Logical Definition Research Articles

Historical Development of Modern Logic

Modern Logic began in 1879, the year in which Gottlob Frege (1848–1925) published his Begriffsschrift. In less than ninety pages this booklet presented a number of discoveries that changed the face of logic. The central achievement of the work is the theory of quantification; but this could not be obtained till the traditional decomposition of the proposition into subject and predicate had been replaced by its analysis into function and argument(s). A preliminary accomplishment was the propositional calculus, with a truth-functional d of the connectives, including the conditional. Of cardinal importance was the realization that, if circularity is to be avoided, logical derivations are to be formal, that is, have to proceed according to rules that are devoid of any intuitive logical force but simply refer to the typographical form of the expressions; thus the notion of formal system made its appearance. The rules of quantification theory, as we know them today, were then introduced. The last part of the book belongs to the foundations of mathematics, rather than to logic, and presents a logical definition of the notion of mathematical sequence. Frege’s contribution marks one of the sharpest breaks that ever occurred in the development of a science. The interest in logic, so alive in the Middle Ages, had died out at the end of the fifteenth century, and the great thinkers of the next three centuries were not attracted by logical studies. In 1787 Kant wrote that logic ‘is to all appearance complete and perfect’. One great philosopher, Leibniz (1646–1716), showed a profound and constant interest in logic. But Leibniz’s investigations are more a program than a realization. He never

Utilising integrated urban water management to assess the viability of decentralised water solutions

Cities worldwide are challenged by a number of urban water issues associated with climate change, population growth and the associated water scarcity, wastewater flows and stormwater run-off. To address these problems decentralised solutions are increasingly being considered by water authorities, and integrated urban water management (IUWM) has emerged as a potential solution to most of these urban water challenges, and as the key to providing solutions incorporating decentralised concepts at a city wide scale. To incorporate decentralised options, there is a need to understand their performance and their impact on a city's total water cycle under alternative water and land management options. This includes changes to flow, nutrient and sediment regimes, energy use, greenhouse gas emissions, and the impacts on rivers, aquifers and estuaries. Application of the IUWM approach to large cities demands revisiting the fundamental role of water system design in sustainable city development. This paper uses the extended urban metabolism model (EUMM) to expand a logical definition for the aims of IUWM, and discusses the role of decentralised systems in IUWM and how IUWM principles can be incorporated into urban water planning.

« La science de l'idée pure »

Résumé Cet article est un exercice pour comprendre la définition par Hegel de la Logique comme « la science de l’idée pure », et pour en examiner les implications. Revenant sur la question du rapport de la Logique et de la Phénoménologie, et proposant une interprétation de l’approche délibérément aporétique de la question du « commencement » par Hegel, il s’efforce ensuite de décrire les principales caractéristiques du « programme » logique, dont elles illustrent la radicalité.

On the Issue of Logic in Holistic Medicine: How to Think About Acupuncture

Abstract There are still legitimate concerns within modern medicine concerning acceptance of medical acupuncture. The core concern involves whether or not diagnosis and treatment with acupuncture has a definite, standardized, and peer-reviewable logic and rational methodology. This article explains the basis of holistic logic and the rational methodology of using acupuncture to treat and manage chronic functional complaints.

Temporally Annotated Extended Logic Programs

Extended logic programs (ELPs) are a set of logic rules with strong negation allowed in the bodies or head of the rules and weak negation ~ allowed in the bodies of the rules. ELPs enable for various forms of reasoning that cannot be achieved by definite logic programs. Answer Set Programming provides a widely acceptable semantics for ELPs. However, ELPs do not provide information regarding the temporal intervals that derived ELP literals or weakly negated ELP literals are valid. In this paper, we associate ELP rules with their validity temporal interval, resulting in a temporally annotated logic program. A ground temporal literal has the form L:i, where L is a ground ELP literal or weakly negated ELP literal and i is a temporal interval. We define (simple) entailment and maximal entailment of a ground temporal literal L:i from a temporally annotated logic program C. Both kinds of entailment are based on Answer Set Programming. Additionally, we provide an algorithm that for an ELP literal or a weakly negated ELP literal L returns a list with all temporal intervals i such that a temporally annotated logic program C maximally entails L:i. Based on this algorithm, the answer of various kinds of temporal queries can be provided.

