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Many-sorted Logic
Many-sorted logic can reflect formally our intention not to handle the universe as a homogeneous collection of objects, but to partition it in a way that is similar to types in typeful programming. Both functional and assertive " parts of speech" in the language of the logic reflect this typeful partitioning of the universe, even on the syntax level: substitution and argument passing can be done only accordingly, respecting the "sorts". There are various ways to formalize the intention mentioned above; a ''many-sorted logic'' is any package of information which fulfils it. In most cases, the following are given: * a set of sorts, ''S'' * an appropriate generalization of the notion of ''signature'' to be able to handle the additional information that comes with the sorts. The domain of discourse of any structure of that signature is then fragmented into disjoint subsets, one for every sort. Example When reasoning about biological organisms, it is useful to distinguish two sorts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous
Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, income, disease, temperature, radioactivity, architectural design, etc.); one that is heterogeneous is distinctly nonuniform in at least one of these qualities. Etymology and spelling The words ''homogeneous'' and ''heterogeneous'' come from Medieval Latin ''homogeneus'' and ''heterogeneus'', from Ancient Greek ὁμογενής (''homogenēs'') and ἑτερογενής (''heterogenēs''), from ὁμός (''homos'', "same") and ἕτερος (''heteros'', "other, another, different") respectively, followed by γένος (''genos'', "kind"); -ous is an adjectival suffix. Alternate spellings omitting the last ''-e-'' (and the associated pronunciations) are common, but mistaken: ''homogenous'' is strictly a biological/pathological term whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Template (C++)
Template may refer to: Tools * Die (manufacturing), used to cut or shape material * Mold, in a molding (process), molding process * Stencil, a pattern or overlay used in graphic arts (drawing, painting, etc.) and sewing to replicate letters, shapes or designs Computing * The main document from which mail merge documents are created * Style sheet (web development) or master page, a sheet or page on which a user can globally edit and format graphic elements and text common to each page of a document * Template (C++), a tool for generic programming in the C++ language * Template (file format), a standardized, non-executable file type used by computer software as a pre-formatted example on which to base other files, especially documents * Template (word processing), a standard document containing layout and styles used to configure word processing software * Template metaprogramming, a programming technique used by a compiler to generate temporary source code * Template method patte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Kaiserslautern-Landau
The University of Kaiserslautern-Landau (German: ''Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau'', also known as RPTU) is a public research university in Kaiserslautern and Landau in der Pfalz, Germany. The university was formed by the merger of the Technical University of Kaiserslautern and the Landau campus of the University of Koblenz and Landau on January 1, 2023. There are numerous institutes around the university, including two Fraunhofer Institutes ( and ITWM), the Max Planck Institute for Software Systems (MPI-SWS), the German Research Center for Artificial Intelligence (DFKI), the Institute for Composite Materials (IVW) and the Institute for Surface and Thin Film Analysis (IFOS), all of which cooperate closely with the university. RPTU is organized into 16 faculties. About 17,000 students are enrolled at the moment. RPTU is part of the Software-Cluster along with the Technische Universität Darmstadt, the Karlsruhe Institute of Technology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Polymorphism
In programming languages and type theory, parametric polymorphism allows a single piece of code to be given a "generic" type, using variables in place of actual types, and then instantiated with particular types as needed. Parametrically polymorphic functions and data types are sometimes called generic functions and generic datatypes, respectively, and they form the basis of generic programming. Parametric polymorphism may be contrasted with ad hoc polymorphism. Parametrically polymorphic definitions are ''uniform'': they behave identically regardless of the type they are instantiated at. In contrast, ad hoc polymorphic definitions are given a distinct definition for each type. Thus, ad hoc polymorphism can generally only support a limited number of such distinct types, since a separate implementation has to be provided for each type. Basic definition It is possible to write functions that do not depend on the types of their arguments. For example, the identity function \ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order-sorted Unification
In logic and computer science, specifically automated reasoning, unification is an algorithmic process of solving equations between symbolic expressions, each of the form ''Left-hand side = Right-hand side''. For example, using ''x'',''y'',''z'' as variables, and taking ''f'' to be an uninterpreted function, the singleton equation set is a syntactic first-order unification problem that has the substitution as its only solution. Conventions differ on what values variables may assume and which expressions are considered equivalent. In first-order syntactic unification, variables range over first-order terms and equivalence is syntactic. This version of unification has a unique "best" answer and is used in logic programming and programming language type system implementation, especially in Hindley–Milner based type inference algorithms. In higher-order unification, possibly restricted to higher-order pattern unification, terms may include lambda expressions, and equivalence i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christoph Walther
