A Graph-Rewriting Paradigm for Discrete Relaxation

1998 ◽  
Vol 12 (06) ◽  
pp. 763-799 ◽  
Author(s):  
H. Fahmy ◽  
D. Blostein
Keyword(s):  
Complex Analysis ◽  
Contextual Information ◽  
A Priori ◽  
Image Interpretation ◽  
Semantic Interpretation ◽  
Music Notation ◽  
Image Domain ◽  
Graph Rewriting ◽  
Time Signature ◽  
Rewriting Rules

In image analysis, recognition of the primitives plays an important role. Subsequent analysis is used to interpret the arrangement of primitives. This subsequent analysis must make allowance for errors or ambiguities in the recognition of primitives. In this paper, we assume that the primitive recognizer produces a set of possible interpretations for each primitive. To reduce this primitive-recognition ambiguity, we use contextual information in the image, and apply constraints from the image domain. This process is variously termed constraint satisfaction, labeling or discrete relaxation. Existing methods for discrete relaxation are limited in that they assume a priori knowledge of the neighborhood model: before relaxation begins, the system is told (or can determine) which sets of primitives are related by constraints. These methods do not apply to image domains in which complex analysis is necessary to determine which primitives are related by constraints. For example, in music notation, we must recognize which notes belong to one measure, before it is possible to apply the constraint that the number of beats in the measure should match the time signature. Such constraints can be handled by our graph-rewriting paradigm for discrete relaxation: here neighborhood-construction is interleaved with constraint-application. In applying this approach to the recognition of simple music notation, we use approximately 180 graph-rewriting rules to express notational constraints and semantic-interpretation rules for music notation. The graph rewriting rules express both binary and higher-order notational constraints. As image-interpretation proceeds, increasingly abstract levels of interpretation are assigned to (groups of) primitives. This allows application of higher-level constraints, which can be formulated only after partial interpretation of the image.

Two Approaches to the Induction of Graph-Rewriting Rules for Function-Based Design Synthesis

2016 ◽  
Author(s):  
Julian R. Eichhoff ◽  
Felix Baumann ◽  
Dieter Roller
Keyword(s):  
Engineering Design ◽  
Conceptual Design ◽  
Automatic Generation ◽  
Production Rules ◽  
Design Synthesis ◽  
Graph Rewriting ◽  
Conceptual Engineering ◽  
Frequent Subgraph ◽  
Rule Set ◽  
Rewriting Rules

In this paper we demonstrate and compare two complementary approaches to the automatic generation of production rules from a set of given graphs representing sample designs. The first approach generates a complete rule set from scratch by means of frequent subgraph discovery. Whereas the second approach is intended to learn additional rules that fit an existing, yet incomplete, rule set using genetic programming. Both approaches have been developed and tested in the context of an application for automated conceptual engineering design, more specifically functional decomposition. They can be considered feasible, complementary approaches to the automatic inference of graph rewriting rules for conceptual design applications.

Coherence of subsumption, minimum typing and type-checking in F ≤

1992 ◽  
Vol 2 (1) ◽  
pp. 55-91 ◽  
Author(s):  
Pierre-Louis Curien ◽  
Giorgio Ghelli
Keyword(s):  
Normal Form ◽  
Type System ◽  
Lambda Calculus ◽  
Complete Information ◽  
Second Order ◽  
Semantic Interpretation ◽  
Type Checking ◽  
Rewriting System ◽  
Different Types ◽  
Rewriting Rules

A subtyping relation ≤ between types is often accompanied by a typing rule, called subsumption: if a term a has type T and T≤U, then a has type U. In presence of subsumption, a well-typed term does not codify its proof of well typing. Since a semantic interpretation is most naturally defined by induction on the structure of typing proofs, a problem of coherence arises: different typing proofs of the same term must have related meanings. We propose a proof-theoretical, rewriting approach to this problem. We focus on F≤, a second-order lambda calculus with bounded quantification, which is rich enough to make the problem interesting. We define a normalizing rewriting system on proofs, which transforms different proofs of the same typing judgement into a unique normal proof, with the further property that all the normal proofs assigning different types to a given term in a given environment differ only by a final application of the subsumption rule. This rewriting system is not defined on the proofs themselves but on the terms of an auxiliary type system, in which the terms carry complete information about their typing proof. This technique gives us three different results:— Any semantic interpretation is coherent if and only if our rewriting rules are satisfied as equations.— We obtain a proof of the existence of a minimum type for each term in a given environment.— From an analysis of the shape of normal form proofs, we obtain a deterministic typechecking algorithm, which is sound and complete by construction.