Provenance and Temporally Annotated Logic Programming

In this paper, we consider provenance and temporally annotated logic rules (pt-logic rules, for short), which are definite logic programming rules associated with the name of the source that they originate and the temporal interval during which they are valid. A collection of pt-logic rules form a provenance and temporally annotated logic program P, called pt-logic program, for short. We develop a model theory for P and define its maximally temporal entailments of the form A:<S, ti>, indicating that atom A is derived from a set of sources S and holds at a maximal temporal interval ti, according to S. We define a consequence operator that derives exactly the maximally temporal entailments of P for a set of sources. We show that the complexity of the considered entailment is EXPTIME-complete.

MIGRAÇÃO E CIDADES MÉDIAS: uma análise de Uberlândia

The migratory question has been integrated to the theoretical speeches as important condicionante in the analysis of the dynamic of the societies. The insertion of migrants in many localities is given in function of internal structural characteristics, as in Uberlândia-MG case, which in some moments receives migratory processes. The main objective of this study is to relate average migrations and cities, in order to present the importance of demographic components in the organization of urban spaces. The methodology privileged the analysis of theories that, later, had been interpreted in the light of the statistical data on migration, and also related with historical data of economic growth of the city. Such procedures allowed us to conclude that the organization of an average city, destination of migrants of intense form, can not have its definitive urban logic without all the migratory insertion considered, either by economic aspects (generation or not of jobs) or by the social benefits (housings and schools), for example. In the context of the average cities, study the insertion of the migratory flows is important since they have significant contents for the organization of such locations.

A specialization of definitions in common knowledge logic

It is known that one of main aims of specializations of derivations in nonclassical logics is the various tools which allow us to simplify the searching of termination of derivations. The traditional techniques used to ensure termination of derivations in various non-classical logics are based on loop-checking. In this paper the reflexive common knowledge logic based on modal logic K2 is considered. For considered logic a sequent calculus with specialized non-logical (loop-type) axioms is presented.&#x0D;

Translation and Interpretation in Ibn Taymiyya's Logical Definition

This article deals with the concepts of translation and interpretation in Ibn Taymiyya's Theory of Definition. Translation is replacement of one name by another or of one named object by another, while, Interpretation is replacement of one name by a named object or of a named object by a name. The relationship between the definition and the definiendum is decided by the law of al-Tard wa al-'Aks (coextensiveness-cumcoexclusiveness) that looks at objects from all sides and decides the traits of the definiendum. It also aims at deciding the signification of the name and this is also the aim of the definition. Since the ‘name’; is a linguistic matter, the definition is related to the signification of the name and its language.

The Gene Ontology: enhancements for 2011

The Gene Ontology (GO) (http://www.geneontology.org) is a community bioinformatics resource that represents gene product function through the use of structured, controlled vocabularies. The number of GO annotations of gene products has increased due to curation efforts among GO Consortium (GOC) groups, including focused literature-based annotation and ortholog-based functional inference. The GO ontologies continue to expand and improve as a result of targeted ontology development, including the introduction of computable logical definitions and development of new tools for the streamlined addition of terms to the ontology. The GOC continues to support its user community through the use of e-mail lists, social media and web-based resources.

Disease Ontology: a backbone for disease semantic integration

The Disease Ontology (DO) database (http://disease-ontology.org) represents a comprehensive knowledge base of 8043 inherited, developmental and acquired human diseases (DO version 3, revision 2510). The DO web browser has been designed for speed, efficiency and robustness through the use of a graph database. Full-text contextual searching functionality using Lucene allows the querying of name, synonym, definition, DOID and cross-reference (xrefs) with complex Boolean search strings. The DO semantically integrates disease and medical vocabularies through extensive cross mapping and integration of MeSH, ICD, NCI's thesaurus, SNOMED CT and OMIM disease-specific terms and identifiers. The DO is utilized for disease annotation by major biomedical databases (e.g. Array Express, NIF, IEDB), as a standard representation of human disease in biomedical ontologies (e.g. IDO, Cell line ontology, NIFSTD ontology, Experimental Factor Ontology, Influenza Ontology), and as an ontological cross mappings resource between DO, MeSH and OMIM (e.g. GeneWiki). The DO project (http://diseaseontology.sf.net) has been incorporated into open source tools (e.g. Gene Answers, FunDO) to connect gene and disease biomedical data through the lens of human disease. The next iteration of the DO web browser will integrate DO's extended relations and logical definition representation along with these biomedical resource cross-mappings.

