against datasets, which requires constructing models with larger domain sizes. This paper presents a first systematic study of the general feasibility of SAT-based model finding with FOL ontologies. We use select spatial ontologies and carefully controlled synthetic datasets to identify key measures that determine the size and difficulty of the resulting SAT problems. We experimentally show that these measures are closely correlated with the runtimes of Vampire and Paradox, two state-of-the-art model finders. We propose a definition elimination technique and demonstrate that it can be a highly effective measure for reducing the problem size and improving the runtime and scalability of model finding.

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.

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