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.

scholarly journals Characterizing Boundedness in Chase Variants

2020 ◽  
Vol 21 (1) ◽  
pp. 51-79
Author(s):  
STATHIS DELIVORIAS ◽  
MICHEL LECLÈRE ◽  
MARIE-LAURE MUGNIER ◽  
FEDERICO ULLIANA
Keyword(s):  
Knowledge Bases ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Universal Models ◽  
Knowing That ◽  
Significant Interest ◽  
Horn Rules ◽  
Boundedness Problem ◽  
Undecidable Problem

AbstractExistential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions.

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 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 Consistent Inference for Dialogue Relation Extraction

2021 ◽  
Author(s):  
Xinwei Long ◽  
Shuzi Niu ◽  
Yucheng Li
Keyword(s):  
Performance Improvement ◽  
Relation Extraction ◽  
Attention Mechanism ◽  
Order Logic ◽  
Experimental Results ◽  
First Order Logic ◽  
Specific Topic ◽  
Inference Method ◽  
First Order ◽  
Benchmark Datasets

Relation Extraction is key to many downstream tasks. Dialogue relation extraction aims at discovering entity relations from multi-turn dialogue scenario. There exist utterance, topic and relation discrepancy mainly due to multi-speakers, utterances, and relations. In this paper, we propose a consistent learning and inference method to minimize possible contradictions from those distinctions. First, we design mask mechanisms to refine utterance-aware and speaker-aware representations respectively from the global dialogue representation for the utterance distinction. Then a gate mechanism is proposed to aggregate such bi-grained representations. Next, mutual attention mechanism is introduced to obtain the entity representation for various relation specific topic structures. Finally, the relational inference is performed through first order logic constraints over the labeled data to decrease logically contradictory predicted relations. Experimental results on two benchmark datasets show that the F1 performance improvement of the proposed method is at least 3.3% compared with SOTA.

scholarly journals A Knowledge Level Account of Forgetting

2017 ◽  
Vol 60 ◽  
pp. 1165-1213 ◽  
Author(s):  
James P. Delgrande
Keyword(s):  
Belief Change ◽  
Description Logics ◽  
Knowledge Bases ◽  
Order Logic ◽  
First Order Logic ◽  
Consequence Relation ◽  
First Order ◽  
Formal Systems ◽  
High Level ◽  
Main Definition

Forgetting is an operation on knowledge bases that has been addressed in different areas of Knowledge Representation and with respect to different formalisms, including classical propositional and first-order logic, modal logics, logic programming, and description logics. Definitions of forgetting have been expressed in terms of manipulation of formulas, sets of postulates, isomorphisms between models, bisimulations, second-order quantification, elementary equivalence, and others. In this paper, forgetting is regarded as an abstract belief change operator, independent of the underlying logic. The central thesis is that forgetting amounts to a reduction in the language, specifically the signature, of a logic. The main definition is simple: the result of forgetting a portion of a signature in a theory is given by the set of logical consequences of this theory over the reduced language. This definition offers several advantages. Foremost, it provides a uniform approach to forgetting, with a definition that is applicable to any logic with a well-defined consequence relation. Hence it generalises a disparate set of logic-specific definitions with a general, high-level definition. Results obtained in this approach are thus applicable to all subsumed formal systems, and many results are obtained much more straightforwardly. This view also leads to insights with respect to specific logics: for example, forgetting in first-order logic is somewhat different from the accepted approach. Moreover, the approach clarifies the relation between forgetting and related operations, including belief contraction.

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.

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