Ibrahim Al-Khalil between Ur the city and the state, a study in the biblical text

Religious books and historical narrations did not give the personality of the Prophet Ibrahim Al-Khalil any consistent and accurate historical connotations, despite the fact that he laid the foundations for religious monotheism in the ancient world. Therefore, confusion and inaccuracy prevailed in the texts that talk about his birth, upbringing, and then his call, and reliable texts did not appear to us in A logical definition of this issue, whether what came in the Torah and the Holy Qur’an, and each of them followed its own approach. The Torah has dealt with the issue of lineage and migration accurately and has significance on the basis of returning the Jews to Abraham and that they are the ones who inherit the land of Canaan ().As for the Holy Qur’an, its mention of Abraham was characterized by a doctrinal and intellectual character in terms of its mention of the prophets and how their work was to establish the foundations of truth so that they would be lessons and lessons for others and a model for them to follow.

Processes in Lingua Cosmica

In a sequence of papers on the topic of message construction for interstellar communication by means of a cosmic language, representations of various kinds of concepts of reality in a Lingua Cosmica system [1]. Those studied were logic relations of a static character. The present contribution contains an important, fundamental extension: groundwork is done for the purpose of interpreting (dynamic) proc esses of various sorts in the linguistic system. Individual processes are abstracted in a logic sense and provided with basic properties as termination and communication functions. They can be combined into kinds of processes: sequential and parallel ones represented by only one inductive definition in logic. Based on concepts from the so-called process algebra, processes are provided with channel s mapping them to their states. State vectors are introduced to represent states of conglomerates of processes. Communication between processes (locally or globally) is effectuated by means of state transitions. Together with a programmed arb itration function, state vectors play a crucial role in representing communication. With these ingredients possibilities for general interpretations of a wide range of processes in the Lingua Cosmica system come in view.

Improving ontologies by automatic reasoning and evaluation of logical definitions

BackgroundOntologies are widely used to represent knowledge in biomedicine. Systematic approaches for detecting errors and disagreements are needed for large ontologies with hundreds or thousands of terms and semantic relationships. A recent approach of defining terms using logical definitions is now increasingly being adopted as a method for quality control as well as for facilitating interoperability and data integration.ResultsWe show how automated reasoning over logical definitions of ontology terms can be used to improve ontology structure. We provide the Java software package GULO (Getting an Understanding of LOgical definitions), which allows fast and easy evaluation for any kind of logically decomposed ontology by generating a composite OWL ontology from appropriate subsets of the referenced ontologies and comparing the inferred relationships with the relationships asserted in the target ontology. As a case study we show how to use GULO to evaluate the logical definitions that have been developed for the Mammalian Phenotype Ontology (MPO).ConclusionsLogical definitions of terms from biomedical ontologies represent an important resource for error and disagreement detection. GULO gives ontology curators a fast and simple tool for validation of their work.

Cataloguing/analogizing: A nonmonotonic view

Reasoning deductively under incomplete information is nonmonotonic in nature since the arrival of additional information may invalidate or reverse previously obtained conclusions. It amounts to apply generic default rules in an appropriate way to a particular (partially described) situation. This type of nonmonotonic reasoning can only provide plausible conclusions. Analogical reasoning is another form of commonly used reasoning that yields brittle conclusions. It is nondeductive in nature and proceeds by putting particular situations in parallel. Analogical reasoning also exhibits nonmonotonic features, as investigated in this paper when particular situations may be incompletely stated. The paper reconsiders the pattern of plausible reasoning proposed by Polya, “a and b are analogous, a is true, then b true is more credible,'' from a nonmonotonic reasoning point of view. A representation of the statement “a and b are analogous” in terms of nonmonotonic consequences relations is presented. This representation is then related to a logical definition of analogical proportions, i.e. statements of the form “a is to b as c is to d” that has been recently proposed and extended to other types of proportions. Remarkably enough, semantic equivalence between conditional objects of the form “b given a,” which have been shown as being at the root of nonmonotonic reasoning, constitutes another type of noticeable proportions. By offering a parallel between two important forms of commonsense reasoning, this paper enriches the comparison between nonmonotonic reasoning and analogical reasoning that is not often made. © 2011 Wiley Periodicals, Inc. (This paper is a revised and expanded version of an unpublished article with the same title presented at the International Conference celebrating 30 years of Nonmonotonic Reasoning ([email protected]), held in Lexington, KY. Oct. 22–25, 2010. Available at http://sites.google.com/site/nonmonat30/conference-materials; accessed on October 6, 2011.)

A LOGICAL ANALYSIS OF RULE INCONSISTENCY

Representing knowledge in a rule-based system takes place by means of "if…then…" statements. These are called production rules for the reason that new information is produced when the rule fires. The logic attached to rule-based systems is taken to be classical inasmuch as "if…then…" is encoded by material implication. However, it appears that the notion of triggering "if…then…" amounts to different logical definitions. The paper investigates the matter, with an emphasis upon consistency because reading "if… then…" statements as rules calls for a notion of rule consistency that does not conform with consistency in the classical sense. Natural deduction is used to explore entailment and equivalence among various formulations and properties.

