text stringlengths 31 999 | source stringclasses 5 values |
|---|---|
A sleeper wall may refer to the following types of walls:
sleeper wall is a short wall used to support floor joists, beam and block or hollowcore slabs at ground floor. It is constructed in this fashion when a suspended floor(Also called suspended slab) is required due to bearing conditions or ground water presence. Essentially it is a wall in the way that it is constructed but a sleeper in the way that it functions | https://huggingface.co/datasets/fmars/wiki_stem |
Snecked masonry has a mixture of roughly squared stones of different sizes. It is laid in horizontal courses with rising stones projecting through the courses of smaller stones. Yet smaller fillers called snecks also occur in the courses | https://huggingface.co/datasets/fmars/wiki_stem |
In architecture, a squinch is a triangular corner that supports the base of a dome. Its visual purpose is to translate a rectangle into an octagon. See also: pendentive | https://huggingface.co/datasets/fmars/wiki_stem |
A stair carpet is a linear carpet or rug, that runs up/down on interior staircases usually, and occasionally on exterior stairways.
Description
Since 'wall to wall' fitted carpeting became very popular in the late 1950s, the word can now also describe a less notable design element than it traditionally did formerly.
A traditional stair carpet was characterized by not covering the full width of the stair but leaving the underlying wood−stone−tile of the tread and risers open to view on the sides | https://huggingface.co/datasets/fmars/wiki_stem |
Stone walls are a kind of masonry construction that has been used for thousands of years. The first stone walls were constructed by farmers and primitive people by piling loose field stones into a dry stone wall. Later, mortar and plaster were used, especially in the construction of city walls, castles, and other fortifications before and during the Middle Ages | https://huggingface.co/datasets/fmars/wiki_stem |
A storefront or shopfront is the facade or entryway of a retail store located on the ground floor or street level of a commercial building, typically including one or more display windows. A storefront functions to attract visual attention to a business and its merchandise.
History
Before the middle of the 19th century, shop fronts did not have large display windows, but often included features such as awnings and bay windows to attract the attention of passersby | https://huggingface.co/datasets/fmars/wiki_stem |
A sunburst is a design or figure commonly used in architectural ornaments and design patterns and possibly pattern books. It consists of rays or "beams" radiating out from a central disk in the manner of sunbeams. Sometimes part of a sunburst, a semicircular or semi-elliptical shape, is used | https://huggingface.co/datasets/fmars/wiki_stem |
In architecture and landscape architecture, a sunken courtyard, sometimes called a sunken plaza, is a courtyard below ground level.
Gallery
References
Al-Mumin, Adil A. (January 2001) | https://huggingface.co/datasets/fmars/wiki_stem |
In classical architecture, a tambour (Fr. : "drum") is the inverted bell of the Corinthian capital around which are carved acanthus leaves for decoration. The term also applies to the wall of a circular structure, whether on the ground or raised aloft on pendentives and carrying a dome (also known as a tholobate), and to the drum-shaped segments of a column, which is built up in several courses | https://huggingface.co/datasets/fmars/wiki_stem |
Twig-work is the term applied to architectural details constructed of twigs and branches to form decorative motifs in buildings and furniture. Carpentry or woodworking using wood that has not been milled into lumber and is still in its natural shape describes the national park service rustic style.
Construction
Joinery on twigs and branches is similar to joinery for lumber | https://huggingface.co/datasets/fmars/wiki_stem |
A wall dormer is a dormer whose facial plane is integral with the facial plane of the wall that it is built into, breaking the line of the eaves of a building.
Wall dormers are less commonly seen than typical “roof dormers”. They locate the window flush with the wall plane above or through the cornice line | https://huggingface.co/datasets/fmars/wiki_stem |
Wallwashing is a popular name for a lighting design technique for illumination of large surfaces. It is mainly used with contemporary architecture; in public cultural buildings, museums and galleries; and in landscape lighting.
Most of what one actually sees, entering a room, are the vertical surfaces | https://huggingface.co/datasets/fmars/wiki_stem |
A water table is a projection of lower masonry on the outside of a wall slightly above the ground.
It is both a functional and architectural feature that consists of a projection that deflects water running down the face of a building away from lower courses or the foundation. A water table may also be primarily decorative, as found near the base of a wall or at a transition between materials, such as from stone to brick | https://huggingface.co/datasets/fmars/wiki_stem |
A wet bar is a small bar used for mixing and serving alcoholic beverages that includes a sink with running water, as opposed to a "dry bar" that does not include a sink. A wet bar can increase the rate at which drinks are served because of the sink, which allows for glasses to be cleaned immediately. The sink may also be used for cleaning glassware as well as spills that may happen | https://huggingface.co/datasets/fmars/wiki_stem |
Window coverings are considered any type of materials used to cover a window to manage sunlight, privacy, additional weatherproofing or for purely decorative purposes.