Christoph Walther (born 9 August 1950) is a German computer scientist, known for his contributions to automated theorem proving. He is Professor emeritus at Darmstadt University of Technology. (Section ''Emeriti und Professoren im Ruhestand'') at Darmstadt University Web Site Selected publications On * * * * * * * * * * *On automated termination analysis
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Overloading (programming)
In programming language theory and type theory, polymorphism is the use of one symbol to represent multiple different types.: "Polymorphic types are types whose operations are applicable to values of more than one type." In object-oriented programming, polymorphism is the provision of one interface to entities of different data types. The concept is borrowed from a principle in biology where an organism or species can have many different forms or stages. The most commonly recognized major forms of polymorphism are: * ''Ad hoc polymorphism'': defines a common interface for an arbitrary set of individually specified types. * ''Parametric polymorphism'': not specifying concrete types and instead use abstract symbols that can substitute for any type. * ''Subtyping'' (also called ''subtype polymorphism'' or ''inclusion polymorphism''): when a name denotes instances of many different classes related by some common superclass. History Interest in polymorphic type systems developed si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Example
Example may refer to: * ''exempli gratia'' (e.g.), usually read out in English as "for example" * .example, reserved as a domain name that may not be installed as a top-level domain of the Internet ** example.com, example.net, example.org, and example.edu: second-level domain names reserved for use in documentation as examples * HMS Example (P165), HMS ''Example'' (P165), an Archer-class patrol and training vessel of the Royal Navy Arts * ''The Example'', a 1634 play by James Shirley * The Example (comics), ''The Example'' (comics), a 2009 graphic novel by Tom Taylor and Colin Wilson * Example (musician), the British dance musician Elliot John Gleave (born 1982) * Example (album), ''Example'' (album), a 1995 album by American rock band For Squirrels See also * Exemplar (other), a prototype or model which others can use to understand a topic better * Exemplum, medieval collections of short stories to be told in sermons * Eixample, a district of Barcelona with di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition (number Theory)
In number theory and combinatorics, a partition of a non-negative integer , also called an integer partition, is a way of writing as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.) For example, can be partitioned in five distinct ways: : : : : : The only partition of zero is the empty sum, having no parts. The order-dependent composition is the same partition as , and the two distinct compositions and represent the same partition as . An individual summand in a partition is called a part. The number of partitions of is given by the partition function . So . The notation means that is a partition of . Partitions can be graphically visualized with Young diagrams or Ferrers diagrams. They occur in a number of branches of mathematics and physics, including the study of symmetric polynomials and of the symmetric group and in group representa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sort Hierarchy
Sort may refer to: * Sorting, any process of arranging items in sequence or in sets ** Sorting algorithm, any algorithm for ordering a list of elements ** Mainframe sort merge, sort utility for IBM mainframe systems ** Sort (Unix), which sorts the lines of a file ** Sort (C++), a function in the C++ Standard Template Library * ''SORT'' (journal) * Sort (mathematical logic), a domain in a many-sorted structure * Sort (typesetting), a piece of metal type * Sort, Lleida, a town in Catalonia * Selective organ targeting, a drug delivery method * Special Operations Response Team Special Operations Response Team (or SORT) is the highly trained tactical unit of the Federal Bureau of Prisons (BOP), a federal law enforcement agency under the United States United States Department of Justice, Department of Justice. It's used t ..., at US prisons * Strategic Offensive Reductions Treaty, between the US and Russia * Symantec Operations Readiness Tools, a web-based suite {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebraic Logic
In mathematical logic, abstract algebraic logic is the study of the algebraization of deductive systems arising as an abstraction of the well-known Lindenbaum–Tarski algebra, and how the resulting algebras are related to logical systems.Font, 2003. History The archetypal association of this kind, one fundamental to the historical origins of algebraic logic and lying at the heart of all subsequently developed subtheories, is the association between the class of Boolean algebra (structure), Boolean algebras and classical propositional calculus. This association was discovered by George Boole in the 1850s, and then further developed and refined by others, especially Charles Sanders Peirce, C. S. Peirce and Ernst Schröder (mathematician), Ernst Schröder, from the 1870s to the 1890s. This work culminated in Lindenbaum–Tarski algebras, devised by Alfred Tarski and his student Adolf Lindenbaum in the 1930s. Later, Tarski and his American students (whose ranks include Don Pigozzi) we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