Can Tymoczko be translated into Africa? Refractions of research methodology in translation studies in African contexts

This article considers the implications of current developments in research methodology in translation studies for translation studies in Africa. It makes use of Tymoczko's (2006, 2007) arguments in favour of the internationalisation of translation studies as well as her notions on the underlying logic of research and definition in translation studies. Tymoczko's suggestions are combined with that of Susam-Sarajevo's (2002) travel theory and Gentzler's (2008) identity theory of translation to ponder the implications of postpositivist research methodology for the African context. The article suggest Indigenous Knowledge Systems (IKS), case study, ethnography, and historiography as research methods that would support the notion that translation research in Africa should be contextualised. It further suggests alternative forms of logic in an effort to decolonise the perspective of the field of study in Africa.

Non-termination analysis of logic programs with integer arithmetics

AbstractIn the past years, analyzers have been introduced to detect classes of non-terminating queries for definite logic programs. Although these non-termination analyzers have shown to be rather precise, their applicability on real-life Prolog programs is limited because most Prolog programs use non-logical features. As a first step towards the analysis of Prolog programs, this paper presents a non-termination condition for Logic Programs containing integer arithmetics. The analyzer is based on our non-termination analyzer presented at International Logic Programming Conference (ICLP) 2009. The analysis starts from a class of queries and infers a subclass of non-terminating ones. In first phase, we ignore the outcome (success or failure) of the arithmetic operations, assuming success of all arithmetic calls. In second phase, we characterize successful arithmetic calls as a constraint problem, the solution of which determines the non-terminating queries.

Automating generation of textual class definitions from OWL to English

BackgroundText definitions for entities within bio-ontologies are a cornerstone of the effort to gain a consensus in understanding and usage of those ontologies. Writing these definitions is, however, a considerable effort and there is often a lag between specification of the main part of an ontology (logical descriptions and definitions of entities) and the development of the text-based definitions. The goal of natural language generation (NLG) from ontologies is to take the logical description of entities and generate fluent natural language. The application described here uses NLG to automatically provide text-based definitions from an ontology that has logical descriptions of its entities, so avoiding the bottleneck of authoring these definitions by hand.ResultsTo produce the descriptions, the program collects all the axioms relating to a given entity, groups them according to common structure, realises each group through an English sentence, and assembles the resulting sentences into a paragraph, to form as ‘coherent’ a text as possible without human intervention. Sentence generation is accomplished using a generic grammar based on logical patterns in OWL, together with a lexicon for realising atomic entities. We have tested our output for the Experimental Factor Ontology (EFO) using a simple survey strategy to explore the fluency of the generated text and how well it conveys the underlying axiomatisation. Two rounds of survey and improvement show that overall the generated English definitions are found to convey the intended meaning of the axiomatisation in a satisfactory manner. The surveys also suggested that one form of generated English will not be universally liked; that intrusion of too much ‘formal ontology’ was not liked; and that too much explicit exposure of OWL semantics was also not liked.ConclusionsOur prototype tools can generate reasonable paragraphs of English text that can act as definitions. The definitions were found acceptable by our survey and, as a result, the developers of EFO are sufficiently satisfied with the output that the generated definitions have been incorporated into EFO. Whilst not a substitute for hand-written textual definitions, our generated definitions are a useful starting point.AvailabilityAn on-line version of the NLG text definition tool can be found at http://swat.open.ac.uk/tools/. The questionaire and sample generated text definitions may be found at http://mcs.open.ac.uk/nlg/SWAT/bio-ontologies.html.

Modal abstractions of concurrent behavior

We present an effective algorithm for the automatic construction of finite modal transition systems as abstractions of potentially infinite concurrent processes. Modal transition systems are recognized as valuable abstractions for model checking because they allow for the validation as well as refutation of safety and liveness properties. However, the algorithmic construction of finite abstractions from potentially infinite concurrent processes is a missing link that prevents their more widespread usage for model checking of concurrent systems. Our algorithm is a worklist algorithm using concepts from abstract interpretation and operating upon mappings from sets to intervals in order to express simultaneous over- and underapproximations of the multisets of process actions available in a particular state. We obtain a finite abstraction that is 3-valued in both states and transitions and that supports the definition of a 3-valued modal logic for validating as well as refuting properties of systems. The construction is illustrated on a few examples, including the Ingemarsson-Tang-Wong key agreement protocol.