Window coverings are typically used on the interior side of windows, but exterior solutions are also available.
Types of coverings include:
Curtains and drapes
Window blinds, including:
Venetian blinds: Natural Wood, Faux Wood, Vinyl, Aluminum
Vertical blinds
Mini blinds: Vinyl, Aluminum, Micro blinds
Window shutters, including:
traditional Colonial style & plantation shutters with larger louver sizes
Window shades, including:
Roman shades
Roller shades
Pleated shades
Sheer shades
Cellular shades
Solar screens
Various types of boarding, nailed or screwed to the window casing, can be used as temporary window covering | https://huggingface.co/datasets/fmars/wiki_stem |
Hylozoic Ground is an interactive model of architecture which was presented in the Venice Biennale of 2010 and the 18th Biennale of Sydney in 2012. Hylozoic Ground is an exemplar of live architecture: it is an installation by Philip Beesley, who is a professor at the University of Waterloo.
Hylozoism
Hylozoism is the word from which "Hylozoic" is derived | https://huggingface.co/datasets/fmars/wiki_stem |
A floating restaurant is a vessel, usually a large steel barge or hulk, used as a restaurant on water. The Jumbo Kingdom, formerly located at Aberdeen in Hong Kong, was at one time the world's largest floating restaurant, until it sank at sea in 2022. Sometimes retired ships are given a second lease on life as floating restaurants | https://huggingface.co/datasets/fmars/wiki_stem |
JUnit is a unit testing framework for the Java programming language. JUnit has been important in the development of test-driven development, and is one of a family of unit testing frameworks which is collectively known as xUnit that originated with SUnit.
JUnit is linked as a JAR at compile-time | https://huggingface.co/datasets/fmars/wiki_stem |
JXTA (Juxtapose) was an open-source peer-to-peer protocol specification begun by Sun Microsystems in 2001. The JXTA protocols were defined as a set of XML messages which allow any device connected to a network to exchange messages and collaborate independently of the underlying network topology.
As JXTA was based upon a set of open XML protocols, it could be implemented in any modern computer language | https://huggingface.co/datasets/fmars/wiki_stem |
Kojo is a programming language and integrated development environment (IDE) for computer programming and learning. It has many different features that enable playing, exploring, creating, and learning in the areas of computer programming, mental skills, (interactive) math, graphics, art, music, science, animation, games, and electronics. Kojo draws ideas from the programming languages Logo and Processing | https://huggingface.co/datasets/fmars/wiki_stem |
Liquibase is an open-source database-independent library for tracking, managing and applying database schema changes. It was started in 2006 to allow easier tracking of database changes, especially in an agile software development environment.
Overview
All changes to the database are stored in text files (XML, YAML, JSON or SQL) and identified by a combination of an "id" and "author" tag as well as the name of the file itself | https://huggingface.co/datasets/fmars/wiki_stem |
NetLogo is a programming language and integrated development environment (IDE) for agent-based modeling.
About
NetLogo was designed by Uri Wilensky, in the spirit of the programming language Logo, to be "low threshold and no ceiling". It teaches programming concepts using agents in the form of turtles, patches, links and the observer | https://huggingface.co/datasets/fmars/wiki_stem |
Netty is a non-blocking I/O client-server framework for the development of Java network applications such as protocol servers and clients. The asynchronous event-driven network application framework and tools are used to simplify network programming such as TCP and UDP socket servers. Netty includes an implementation of the reactor pattern of programming | https://huggingface.co/datasets/fmars/wiki_stem |
Object-Graph Navigation Language (OGNL) is an open-source Expression Language (EL) for Java, which, while using simpler expressions than the full range of those supported by the Java language, allows getting and setting properties (through defined setProperty and getProperty methods, found in JavaBeans), and execution of methods of Java classes. It also allows for simpler array manipulation.