AN ABDUCTIVE REASONING BASED IMAGE INTERPRETATION SYSTEM

1996 ◽  
Vol 10 (06) ◽  
pp. 613-641
Author(s):  
SANTANU CHAUDHURY ◽  
ARBIND GUPTA ◽  
GUTURU PARTHASARATHY ◽  
S. SUBRAMANIAN
Keyword(s):  
Object Recognition ◽  
Domain Knowledge ◽  
A Priori ◽  
Image Interpretation ◽  
Abductive Reasoning ◽  
Recognition Problem ◽  
Aerial Image ◽  
Interpretation System ◽  
Different Types

This paper describes an abductive reasoning based inferencing engine for image interpretation. The inferencing strategy finds an acceptable and consistent explanation of the features detected in the image in terms of the objects known a priori. The inferencing scheme assumes representation of the domain knowledge about the objects in terms of local and/or relational features. The inferencing system can be applied for different types of image interpretation problems like 2-D and 3-D object recognition, aerial image interpretation, etc. In this paper, we illustrate functioning of the system with the help of a 2-D object recognition problem.

scholarly journals Pitch Spelling: A Computational Model

2003 ◽  
Vol 20 (4) ◽  
pp. 411-429 ◽  
Author(s):  
Emilios Cambouropoulos
Keyword(s):  
Computational Model ◽  
Success Rate ◽  
A Priori ◽  
Music Notation ◽  
Optimization Approach ◽  
Interval Optimization ◽  
Piano Sonatas ◽  
Pitch Interval ◽  
Interval Representations ◽  
Spelling Strategies

In this article, cognitive and musicological aspects of pitch and pitch interval representations are explored via computational modeling. The specific task under investigation is pitch spelling, that is, how traditional score notation can be derived from a simple unstructured 12-tone representation (e.g., pitch-class set or MIDI pitch representation). This study provides useful insights both into the domain of pitch perception and into musicological aspects of score notation strategies. A computational model is described that transcribes polyphonic MIDI pitch files into the Western traditional music notation. Input to the proposed algorithm is merely a sequence of MIDI pitch numbers in the order they appear in a MIDI file. No a priori knowledge such as key signature, tonal centers, time signature, chords, or voice separation is required. Output of the algorithm is a sequence of "correctly" spelled pitches. The algorithm is based on an interval optimization approach that takes into account the frequency of occurrence of pitch intervals within the major-minor tonal scale framework. The algorithm was evaluated on 10 complete piano sonatas by Mozart and had a success rate of 98.8% (634 pitches were spelled incorrectly out of a total of 54,418 notes); it was tested additionally on three Chopin waltzes and had a slightly worse success rate. The proposed pitch interval optimization approach is also compared with and tested against other pitch-spelling strategies.

Graph rewriting rules for RDF database evolution: optimizing side-effect processing

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jacques Chabin ◽  
Cédric Eichler ◽  
Mirian Halfeld Ferrari ◽  
Nicolas Hiot
Keyword(s):  
Side Effects ◽  
Side Effect ◽  
Choice Functions ◽  
Graph Rewriting ◽  
Content Type ◽  
Closed World ◽  
Rdf Database ◽  
Description Framework ◽  
Resource Description ◽  
Rewriting Rules

Purpose Graph rewriting concerns the technique of transforming a graph; it is thus natural to conceive its application in the evolution of graph databases. This paper aims to propose a two-step framework where rewriting rules formalize instance or schema changes, ensuring graph’s consistency with respect to constraints, and updates are managed by ensuring rule applicability through the generation of side effects: new updates which guarantee that rule application conditions hold. Design/methodology/approach This paper proposes Schema Evolution Through UPdates, optimized version (SetUpOPT), a theoretical and applied framework for the management of resource description framework (RDF)/S database evolution on the basis of graph rewriting rules. The framework is an improvement of SetUp which avoids the computation of superfluous side effects and proposes, via SetUpoptND, a flexible and extensible package of solutions to deal with non-determinism. Findings This paper shows graph rewriting into a practical and useful application which ensures consistent evolution of RDF databases. It introduces an optimised approach for dealing with side effects and a flexible and customizable way of dealing with non-determinism. Experimental evaluation of SetUpoptND demonstrates the importance of the proposed optimisations as they significantly reduce side-effect generation and limit data degradation. Originality/value SetUp originality lies in the use of graph rewriting techniques under the closed world assumption to set an updating system which preserves database consistency. Efficiency is ensured by avoiding the generation of superfluous side effects. Flexibility is guaranteed by offering different solutions for non-determinism and allowing the integration of customized choice functions.

scholarly journals Parallel Multiset Rewriting Systems with Distorted Rules

Processes ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 347
Author(s):  
Cristina Sburlan ◽  
Dragoş-Florin Sburlan
Keyword(s):  
A Priori ◽  
Rewriting Systems ◽  
Computational Universality ◽  
Level 1 ◽  
Robust Systems ◽  
Rewriting Rules

Most of the parallel rewriting systems which model (or which are inspired by) natural/artificial phenomena consider fixed, a priori defined sets of string/multiset rewriting rules whose definitions do not change during the computation. Here we modify this paradigm by defining level-t distorted rules—rules for which during their applications one does not know the exact multiplicities of at most t∈N species of objects in their output (although one knows that such objects will appear at least once in the output upon the execution of this type of rules). Subsequently, we define parallel multiset rewriting systems with t-distorted computations and we study their computational capabilities when level-1 distorted catalytic promoted rules are used. We construct robust systems able to cope with the level-1 distortions and prove the computational universality of the model.

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