scholarly journals Space Efficiency of Propositional Knowledge Representation Formalisms

2000 ◽  
Vol 13 ◽  
pp. 1-31 ◽  
Author(s):  
M. Cadoli ◽  
F. M. Donini ◽  
P. Liberatore ◽  
M. Schaerf
Keyword(s):  
Knowledge Representation ◽  
Belief Revision ◽  
Time Complexity ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Propositional Knowledge ◽  
Stable Model ◽  
Logic Programs ◽  
Space Efficiency ◽  
Relative Ability

We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge A, is the size of the shortest formula of F that represents A. In this paper we assume that knowledge is either a set of propositional interpretations (models) or a set of propositional formulae (theorems). We provide a formal way of talking about the relative ability of PKR formalisms to compactly represent a set of models or a set of theorems. We introduce two new compactness measures, the corresponding classes, and show that the relative space efficiency of a PKR formalism in representing models/theorems is directly related to such classes. In particular, we consider formalisms for nonmonotonic reasoning, such as circumscription and default logic, as well as belief revision operators and the stable model semantics for logic programs with negation. One interesting result is that formalisms with the same time complexity do not necessarily belong to the same space efficiency class.

scholarly journals Deriving conclusions from non-monotonic cause-effect relations

2016 ◽  
Vol 16 (5-6) ◽  
pp. 670-687 ◽  
Author(s):  
JORGE FANDINNO
Keyword(s):  
Knowledge Representation ◽  
Logic Programming ◽  
Causal Effect ◽  
Stable Model ◽  
Logic Programs ◽  
Causal Relations ◽  
Initial Approach ◽  
Sufficient Cause ◽  
Different Types ◽  
Normal Logic

AbstractWe present an extension of Logic Programming (under stable models semantics) that, not only allows concluding whether a true atom is a cause of another atom, but alsoderiving new conclusionsfrom these causal-effect relations. This is expressive enough to capture informal rules like “if some agent's actionshave beennecessaryto cause an eventEthen conclude atomcaused(,E),” something that, to the best of our knowledge, had not been formalised in the literature. To this aim, we start from a first attempt that proposed extending the syntax of logic programs with so-calledcausal literals. These causal literals are expressions that can be used in rule bodies and allow inspecting the derivation of some atomAin the program with respect to some query function ψ. Depending on how these query functions are defined, we can model different types of causal relations such as sufficient, necessary or contributory causes, for instance. The initial approach was specifically focused on monotonic query functions. This was enough to cover sufficient cause-effect relations but, unfortunately, necessary and contributory are essentiallynon-monotonic. In this work, we define a semantics for non-monotonic causal literals showing that, not only extends the stable model semantics for normal logic programs, but also preserves many of its usual desirable properties for the extended syntax. Using this new semantics, we provide precise definitions ofnecessaryandcontributorycausal relations and briefly explain their behaviour on a pair of typical examples from the Knowledge Representation literature.

scholarly journals On elementary loops of logic programs

2011 ◽  
Vol 11 (6) ◽  
pp. 953-988 ◽  
Author(s):  
MARTIN GEBSER ◽  
JOOHYUNG LEE ◽  
YULIYA LIERLER
Keyword(s):  
Nonmonotonic Reasoning ◽  
The Body ◽  
The Other ◽  
Stable Model ◽  
Logic Programs ◽  
Graph Theoretic ◽  
Theoretic Characterization ◽  
Definition Of ◽  
Disjunctive Programs

AbstractUsing the notion of an elementary loop, Gebser and Schaub (2005. Proceedings of the Eighth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'05), 53–65) refined the theorem on loop formulas attributable to Lin and Zhao (2004) by considering loop formulas of elementary loops only. In this paper, we reformulate the definition of an elementary loop, extend it to disjunctive programs, and study several properties of elementary loops, including how maximal elementary loops are related to minimal unfounded sets. The results provide useful insights into the stable model semantics in terms of elementary loops. For a nondisjunctive program, using a graph-theoretic characterization of an elementary loop, we show that the problem of recognizing an elementary loop is tractable. On the other hand, we also show that the corresponding problem is coNP-complete for a disjunctive program. Based on the notion of an elementary loop, we present the class of Head-Elementary-loop-Free (HEF) programs, which strictly generalizes the class of Head-Cycle-Free (HCF) programs attributable to Ben-Eliyahu and Dechter (1994. Annals of Mathematics and Artificial Intelligence 12, 53–87). Like an HCF program, an HEF program can be turned into an equivalent nondisjunctive program in polynomial time by shifting head atoms into the body.