It is aimed to be used in Java EE applications with taglibs as expression language | https://huggingface.co/datasets/fmars/wiki_stem |
OpenPDF is a free Java library for creating and editing PDF files with the Mozilla Public License and the GNU Library General Public License free software license. It is a fork of iText, created because the license of iText was changed from LGPL / MPL to a dual AGPL and proprietary license in order for the original authors to sell a proprietary version of the software. Version 1 | https://huggingface.co/datasets/fmars/wiki_stem |
Jakarta EE, formerly Java Platform, Enterprise Edition (Java EE) and Java 2 Platform, Enterprise Edition (J2EE), is a set of specifications, extending Java SE with specifications for enterprise features such as distributed computing and web services. Jakarta EE applications are run on reference runtimes, that can be microservices or application servers, which handle transactions, security, scalability, concurrency and management of the components they are deploying.
Jakarta EE is defined by its specification | https://huggingface.co/datasets/fmars/wiki_stem |
The phoneME project is Sun Microsystems reference implementation of Java virtual machine and associated libraries of Java ME with source, licensed under the GNU General Public License.
The phoneME library includes implementations of Connected Limited Device Configuration (CLDC) and Mobile Information Device Profile (MIDP) as well as complete or partial implementations for some optional package JSRs.
Optional Java ME packages implementations
phoneME provide complete or partial implementations for the following JSRs:
PDA Optional Packages for the J2ME Platform (JSR 75)
Java APIs for Bluetooth (JSR 82)
Wireless Messaging API and Wireless Messaging API 2 | https://huggingface.co/datasets/fmars/wiki_stem |
Play Framework is an open-source web application framework which follows the model–view–controller (MVC) architectural pattern. It is written in Scala and usable from other programming languages that are compiled to JVM bytecode, e. g | https://huggingface.co/datasets/fmars/wiki_stem |
PlayN is an open source Java software framework and set of libraries intended to create multi-platform games and distributed under the Apache License 2. 0. It was started on January 19, 2011 as a game abstraction library built over GWT and was previously named Forplay | https://huggingface.co/datasets/fmars/wiki_stem |
Processing is a free graphical library and integrated development environment (IDE) built for the electronic arts, new media art, and visual design communities with the purpose of teaching non-programmers the fundamentals of computer programming in a visual context.
Processing uses the Java language, with additional simplifications such as additional classes and aliased mathematical functions and operations. It also provides a graphical user interface for simplifying the compilation and execution stage | https://huggingface.co/datasets/fmars/wiki_stem |
RiTa is an open-source software toolkit for generative writing and English natural language, originally developed using the Java language by Daniel C. Howe and collaborators, and later implemented in JavaScript as rita. js | https://huggingface.co/datasets/fmars/wiki_stem |
RMI-IIOP (read as "RMI over IIOP") denotes the Java Remote Method Invocation (RMI) interface over the Internet Inter-Orb Protocol (IIOP), which delivers Common Object Request Broker Architecture (CORBA) distributed computing capabilities to the Java platform. It was initially based on two specifications: the Java Language Mapping to OMG IDL, and CORBA/IIOP 2. 3 | https://huggingface.co/datasets/fmars/wiki_stem |
SafeTSA (Safe Typed Single Assignment) is a static single assignment form (SSA) intermediate representation capable of representing all of the type safety of the Java programming language and the standard Java Virtual Machine (JVM) byte-code.
As of 2005, many optimizing compilers (including just-in-time compilers used by JVMs) use SSA representations internally.
A typical just-in-time compiler for a JVM converts JVM stack-machine byte-code into an internal static-single-assignment representation, performs optimizations, converts the SSA form to a low-level form similar to the host CPU's machine code, and performs some platform-specific optimizations before finally creating the native code that gets executed | https://huggingface.co/datasets/fmars/wiki_stem |
Scalatra is a free and open source web application framework written in Scala. It is a port of the Sinatra framework written in Ruby. Scalatra is an alternative to the Lift, Play!, and Unfiltered frameworks | https://huggingface.co/datasets/fmars/wiki_stem |
The service-oriented computing environment (SORCER) is a distributed computing platform implemented in Java. It allows writing network-programs (called "exertions") that operate on wrapped applications (services) to spread across the network. SORCER is often utilized in scenarios similar to those where grids are used (grid computing) in order to run parallel tasks | https://huggingface.co/datasets/fmars/wiki_stem |
Apache Spark is an open-source unified analytics engine for large-scale data processing. Spark provides an interface for programming clusters with implicit data parallelism and fault tolerance. Originally developed at the University of California, Berkeley's AMPLab, the Spark codebase was later donated to the Apache Software Foundation, which has maintained it since | https://huggingface.co/datasets/fmars/wiki_stem |
Streaming API for XML (StAX) is an application programming interface (API) to read and write XML documents, originating from the Java programming language community.
