# 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 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 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 Recurrent themes include: What is the role of Mankind in developing mathematics? History The origin of mathematics is subject to argument. Some[who?]

Semantic network Typical standardized semantic networks are expressed as semantic triples. History 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 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

Holographic principle In a larger sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure "painted" on the cosmological horizon[clarification needed], such that the three dimensions we observe are an effective description only at macroscopic scales and at low energies. Cosmological holography has not been made mathematically precise, partly because the particle horizon has a finite area and grows with time.[4][5] The holographic principle was inspired by black hole thermodynamics, which conjectures that the maximal entropy in any region scales with the radius squared, and not cubed as might be expected. In the case of a black hole, the insight was that the informational content of all the objects that have fallen into the hole might be entirely contained in surface fluctuations of the event horizon. Black hole entropy An object with entropy is microscopically random, like a hot gas. Black hole information paradox Limit on information density

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 References ^ Jump up to: a b c Peter Van Inwagen (1998). Further reading David Chalmers, David Manley, Ryan Wasserman (2009). External links

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.

Direct and indirect realism Naïve realism argues we perceive the world directly Naïve realism, also known as direct realism or common sense realism, is a philosophy of mind rooted in a theory of perception that claims that the senses provide us with direct awareness of the external world. In contrast, some forms of idealism assert that no world exists apart from mind-dependent ideas and some forms of skepticism say we cannot trust our senses. Naïve realism is known as direct as against indirect or representative realism when its arguments are developed to counter the latter position, also known as epistemological dualism;[2] that our conscious experience is not of the real world but of an internal representation of the world. Theory The naïve realist theory may be characterized as the acceptance of the following five beliefs: In the area of visual perception in psychology, the leading direct realist theorist was J. Naïve and scientific realism Realism and quantum physics References See also

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 Lyapunov fractals are generally drawn for values of A and B in the interval . Algorithm for generating Lyapunov fractals

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.

Geometrical frustration In condensed matter physics, the term geometrical frustration (or in short: frustration [1]) refers to a phenomenon, where atoms tend to stick to non-trivial positions or where, on a regular crystal lattice, conflicting inter-atomic forces (each one favoring rather simple, but different structures) lead to quite complex structures. As a consequence of the frustration in the geometry or in the forces, a plenitude of distinct ground states may result, at zero temperature, and usual thermal ordering may be suppressed, at higher temperatures. Much studied examples are amorphous materials, glasses, or dilute magnets. Magnetic ordering Similarly in three dimensions, four spins arranged in a tetrahedron (Figure 2) may experience geometric frustration. Figure 1: Antiferromagnetically interacting spins in a triangular arrangement Figure 2: Antiferromagnetically interacting spins in a tetrahedral arrangement Figure 3: Spins along the easy axes of a tetrahedron Mathematical definition resp.

Ontology Parmenides was among the first to propose an ontological characterization of the fundamental nature of reality. Etymology 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 Some fundamental questions Concepts Types

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