A Framework for Nonmonotonic Reasoning with Rule Priorities

1998 ◽  
Vol 2 (1) ◽  
pp. 16-25
Author(s):  
Masato Shibasaki ◽  
◽  
Katsumi Nitta
Keyword(s):  
Special Form ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Logic Programs ◽  
Rule Based ◽  
Argumentation Framework ◽  
Default Rules

In the 1990, a number of studies was made on nonmonotonic reasoning with rule priorities. Little is known, however, about relationships among these semantics because there is no framework in which these semantics can be compared. In this paper, we give the basis of this framework, which is a special form of Dung’s argumentation framework, although not covering all semantics of past studies in this category. To be concrete, we provide rule-based framework (RF) for extended logic programs (ELPs), clarify semantics of default rules and rule priorities, and extend it to RF for prioritized extended default logic programs (EDLPs). By means of RF for prioritized EDLPs, we reformulate several semantics of past studies , indicate their improvements, and give new prioritized EDLPs semantics.

Default Logic Models of Certain Inheritance Systems with Exceptions

1993 ◽  
Vol 18 (2-4) ◽  
pp. 129-149
Author(s):  
Serge Garlatti
Keyword(s):  
Hierarchical Structure ◽  
Formal Semantics ◽  
Sufficient Conditions ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Representation Systems ◽  
The Hierarchical Structure ◽  
Necessary And Sufficient ◽  
Structure Of Knowledge ◽  
Made In

Representation systems based on inheritance networks are founded on the hierarchical structure of knowledge. Such representation is composed of a set of objects and a set of is-a links between nodes. Objects are generally defined by means of a set of properties. An inheritance mechanism enables us to share properties across the hierarchy, called an inheritance graph. It is often difficult, even impossible to define classes by means of a set of necessary and sufficient conditions. For this reason, exceptions must be allowed and they induce nonmonotonic reasoning. Many researchers have used default logic to give them formal semantics and to define sound inferences. In this paper, we propose a survey of the different models of nonmonotonic inheritance systems by means of default logic. A comparison between default theories and inheritance mechanisms is made. In conclusion, the ability of default logic to take some inheritance mechanisms into account is discussed.

The Role of Nonmonotonic Representations in Requirements Engineering

1998 ◽  
Vol 08 (03) ◽  
pp. 385-399 ◽  
Author(s):  
Grigoris Antoniou
Keyword(s):  
Software Engineering ◽  
Knowledge Representation ◽  
Requirements Engineering ◽  
Nonmonotonic Reasoning ◽  
Default Reasoning ◽  
Requirements Prioritization ◽  
Evolving System ◽  
System Requirements

This paper discusses the significance of nonmonotonic reasoning, a method from the knowledge representation area, to mainstream software engineering. In particular, we discuss why the use of defaults in specifications is an adequate way of addressing some of the most important problems in requirements engineering, such as: The problem of identifying and dealing with inconsistencies; evolving system requirements; requirements prioritization; and the quality of specifications with respect to naturalness and compactness. We argue that these problems need to be addressed in a principled, formal way, and that default reasoning provides adequate mechanisms to deal with them.

scholarly journals Query Answering with Guarded Existential Rules under Stable Model Semantics

2020 ◽  
Vol 34 (03) ◽  
pp. 3017-3024
Author(s):  
Hai Wan ◽  
Guohui Xiao ◽  
Chenglin Wang ◽  
Xianqiao Liu ◽  
Junhong Chen ◽  
...  
Keyword(s):  
Answer Set Programming ◽  
Query Answering ◽  
Prototype System ◽  
Stable Model ◽  
Logic Programs ◽  
Termination Problem ◽  
Answer Set