Traditionally, XML APIs are either:
DOM based - the entire document is read into memory as a tree structure for random access by the calling application
event based - the application registers to receive events as entities are encountered within the source document. Both have advantages: DOM, for example, allows for random access to the document, and event driven algorithm like SAX has a small memory footprint and is typically much faster | https://huggingface.co/datasets/fmars/wiki_stem |
SwingWorker is a popular utility class developed by Sun Microsystems for the Swing library of the Java programming language. SwingWorker enables proper use of the event dispatching thread. As of Java 6, SwingWorker is included in the JRE | https://huggingface.co/datasets/fmars/wiki_stem |
Apache SystemDS (Previously, Apache SystemML) is an open source ML system for the end-to-end data science lifecycle.
SystemDS's distinguishing characteristics are:
Algorithm customizability via R-like and Python-like languages.
Multiple execution modes, including Standalone, Spark Batch, Spark MLContext, Hadoop Batch, and JMLC | https://huggingface.co/datasets/fmars/wiki_stem |
TestNG is a testing framework for the Java programming language created by Cédric Beust and inspired by JUnit and NUnit. The design goal of TestNG is to cover a wider range of test categories: unit, functional, end-to-end, integration, etc. , with more powerful and easy-to-use functionalities | https://huggingface.co/datasets/fmars/wiki_stem |
A tuple space is an implementation of the associative memory paradigm for parallel/distributed computing. It provides a repository of tuples that can be accessed concurrently. As an illustrative example, consider that there are a group of processors that produce pieces of data and a group of processors that use the data | https://huggingface.co/datasets/fmars/wiki_stem |
Virtual Token Descriptor for eXtensible Markup Language (VTD-XML) refers to a collection of cross-platform XML processing technologies centered on a non-extractive XML, "document-centric" parsing technique called Virtual Token Descriptor (VTD). Depending on the perspective, VTD-XML can be viewed as one of the following:
A "Document-Centric" XML parser
A native XML indexer or a file format that uses binary data to enhance the text XML
An incremental XML content modifier
An XML slicer/splitter/assembler
An XML editor/eraser
A way to port XML processing on chip
A non-blocking, stateless XPath evaluatorVTD-XML is developed by XimpleWare and dual-licensed under GPL and proprietary license. It is originally written in Java, but is now available in C, C++ and C# | https://huggingface.co/datasets/fmars/wiki_stem |
A web container (also known as a servlet container;
and compare "webcontainer") is the component of a web server that interacts with Jakarta Servlets. A web container is responsible for managing the lifecycle of servlets, mapping a URL to a particular servlet and ensuring that the URL requester has the correct access-rights. A web container handles requests to servlets, Jakarta Server Pages (JSP) files, and other types of files that include server-side code | https://huggingface.co/datasets/fmars/wiki_stem |
XMLBeans is a Java-to-XML binding framework which is part of the Apache Software Foundation XML project.
Description
XMLBeans is a tool that allows access to the full power of XML in a Java friendly way. The idea is to take advantage of the richness and features of XML and XML Schema and have these features mapped as naturally as possible to the equivalent Java language and typing constructs | https://huggingface.co/datasets/fmars/wiki_stem |
ZK is an open-source Ajax Web application framework, written in Java, that enables creation of graphical user interfaces for Web applications with little required programming knowledge.
The core of ZK consists of an Ajax-based event-driven mechanism, over 123 XUL and 83 XHTML-based components, and a mark-up language for designing user interfaces. Programmers design their application pages in feature-rich XUL/XHTML components, and manipulate them upon events triggered by end user's activity | https://huggingface.co/datasets/fmars/wiki_stem |
Flake or a Vector Shape is a programming library that is used in Calligra Suite and the KOffice 2 series. Flake provides the basic concept of a "shape". To the end user a shape appears as some piece of content such as an image or a text | https://huggingface.co/datasets/fmars/wiki_stem |
KHTML is a discontinued browser engine that was developed by the KDE project. It originated as the engine of the Konqueror browser in the late 1990s, but active development ceased in 2016. It was officially discontinued in 2023 | https://huggingface.co/datasets/fmars/wiki_stem |
Kross is a scripting framework for KDE Frameworks. Originally Kross was designed for use in KOffice but eventually became the official scripting framework in KDE Software Compilation 4. Kross is designed to provide full scripting power for users of KDE applications, with a language of their own choice; and make it easy for developers targeting the KDE platform to enable their application with support for multiple scripting languages (without themselves needing to be proficient in any of them) | https://huggingface.co/datasets/fmars/wiki_stem |
NEPOMUK (Networked Environment for Personal, Ontology-based Management of Unified Knowledge) is an open-source software specification that is concerned with the development of a social semantic desktop that enriches and interconnects data from different desktop applications using semantic metadata stored as RDF. Between 2006 and 2008 it was funded by a European Union research project of the same name that grouped together industrial and academic actors to develop various Semantic Desktop technologies.
