background preloader

Mereology

Mereology
Mereology has been axiomatized in various ways as applications of predicate logic to formal ontology, of which mereology is an important part. A common element of such axiomatizations is the assumption, shared with inclusion, that the part-whole relation orders its universe, meaning that everything is a part of itself (reflexivity), that a part of a part of a whole is itself a part of that whole (transitivity), and that two distinct entities cannot each be a part of the other (antisymmetry). A variant of this axiomatization denies that anything is ever part of itself (irreflexive) while accepting transitivity, from which antisymmetry follows automatically. Standard university texts on logic and mathematics are silent about mereology, which has undoubtedly contributed to its obscurity. History[edit] A.N. In 1930, Henry Leonard completed a Harvard Ph.D. dissertation in philosophy, setting out a formal theory of the part-whole relation. Axioms and primitive notions[edit] The axioms are: Related:  philosophy treeSemantic Web

Philosophy of mathematics The terms philosophy of mathematics and mathematical philosophy are frequently used as synonyms.[1] The latter, however, may be used to refer to several other areas of study. One refers to a project of formalizing a philosophical subject matter, say, aesthetics, ethics, logic, metaphysics, or theology, in a purportedly more exact and rigorous form, as for example the labors of scholastic theologians, or the systematic aims of Leibniz and Spinoza. Another refers to the working philosophy of an individual practitioner or a like-minded community of practicing mathematicians. Additionally, some understand the term "mathematical philosophy" to be an allusion to the approach to the foundations of mathematics taken by Bertrand Russell in his books The Principles of Mathematics and Introduction to Mathematical Philosophy. Recurrent themes[edit] Recurrent themes include: What is the role of Mankind in developing mathematics? History[edit] The origin of mathematics is subject to argument. Some[who?]

Semantic network Typical standardized semantic networks are expressed as semantic triples. History[edit] Example of a semantic network "Semantic Nets" were first invented for computers by Richard H. Richens of the Cambridge Language Research Unit in 1956 as an "interlingua" for machine translation of natural languages.[2] They were independently developed by Robert F. In the late 1980s, two Netherlands universities, Groningen and Twente, jointly began a project called Knowledge Graphs, which are semantic networks but with the added constraint that edges are restricted to be from a limited set of possible relations, to facilitate algebras on the graph.[12] In the subsequent decades, the distinction between semantic networks and knowledge graphs was blurred.[13][14] In 2012, Google gave their knowledge graph the name Knowledge Graph. Basics of semantic networks[edit] A semantic network is used when one has knowledge that is best understood as a set of concepts that are related to one another. Examples[edit]

Meta-ontology Meta-ontology is a term of recent origin first used by Peter van Inwagen in analyzing Willard Van Orman Quine's critique of Rudolf Carnap's metaphysics,[1] where Quine introduced a formal technique for determining the ontological commitments in a comparison of ontologies.[2] Thomas Hofweber, while acknowledging that the use of the term is controversial, suggests that, although strictly construed meta-ontology is a separate metatheory of ontology, the field of ontology can be more broadly construed as containing its metatheory.[3][4] Advocates of the term 'meta-ontology' seek to distinguish 'ontology' (which investigates what there is) from 'meta'-ontology (which investigates what we are asking when we ask what there is).[1][5][6] Amie L. See also[edit] References[edit] ^ Jump up to: a b c Peter Van Inwagen (1998). Further reading[edit] David Chalmers, David Manley, Ryan Wasserman (2009). External links[edit]

untitled Part I. Getting Started Chapter 1. 1.1. rdf:about Sesame 2 ¶ 1.1.1. Sesame is an open source Java framework for storage and querying of RDF data. Of course, a framework isn't very useful without implementations of the various APIs. Originally, Sesame was developed by Aduna (then known as Aidministrator) as a research prototype for the hugely successful EU research project On-To-Knowledge. Sesame is currently developed as a community project, with Aduna as the project leader. 1.1.2. This user manual covers most aspects of working with Sesame in a variety of settings. The basics of programming with Sesame are covered in chapter-repository-api. chapter-http-protocol gives an overview of the structure of the HTTP REST protocol for the Sesame Server, which is useful if you want to communicate with a Sesame Server from a programming language other than Java. Chapter 2. 2.1. Sesame releases can be downloaded from Sourceforge. openrdf-sesame-(version)-sdk.tar.gz. 2.1.1. 2.1.2. 2.2. 2.3. 2.3.1.