In this paper, we study the problem of query answering with guarded existential rules (also called GNTGDs) under stable model semantics. Our goal is to use existing answer set programming (ASP) solvers. However, ASP solvers handle only finitely-ground logic programs while the program translated from GNTGDs by Skolemization is not in general. To address this challenge, we introduce two novel notions of (1) guarded instantiation forest to describe the instantiation of GNTGDs and (2) prime block to characterize the repeated infinitely-ground program translated from GNTGDs. Using these notions, we prove that the ground termination problem for GNTGDs is decidable. We also devise an algorithm for query answering with GNTGDs using ASP solvers. We have implemented our approach in a prototype system. The evaluation over a set of benchmarks shows encouraging results.

scholarly journals Negative Sampling in Knowledge Representation Learning: A Mini-Review

2020 ◽  
Author(s):  
Jing Qian ◽  
Gangmin Li ◽  
Katie Atkinson ◽  
Yong Yue
Keyword(s):  
Knowledge Representation ◽  
Link Prediction ◽  
Representation Learning ◽  
Cluster Sampling ◽  
Continuous Space ◽  
Knowledge Representations ◽  
Space Efficiency ◽  
Low Dimensional ◽  
Fixed Distribution

Knowledge representation learning (KRL) aims at encoding components of a knowledge graph (KG) into a low-dimensional continuous space, which has brought considerable successes in applying deep learning to graph embedding. Most famous KGs contain only positive instances for space efficiency. Typical KRL techniques, especially translational distance-based models, are trained through discriminating positive and negative samples. Thus, negative sampling is unquestionably a non-trivial step in KG embedding. The quality of generated negative samples can directly influence the performance of final knowledge representations in downstream tasks, such as link prediction and triple classification. This review summarizes current negative sampling methods in KRL and we categorize them into three sorts, fixed distribution-based, generative adversarial net (GAN)-based and cluster sampling. Based on this categorization we discuss the most prevalent existing approaches and their characteristics.

scholarly journals Characterization of logic program revision as an extension of propositional revision

2015 ◽  
Vol 16 (1) ◽  
pp. 111-138 ◽  
Author(s):  
NICOLAS SCHWIND ◽  
KATSUMI INOUE
Keyword(s):  
Logic Program ◽  
Nonmonotonic Reasoning ◽  
Knowledge Representation And Reasoning ◽  
Logic Programs ◽  
Characterization Result ◽  
International Conference ◽  
Complete Procedure ◽  
Boolean Lattices ◽  
Computational Properties

AbstractWe address the problem of belief revision of logic programs (LPs), i.e., how to incorporate to a LP P a new LP Q. Based on the structure of SE interpretations, Delgrande et al. (2008. Proc. of the 11th International Conference on Principles of Knowledge Representation and Reasoning (KR'08), 411–421; 2013b. Proc. of the 12th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'13), 264–276) adapted the well-known AGM framework (Alchourrón et al. 1985. Journal of Symbolic Logic 50, 2, 510–530) to LP revision. They identified the rational behavior of LP revision and introduced some specific operators. In this paper, a constructive characterization of all rational LP revision operators is given in terms of orderings over propositional interpretations with some further conditions specific to SE interpretations. It provides an intuitive, complete procedure for the construction of all rational LP revision operators and makes easier the comprehension of their semantic and computational properties. We give a particular consideration to LPs of very general form, i.e., the generalized logic programs (GLPs). We show that every rational GLP revision operator is derived from a propositional revision operator satisfying the original AGM postulates. Interestingly, the further conditions specific to GLP revision are independent from the propositional revision operator on which a GLP revision operator is based. Taking advantage of our characterization result, we embed the GLP revision operators into structures of Boolean lattices, that allow us to bring to light some potential weaknesses in the adapted AGM postulates. To illustrate our claim, we introduce and characterize axiomatically two specific classes of (rational) GLP revision operators which arguably have a drastic behavior. We additionally consider two more restricted forms of LPs, i.e., the disjunctive logic programs (DLPs) and the normal logic programs (NLPs) and adapt our characterization result to disjunctive logic program and normal logic program revision operators.

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