Implementations
Three active implementations of NEPOMUK exist: A C++/KDE-based variant, a Java-based variant, and a commercial version | https://huggingface.co/datasets/fmars/wiki_stem |
Phonon is the multimedia API provided by KDE and is the standard abstraction for handling multimedia streams within KDE software and also used by several Qt applications.
Phonon was originally created to allow KDE and Qt software to be independent of any single multimedia framework such as GStreamer or xine and to provide a stable API for a major version's lifetime. It was done for various reasons: to create a simple KDE/Qt style multimedia API, to better support native multimedia frameworks on Windows and macOS, and to fix problems of frameworks becoming unmaintained or having API or ABI instability | https://huggingface.co/datasets/fmars/wiki_stem |
ThreadWeaver is a system library initially developed for KDE Software Compilation 4 and later refactored for KDE Frameworks 5. ThreadWeaver allows developers to easily take advantage of multi-core processors and multithreading. In ThreadWeaver the workload is divided into individual jobs, then relationship between jobs (what order they should be completed or which has a higher priority); from that ThreadWeaver will work out the most efficient way to execute them | https://huggingface.co/datasets/fmars/wiki_stem |
XMLGUI is a KDE framework for designing the user interface of an application using XML, using the idea of actions.
In this framework, the programmer designs various actions that their application can implement, with several actions defined for the programmer by the KDE framework, such as opening a file or closing the application. Each action can be associated with various data including icons, explanatory text, and tooltips | https://huggingface.co/datasets/fmars/wiki_stem |
aRts (which stands for analog real time synthesizer) is an audio framework that is no longer under development. It was best known for previously being used in K Desktop Environment 2 and 3 to simulate an analog synthesizer.
A key component of aRts was the sound server which mixes several sound streams in real time | https://huggingface.co/datasets/fmars/wiki_stem |
Desktop Communication Protocol (DCOP) was an inter-process communication (IPC) daemon by KDE used in K Desktop Environment 3. The design goal for the protocol was to allow applications to interoperate, and share complex tasks. Essentially, DCOP was a ‘remote control’ system, which allowed applications or scripts to enlist the help of other applications | https://huggingface.co/datasets/fmars/wiki_stem |
The Oxygen Project is a project created to give a visual refresh to KDE Plasma Workspaces.
It consists of a set of computer icons, a window decoration for KWin, widget toolkit themes for GTK and Qt, two themes for Plasma Workspaces, and a TrueType font family.
The Oxygen theme set was used by default for Plasma Workspaces in most Linux distributions, like Fedora, Kubuntu, and openSUSE | https://huggingface.co/datasets/fmars/wiki_stem |
QtRuby is a binding of the application framework Qt for Ruby. Korundum is an additional set of bindings for KDE which extend QtRuby.
QtRuby is cross-platform, as all the underlying technologies are platform agnostic | https://huggingface.co/datasets/fmars/wiki_stem |
In first-order logic, a Herbrand structure S is a structure over a vocabulary σ that is defined solely by the syntactical properties of σ. The idea is to take the symbols of terms as their values, e. g | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematical logic, the Hilbert–Bernays provability conditions, named after David Hilbert and Paul Bernays, are a set of requirements for formalized provability predicates in formal theories of arithmetic (Smith 2007:224).
These conditions are used in many proofs of Kurt Gödel's second incompleteness theorem. They are also closely related to axioms of provability logic | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematical logic, a Hintikka set is a set of logical formulas whose elements satisfy the following properties:
An atom or its conjugate can appear in the set but not both,
If a formula in the set has a principle operator that is of "conjuctive-type", then its two operands appear in the set,
If a formula in the set has a principle operator that is of "disjuntive-type", then at least one of its two operands appears in the set. The exact meaning of "conjuctive-type" and "disjunctive-type" is defined by the method of semantic tableaux.
Hintikka sets arise when attempting to prove completeness of propositional logic using semantic tableaux | https://huggingface.co/datasets/fmars/wiki_stem |
In computer science, hub labels or the hub-labelling algorithm is a method that consumes much fewer resources than the lookup table but is still extremely fast for finding the shortest paths between nodes in a graph, which may represent, for example, road networks. This method allows at the most with two SELECT statements and the analysis of two strings to compute the shortest path between two vertices of a graph.
