scholarly journals On the Expressiveness of Levesque's Normal Form

2008 ◽  
Vol 31 ◽  
pp. 259-272
Author(s):  
Y. Liu ◽  
G. Lakemeyer
Keyword(s):  
Normal Form ◽  
Knowledge Base ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Method ◽  
Closed World Assumption ◽  
First Order ◽  
Closed World ◽  
Polynomial Size

Levesque proposed a generalization of a database called a proper knowledge base (KB), which is equivalent to a possibly infinite consistent set of ground literals. In contrast to databases, proper KBs do not make the closed-world assumption and hence the entailment problem becomes undecidable. Levesque then proposed a limited but efficient inference method V for proper KBs, which is sound and, when the query is in a certain normal form, also logically complete. He conjectured that for every first-order query there is an equivalent one in normal form. In this note, we show that this conjecture is false. In fact, we show that any class of formulas for which V is complete must be strictly less expressive than full first-order logic. Moreover, in the propositional case it is very unlikely that a formula always has a polynomial-size normal form.

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.

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.

A NORMAL FORM FOR FIRST-ORDER LOGIC OVER DOUBLY-LINKED DATA STRUCTURES

2008 ◽  
Vol 19 (01) ◽  
pp. 205-217 ◽  
Author(s):  
STEVEN LINDELL
Keyword(s):  
Normal Form ◽  
Data Structures ◽  
Linked Data ◽  
Linear Time ◽  
Order Logic ◽  
Information Storage ◽  
First Order Logic ◽  
Total Size ◽  
Bounded Degree ◽  
First Order

We use singulary vocabularies to analyze first-order definability over doubly-linked data structures. Singulary vocabularies contain only monadic predicate and monadic function symbols. A class of mathematical structures in any vocabulary can be elementarily interpreted in a singulary vocabulary, while preserving notions of total size and degree. Doubly-linked data structures are a special case of bounded-degree finite structures in which there are reciprocal connections between elements, corresponding closely with physically feasible models of information storage. They can be associated with logical models involving unary relations and bijective functions in what we call an invertible singulary vocabulary. Over classes of these models, there is a normal form for first-order logic which eliminates all quantification of dependent variables. The paper provides a syntactically based proof using counting quantifiers. It also makes precise the notion of implicit calculability for arbitrary arity first-order formulas. Linear-time evaluation of first-order logic over doubly-linked data structures becomes a direct corollary. Included is a discussion of why these special data structures are appropriate for physically realizable models of information.

Robot Task Planning Using First-Order Logic

2000 ◽  
Author(s):  
Lei Yan ◽  
K. Krishnamurthy
Keyword(s):  
Inference Engine ◽  
Knowledge Bases ◽  
Order Logic ◽  
First Order Logic ◽  
Task Planning ◽  
Inference Method ◽  
First Order ◽  
Simulation Results ◽  
Robot Task ◽  
Domain Information

Abstract Task planning for a robot operating in an unknown environment using first-order logic is considered in this study. The approach is to use one agent to simulate the robot and a second agent to simulate the environment. Both agents employ knowledge bases and an inference engine. The rules for the knowledge bases are developed using first-order logic and the inference method is based on hyper-resolution. A weighting scheme is used by the robot to decide on the action to be taken. After enough domain information is obtained, a task planner, which is also based on rules, is employed. Simulation results validating the methodology are presented for a robot moving inside a warehouse with four rooms. In this example, the environment is initially unknown to the robot. But after mapping the environment, the robot can efficiently plan tasks such as moving an object from one room to another.

RULES FOR SUBATOMIC DERIVATION

2010 ◽  
Vol 4 (2) ◽  
pp. 219-236 ◽  
Author(s):  
BARTOSZ WIĘCKOWSKI
Keyword(s):  
Normal Form ◽  
Atomic System ◽  
Atomic Level ◽  
Order Logic ◽  
First Order Logic ◽  
Atomic Sentence ◽  
Theoretic Analysis ◽  
Alternative Account ◽  
First Order ◽  
Normal Form Theorem

In proof-theoretic semantics the meaning of an atomic sentence is usually determined by a set of derivations in an atomic system which contain that sentence as a conclusion (see, in particular, Prawitz, 1971, 1973). The paper critically discusses this standard approach and suggests an alternative account which proceeds in terms of subatomic introduction and elimination rules for atomic sentences. A simple subatomic normal form theorem by which this account of the semantics of atomic sentences and the terms from which they are composed is underpinned, shows moreover that the proof-theoretic analysis of first-order logic can be pursued also beneath the atomic level.

scholarly journals On the Union Closed Fragment of Existential Second-Order Logic and Logics with Team Semantics

2021 ◽  
Vol Volume 17, Issue 3 ◽  
Author(s):  
Matthias Hoelzel ◽  
Richard Wilke
Keyword(s):  
Normal Form ◽  
Second Order ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Team Semantics ◽  
Key Factor ◽  
Undecidable Property ◽  
Open Question ◽  
Second Order Logic

We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables the handling and provides a better understanding of this fragment. We also introduce inclusion-exclusion games that turn out to be precisely the corresponding model-checking games. These games are not only interesting in their own right, but they also are a key factor towards building a bridge between the semantic and syntactic fragments. On the level of logics with team semantics we additionally present restrictions of inclusion-exclusion logic to capture the union closed fragment. Moreover, we define a team based atom that when adding it to first-order logic also precisely captures the union closed fragment of existential second-order logic which answers an open question by Galliani and Hella.

scholarly journals Creation of a consulting tool and implementation of an ontology for a Master’s Degree Program in Computer Sciences

2018 ◽  
Vol 19 (1) ◽  
pp. 29-38
Author(s):  
Cecilia Reyes Peña ◽  
Mireya Tovar Vidal ◽  
Concepción Stephanie Vázquez González
Keyword(s):  
Knowledge Base ◽  
Master's Degree ◽  
Order Logic ◽  
First Order Logic ◽  
Class Diagram ◽  
Design Phase ◽  
Master Program ◽  
First Order ◽  
Python Language ◽  
Master’S Degree

In this paper, a manual ontology for a Computer Sciences Master program constructed, that uses some elements from the METHONTOLOGY, Grüninger and Fox, and Bravo’s methodologies, is presented. A series of steps to identify and represent the Master’s Degree program’s knowledge base has been followed. Afterwards, first order logic axioms and competency questions to evaluate the ontology are used. The development of a module written in Python language is used for evaluating the ontology through competency questions defined during design phase. This module is flexible enough to present predefined or defined questions by the user in running time and to obtain results to the queries representing the competency questions. Elements as a hierarchy class diagram and a description of the relations and attributes are used in this ontology’s construction. Keywords: Ontology; Python tool; SPARQL language.

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