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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]

Gunk (mereology) In mereology, an area of philosophical logic, the term gunk applies to any whole whose parts all have further proper parts. That is, a gunky object is not made of indivisible atoms: If something is made of atomless gunk then it divides forever into smaller and smaller parts—it is infinitely divisible. However, a line segment is infinitely divisible, and yet has atomic parts: the points. If point-sized objects are always simple, then a gunky object does not have any point-sized parts. Gunk is an important test case for accounts of the composition of material objects: for instance, Ted Sider has challenged Peter van Inwagen's account of composition because it is inconsistent with the possibility of gunk. Gunk has also played an important role in the history of topology[citation needed] (Zimmerman 1996a) and in recent debates concerning change, contact, and the structure of physical space. The term was first used by David Lewis in his work Parts of Classes (1991).

General formal ontology includes objects as well as processes and both are integrated into one coherent system,includes levels of reality,[2]is designed to support interoperability by principles of ontological mapping and reduction,contains several novel ontological modules, in particular, a module for functions and a module for roles, andis designed for applications, firstly in medical, biological, and biomedical areas, but also in the fields of economics and sociology. Taxonomic tree of GFO[edit] Basic taxonomic tree of the General Formal Ontology Categories[edit] The common property of all categories is that they can be predicated of an entity. Conceptual structures are mental representations of entities or universals, and they exist in an agent's mind. Symbolic structures are signs which may be instantiated by tokens. Space and time[edit] Connected three-dimensional parts of space are called "topoids". Processes and objects[edit] See also[edit] References[edit] External links[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.

Phylogenetic tree In a rooted phylogenetic tree, each node with descendants represents the inferred most recent common ancestor of the descendants, and the edge lengths in some trees may be interpreted as time estimates. Each node is called a taxonomic unit. Internal nodes are generally called hypothetical taxonomic units, as they cannot be directly observed. Trees are useful in fields of biology such as bioinformatics, systematics, and comparative phylogenetics. Unrooted trees illustrate only the relatedness of the leaf nodes and do not require the ancestral root to be known or inferred. History[edit] Charles Darwin (1859) also produced one of the first illustrations and crucially popularized the notion of an evolutionary "tree" in his seminal book The Origin of Species. Types[edit] Rooted tree[edit] Unrooted tree[edit] Unrooted trees illustrate the relatedness of the leaf nodes without making assumptions about ancestry. Bifurcating tree[edit] total rooted trees and total unrooted trees, where leaves.[4]

Upper ontology The seemingly conflicting use of metaphors implying a solid rigorous bottom-up "foundation" or a top-down imposition of somewhat arbitrary, and possibly political, decisions is no accident – the field is characterized by the usual mix of controversy, politics, competing approaches and academic rivalry. Some upper ontologies have led to commercial products, causing a financial incentive to promote one ontology over the competing systems. Debates notwithstanding, it can be said that a very important part of each upper ontology can be considered as the computational implementation of natural philosophy, which itself is a more empirical method for investigating the topics within the philosophical discipline of physical ontology. Library classification systems predate these upper ontology systems. Though library classifications organize and categorize knowledge using general concepts that are the same across all knowledge domains, neither system is a replacement for the other. Cyc[edit]

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.