For a graph that is oriented like a road graph, this technique requires the prior computation of two tables from structures constructed using the method of the contraction hierarchies | https://huggingface.co/datasets/fmars/wiki_stem |
Hypostatic abstraction in mathematical logic, also known as hypostasis or subjectal abstraction, is a formal operation that transforms a predicate into a relation; for example "Honey is sweet" is transformed into "Honey has sweetness". The relation is created between the original subject and a new term that represents the property expressed by the original predicate.
Description
Technical definition
Hypostasis changes a propositional formula of the form X is Y to another one of the form X has the property of being Y or X has Y-ness | https://huggingface.co/datasets/fmars/wiki_stem |
This article examines the implementation of mathematical concepts in set theory. The implementation of a number of basic mathematical concepts is carried out in parallel in ZFC (the dominant set theory) and in NFU, the version of Quine's New Foundations shown to be consistent by R. B | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, logic and philosophy of mathematics, something that is impredicative is a self-referencing definition. Roughly speaking, a definition is impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set that contains the thing being defined. There is no generally accepted precise definition of what it means to be predicative or impredicative | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematical logic, independence is the unprovability of a sentence from other sentences.
A sentence σ is independent of a given first-order theory T if T neither proves nor refutes σ; that is, it is impossible to prove σ from T, and it is also impossible to prove from T that σ is false. Sometimes, σ is said (synonymously) to be undecidable from T; this is not the same meaning of "decidability" as in a decision problem | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinity-th" item in a sequence.
Infinitesimals do not exist in the standard real number system, but they do exist in other number systems, such as the surreal number system and the hyperreal number system, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities; the augmentations are the reciprocals of one another | https://huggingface.co/datasets/fmars/wiki_stem |
This page is about the concept in mathematical logic. For the concepts in sociology, see Institutional theory and Institutional logic. In mathematical logic, institutional model theory generalizes a large portion of first-order model theory to an arbitrary logical system | https://huggingface.co/datasets/fmars/wiki_stem |
In abstract algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are to topology and the modal logic S4 what Boolean algebras are to set theory and ordinary propositional logic. Interior algebras form a variety of modal algebras | https://huggingface.co/datasets/fmars/wiki_stem |
Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joyal. It was first conceived for modal logics, and later adapted to intuitionistic logic and other non-classical systems. The development of Kripke semantics was a breakthrough in the theory of non-classical logics, because the model theory of such logics was almost non-existent before Kripke (algebraic semantics existed, but were considered 'syntax in disguise') | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, Laver tables (named after Richard Laver, who discovered them towards the end of the 1980s in connection with his works on set theory) are tables of numbers that have certain properties of algebraic and combinatorial interest. They occur in the study of racks and quandles.
Definition
For any nonnegative integer n, the n-th Laver table is the 2n × 2n table whose entry in the cell at row p and column q (1 ≤ p,q ≤ 2n) is defined as
L
n
(
p
,
q
)
:=
p
⋆
n
q
{\displaystyle L_{n}(p,q):=p\star _{n}q}
where
⋆
n
{\displaystyle \star _{n}}
is the unique binary operation that satisfies the following two equations for all p, q in {1, | https://huggingface.co/datasets/fmars/wiki_stem |
Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. LoF describes three distinct logical systems:
The "primary arithmetic" (described in Chapter 4 of LoF), whose models include Boolean arithmetic;
The "primary algebra" (Chapter 6 of LoF), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean logic, and the classical propositional calculus;
"Equations of the second degree" (Chapter 11), whose interpretations include finite automata and Alonzo Church's Restricted Recursive Arithmetic (RRA) | https://huggingface.co/datasets/fmars/wiki_stem |
In set theory and mathematical logic, the Lévy hierarchy, introduced by Azriel Lévy in 1965, is a hierarchy of formulas in the formal language of the Zermelo–Fraenkel set theory, which is typically called just the language of set theory. This is analogous to the arithmetical hierarchy, which provides a similar classification for sentences of the language of arithmetic.
Definitions
In the language of set theory, atomic formulas are of the form x = y or x ∈ y, standing for equality and set membership predicates, respectively | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematical logic, Lindenbaum's lemma, named after Adolf Lindenbaum, states that any consistent theory of predicate logic can be extended to a complete consistent theory. The lemma is a special case of the ultrafilter lemma for Boolean algebras, applied to the Lindenbaum algebra of a theory.
Uses
It is used in the proof of Gödel's completeness theorem, among other places | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematical logic, a literal is an atomic formula (also known as an atom or prime formula) or its negation. The definition mostly appears in proof theory (of classical logic), e. g | https://huggingface.co/datasets/fmars/wiki_stem |
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality | https://huggingface.co/datasets/fmars/wiki_stem |
A logical graph is a special type of diagrammatic structure of graphical syntax developed for logic (such as those developed by Charles Sanders Peirce).
In his papers on qualitative logic, entitative graphs, and existential graphs, Peirce developed several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.
In the century since Peirce initiated this line of development, a variety of formal graph-theoretic structures that have branched out from what is abstractly the same formal base | https://huggingface.co/datasets/fmars/wiki_stem |
A logical machine is a tool containing a set of parts that uses energy to perform formal logic operations. Early logical machines were mechanical devices that performed basic operations in Boolean logic. Contemporary logical machines are computer-based electronic programs that perform proof assistance with theorems in mathematical logic | https://huggingface.co/datasets/fmars/wiki_stem |
In proof theory, ludics is an analysis of the principles governing inference rules of mathematical logic. Key features of ludics include notion of compound connectives, using a technique known as focusing or focalisation (invented by the computer scientist Jean-Marc Andreoli), and its use of locations or loci over a base instead of propositions.
More precisely, ludics tries to retrieve known logical connectives and proof behaviours by following the paradigm of interactive computation, similarly to what is done in game semantics to which it is closely related | https://huggingface.co/datasets/fmars/wiki_stem |
Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the term itself) owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century | https://huggingface.co/datasets/fmars/wiki_stem |
The Mivar-based approach is a mathematical tool for designing artificial intelligence (AI) systems. Mivar (Multidimensional Informational Variable Adaptive Reality) was developed by combining production and Petri nets. The Mivar-based approach was developed for semantic analysis and adequate representation of humanitarian epistemological and axiological principles in the process of developing artificial intelligence | https://huggingface.co/datasets/fmars/wiki_stem |
Modal logic is a kind of logic used to represent statements about necessity and possibility. It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation. For instance, in epistemic modal logic, the formula
◻
P
{\displaystyle \Box P}
can be used to represent the statement that
P
{\displaystyle P}
is known | https://huggingface.co/datasets/fmars/wiki_stem |
In model theory, a first-order theory is called model complete if every embedding of its models is an elementary embedding.
Equivalently, every first-order formula is equivalent to a universal formula.
This notion was introduced by Abraham Robinson | https://huggingface.co/datasets/fmars/wiki_stem |
Model-theoretic grammars, also known as constraint-based grammars, contrast with generative grammars in the way they define sets of sentences: they state constraints on syntactic structure rather than providing operations for generating syntactic objects. A generative grammar provides a set of operations such as rewriting, insertion, deletion, movement, or combination, and is interpreted as a definition of the set of all and only the objects that these operations are capable of producing through iterative application. A model-theoretic grammar simply states a set of conditions that an object must meet, and can be regarded as defining the set of all and only the structures of a certain sort that satisfy all of the constraints | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification over sets. It is particularly important in the logic of graphs, because of Courcelle's theorem, which provides algorithms for evaluating monadic second-order formulas over graphs of bounded treewidth. It is also of fundamental importance in automata theory, where the Büchi–Elgot–Trakhtenbrot theorem gives a logical characterization of the regular languages | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematical logic, a non-standard model of arithmetic is a model of (first-order) Peano arithmetic that contains non-standard numbers. The term standard model of arithmetic refers to the standard natural numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers | https://huggingface.co/datasets/fmars/wiki_stem |
In philosophy, specifically metaphysics, mereology is the study of parthood relationships. In mathematics and formal logic, wellfoundedness prohibits
⋯
<
x
<
⋯
<
x
<
⋯
{\displaystyle \cdots <x<\cdots <x<\cdots }
for any x.
Thus non-wellfounded mereology treats topologically circular, cyclical, repetitive, or other eventual self-containment | https://huggingface.co/datasets/fmars/wiki_stem |
The Notre Dame Journal of Formal Logic is a quarterly peer-reviewed scientific journal covering the foundations of mathematics and related fields of mathematical logic, as well as philosophy of mathematics. It was established in 1960 and is published by Duke University Press on behalf of the University of Notre Dame. The editors-in-chief are Curtis Franks and Anand Pillay (University of Notre Dame) | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematical logic, and more specifically in model theory, an infinite structure (M,<,. . | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, ordinal logic is a logic associated with an ordinal number by recursively adding elements to a sequence of previous logics. The concept was introduced in 1938 by Alan Turing in his PhD dissertation at Princeton in view of Gödel's incompleteness theorems. While Gödel showed that every logic system suffers from some form of incompleteness, Turing focused on a method so that a complete system of logic may be constructed from a given system of logic | https://huggingface.co/datasets/fmars/wiki_stem |
In logic, Peirce's law is named after the philosopher and logician Charles Sanders Peirce. It was taken as an axiom in his first axiomatisation of propositional logic. It can be thought of as the law of excluded middle written in a form that involves only one sort of connective, namely implication | https://huggingface.co/datasets/fmars/wiki_stem |
In logic, a predicate is a symbol that represents a property or a relation. For instance, in the first-order formula
P
(
a
)
{\displaystyle P(a)}
, the symbol
P
{\displaystyle P}
is a predicate that applies to the individual constant
a
{\displaystyle a}
. Similarly, in the formula
R
(
a
,
b
)
{\displaystyle R(a,b)}
, the symbol
R
{\displaystyle R}
is a predicate that applies to the individual constants
a
{\displaystyle a}
and
b
{\displaystyle b}
| https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, and in particular model theory, a prime model is a model that is as simple as possible. Specifically, a model
P
{\displaystyle P}
is prime if it admits an elementary embedding into any model
M
{\displaystyle M}
to which it is elementarily equivalent (that is, into any model
M
{\displaystyle M}
satisfying the same complete theory as
P
{\displaystyle P}
).
Cardinality
In contrast with the notion of saturated model, prime models are restricted to very specific cardinalities by the Löwenheim–Skolem theorem | https://huggingface.co/datasets/fmars/wiki_stem |
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation" | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a proof of impossibility is a proof that demonstrates that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general. Such a case is also known as a negative proof, proof of an impossibility theorem, or negative result. Proofs of impossibility often are the resolutions to decades or centuries of work attempting to find a solution, eventually proving that there is no solution | https://huggingface.co/datasets/fmars/wiki_stem |
This article gives a sketch of a proof of Gödel's first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses, which are discussed as needed during the sketch. We will assume for the remainder of the article that a fixed theory satisfying these hypotheses has been selected | https://huggingface.co/datasets/fmars/wiki_stem |
Proof-theoretic semantics is an approach to the semantics of logic that attempts to locate the meaning of propositions and logical connectives not in terms of interpretations, as in Tarskian approaches to semantics, but in the role that the proposition or logical connective plays within the system of inference.
Overview
Gerhard Gentzen is the founder of proof-theoretic semantics, providing the formal basis for it in his account of cut-elimination for the sequent calculus, and some provocative philosophical remarks about locating the meaning of logical connectives in their introduction rules within natural deduction. The history of proof-theoretic semantics since then has been devoted to exploring the consequences of these ideas | https://huggingface.co/datasets/fmars/wiki_stem |
A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. Propositions are also often characterized as being the kind of thing that declarative sentences denote. For instance the sentence "The sky is blue" denotes the proposition that the sky is blue | https://huggingface.co/datasets/fmars/wiki_stem |
Pure inductive logic (PIL) is the area of mathematical logic concerned with the philosophical and mathematical foundations of probabilistic inductive reasoning. It combines classical predicate logic and probability theory (Bayesian inference). Probability values are assigned to sentences of a first-order relational language to represent degrees of belief that should be held by a rational agent | https://huggingface.co/datasets/fmars/wiki_stem |
In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The formal system takes as its starting point an observation of Garrett Birkhoff and John von Neumann, that the structure of experimental tests in classical mechanics forms a Boolean algebra, but the structure of experimental tests in quantum mechanics forms a much more complicated structure.
A number of other logics have also been proposed to analyze quantum-mechanical phenomena, unfortunately also under the name of "quantum logic(s) | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff). Some examples of recursively-definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set.
A recursive definition of a function defines values of the function for some inputs in terms of the values of the same function for other (usually smaller) inputs | https://huggingface.co/datasets/fmars/wiki_stem |
In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice x ≤ y and a monoid x•y which admits operations x\z and z/y, loosely analogous to division or implication, when x•y is viewed as multiplication or conjunction, respectively. Called respectively right and left residuals, these operations coincide when the monoid is commutative. The general concept was introduced by Morgan Ward and Robert P | https://huggingface.co/datasets/fmars/wiki_stem |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.