Lyapunov fractal Standard Lyapunov logistic fractal with iteration sequence AB, in the region [2, 4] × [2, 4]. Generalized Lyapunov logistic fractal with iteration sequence AABAB, in the region [2, 4] × [2, 4]. Generalized Lyapunov logistic fractal with iteration sequence BBBBBBAAAAAA, in the growth parameter region (A,B) in [3.4, 4.0] × [2.5, 3.4], known as Zircon Zity. In mathematics, Lyapunov fractals (also known as Markus–Lyapunov fractals) are bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population, r, periodically switches between two values A and B. A Lyapunov fractal is constructed by mapping the regions of stability and chaotic behaviour (measured using the Lyapunov exponent ) in the a−b plane for given periodic sequences of a and b. (stability), and blue corresponds to (chaos). Properties[edit] Lyapunov fractals are generally drawn for values of A and B in the interval . Algorithm for generating Lyapunov fractals[edit]

Semantic University Semantic University is the largest and most accessible source of educational material relating to semantics and Semantic Web technologies. It includes: Lessons suitable to those brand new to the space. Comparisons, both high-level and in-depth, with related technologies, such as SQL, NoSQL and Big Data. Interactive, hands on tutorials. There's much more, too—learn more about Semantic University. Semantic University content is split into two sections, each with several tracks. Every lesson comes with its own Forum for further discussion.

Ontology Parmenides was among the first to propose an ontological characterization of the fundamental nature of reality. Etymology[edit] While the etymology is Greek, the oldest extant record of the word itself, the New Latin form ontologia, appeared in 1606 in the work Ogdoas Scholastica by Jacob Lorhard (Lorhardus) and in 1613 in the Lexicon philosophicum by Rudolf Göckel (Goclenius). The first occurrence in English of ontology as recorded by the OED (Oxford English Dictionary, online edition, 2008) came in a work by Gideon Harvey (1636/7–1702): Archelogia philosophica nova; or, New principles of Philosophy. Containing Philosophy in general, Metaphysicks or Ontology, Dynamilogy or a Discourse of Power, Religio Philosophi or Natural Theology, Physicks or Natural philosophy, London, Thomson, 1663.[5] The word was first used in its Latin form by philosophers based on the Latin roots, which themselves are based on the Greek. Overview[edit] Some fundamental questions[edit] Concepts[edit] Types[edit]

YAGO - D5: Databases and Information Systems (Max-Planck-Institut für Informatik) Overview YAGO is a huge semantic knowledge base, derived from Wikipedia WordNet and GeoNames. Currently, YAGO has knowledge of more than 10 million entities (like persons, organizations, cities, etc.) and contains more than 120 million facts about these entities. YAGO is special in several ways: The accuracy of YAGO has been manually evaluated, proving a confirmed accuracy of 95%. YAGO is developed jointly with the DBWeb group at Télécom ParisTech University. Philosophical realism Realists tend to believe that whatever we believe now is only an approximation of reality and that every new observation brings us closer to understanding reality.[2] In its Kantian sense, realism is contrasted with idealism. In a contemporary sense, realism is contrasted with anti-realism, primarily in the philosophy of science. History[edit] Platonic realism[edit] The Scottish School of Common Sense Realism[edit] Scottish Common Sense Realism is a school of philosophy that sought to defend naive realism against philosophical paradox and scepticism, arguing that matters of common sense are within the reach of common understanding and that common-sense beliefs even govern the lives and thoughts of those who hold non-commonsensical beliefs. Its roots can be found in responses to such philosophers as John Locke, George Berkeley and David Hume. Naïve realism[edit] Scientific realism[edit] Aesthetic realism[edit] See also[edit] Notes[edit] References[edit]

Freebase Freebase is a large collaborative knowledge base consisting of metadata composed mainly by its community members. It is an online collection of structured data harvested from many sources, including individual 'wiki' contributions.[2] Freebase aims to create a global resource which allows people (and machines) to access common information more effectively. It was developed by the American software company Metaweb and has been running publicly since March 2007. Metaweb was acquired by Google in a private sale announced July 16, 2010.[3] Google's Knowledge Graph is powered in part by Freebase.[4] Freebase data is freely available for commercial and non-commercial use under a Creative Commons Attribution License, and an open API, RDF endpoint, and database dump are provided for programmers. Overview[edit] Described by Tim O'Reilly upon their launch, "Freebase is the bridge between the bottom up vision of Web 2.0 collective intelligence and the more structured world of the semantic web

Related: