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Institution (computer Science)
The notion of institution was created by Joseph Goguen and Rod Burstall in the late 1970s, in order to deal with the "population explosion among the logical systems used in computer science". The notion attempts to "formalize the informal" concept of logical system. The use of institutions makes it possible to develop concepts of specification languages (like structuring of specifications, parameterization, implementation, refinement, and development), proof calculi, and even tools in a way completely independent of the underlying logical system. There are also morphisms that allow to relate and translate logical systems. Important applications of this are re-use of logical structure (also called borrowing), and heterogeneous specification and combination of logics. The spread of institutional model theory has generalized various notions and results of model theory, and institutions themselves have impacted the progress of universal logic. Definition The theory of institutions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Goguen
__NOTOC__ Joseph Amadee Goguen ( ; June 28, 1941 – July 3, 2006) was an American computer scientist. He was professor of Computer Science at the University of California and University of Oxford, and held research positions at IBM and SRI International. In the 1960s, along with Lotfi Zadeh, Goguen was one of the earliest researchers in fuzzy logic and made profound contributions to fuzzy set theory. In the 1970s Goguen's work was one of the earliest approaches to the algebraic characterisation of abstract data types and he originated and helped develop the OBJ family of programming languages. He was author of ''A Categorical Manifesto'' and founderBurstall R., "My friend Joseph Goguen", in ''Goguen Festschrift'', K. Futatsugi et al. (Eds.), Lecture Notes in Computer Science 4060, Springer, pp. 25–30 (2006). and Editor-in-Chief of the '' Journal of Consciousness Studies''. His development of institution theory impacted the field of universal logic. Standard implication in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Category Of Small Categories
In mathematics, specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms are functors between categories. Cat may actually be regarded as a 2-category with natural transformations serving as 2-morphisms. The initial object of Cat is the ''empty category'' 0, which is the category of no objects and no morphisms. The terminal object is the ''terminal category'' or ''trivial category'' 1 with a single object and morphism. at nLab The category Cat is itself a large category, and therefore not an object of itself. In order to avoid problems analogous to [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Model Theory
In mathematical logic, abstract model theory is a generalization of model theory that studies the general properties of extensions of first-order logic and their models. Abstract model theory provides an approach that allows us to step back and study a wide range of logics and their relationships. The starting point for the study of abstract models, which resulted in good examples was Lindström's theorem. In 1974 Jon Barwise provided an axiomatization of abstract model theory.J. Barwise, 1974 , Annals of Mathematical Logic 7:221–265 See also * Lindström's theorem In mathematical logic, Lindström's theorem (named after Swedish logician Per Lindström, who published it in 1969) states that first-order logic is the '' strongest logic'' (satisfying certain conditions, e.g. closure under classical negation) ... * Institution (computer science) * Institutional model theory References Further reading * Mathematical logic Model theory {{Mathlogic-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Web Ontology Language
The Web Ontology Language (OWL) is a family of Knowledge representation and reasoning, knowledge representation languages for authoring Ontology (information science), ontologies. Ontologies are a formal way to describe Taxonomy, taxonomies and classification networks, essentially defining the structure of knowledge for various domains: the nouns representing classes of objects and the verbs representing relations between the objects. Ontologies resemble class hierarchies in object-oriented programming but there are several critical differences. Class hierarchies are meant to represent structures used in source code that evolve fairly slowly (perhaps with monthly revisions) whereas ontologies are meant to represent information on the Internet and are expected to be evolving almost constantly. Similarly, ontologies are typically far more flexible as they are meant to represent information on the Internet coming from all sorts of heterogeneous data sources. Class hierarchies on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Temporal Logic
In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am ''always'' hungry", "I will ''eventually'' be hungry", or "I will be hungry ''until'' I eat something"). It is sometimes also used to refer to tense logic, a modal logic-based system of temporal logic introduced by Arthur Prior in the late 1950s, with important contributions by Hans Kamp. It has been further developed by computer scientists, notably Amir Pnueli, and logicians. Temporal logic has found an important application in formal verification, where it is used to state requirements of hardware or software systems. For instance, one may wish to say that ''whenever'' a request is made, access to a resource is ''eventually'' granted, but it is ''never'' granted to two requestors simultaneously. Such a statement can conveniently be expressed in a temporal logic. Motivation Consider the statement "I am hungry". Though it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositional Logic
The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. Sometimes, it is called ''first-order'' propositional logic to contrast it with System F, but it should not be confused with first-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives representing the truth functions of conjunction, disjunction, implication, biconditional, and negation. Some sources include other connectives, as in the table below. Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic
Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality, causation. For instance, in epistemic modal logic, the well-formed_formula, formula \Box P can be used to represent the statement that P is known. In deontic modal logic, that same formula can represent that P is a moral obligation. Modal logic considers the inferences that modal statements give rise to. For instance, most epistemic modal logics treat the formula \Box P \rightarrow P as a Tautology_(logic), tautology, representing the principle that only true statements can count as knowledge. However, this formula is not a tautology in deontic modal logic, since what ought to be true can be false. Modal logics are formal systems that include unary operation, unary operators such as \Diamond and \Box, representing possibility and necessi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intuitionistic Logic
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not assume the law of excluded middle and double negation elimination, which are fundamental inference rules in classical logic. Formalized intuitionistic logic was originally developed by Arend Heyting to provide a formal basis for L. E. J. Brouwer's programme of intuitionism. From a proof-theoretic perspective, Heyting’s calculus is a restriction of classical logic in which the law of excluded middle and double negation elimination have been removed. Excluded middle and double negation elimination can still be proved for some propositions on a case by case basis, however, but do not hold universally as they do with classical logic. The standard explanation of intuitionistic logic is the BHK interpre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Higher-order Logic
In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic properties are less well-behaved than those of first-order logic. The term "higher-order logic" is commonly used to mean higher-order simple predicate logic. Here "simple" indicates that the underlying type theory is the ''theory of simple types'', also called the ''simple theory of types''. Leon Chwistek and Frank P. Ramsey proposed this as a simplification of ''ramified theory of types'' specified in the '' Principia Mathematica'' by Alfred North Whitehead and Bertrand Russell. ''Simple types'' is sometimes also meant to exclude polymorphic and dependent types. Quantification scope First-order logic quantifies only variables that range over individuals; '' second-order logic'', also qua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Logic
First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions such as "all humans are mortal", in first-order logic one can have expressions in the form "for all ''x'', if ''x'' is a human, then ''x'' is mortal", where "for all ''x"'' is a quantifier, ''x'' is a variable, and "... ''is a human''" and "... ''is mortal''" are predicates. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic. A theory about a topic, such as set theory, a theory for groups,A. Tarski, ''Undecidable Theories'' (1953), p. 77. Studies in Logic and the Foundation of Mathematics, North-Holland or a formal theory o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Algebraic Specification Language
The Common Algebraic Specification Language (CASL) is a general-purpose specification language based on first-order logic with induction. Partial functions and subsorting are also supported. Overview CASL has been designed by CoFI, the Common Framework Initiative (CoFI), with the aim to subsume many existing specification languages. CASL comprises four levels: * basic specifications, for the specification of single software modules, * structured specifications, for the modular specification of modules, * architectural specifications, for the prescription of the structure of implementations, * specification libraries, for storing specifications distributed over the Internet. The four levels are orthogonal to each other. In particular, it is possible to use CASL structured and architectural specifications and libraries with logics other than CASL. For this purpose, the logic has to be formalized as an institution. This feature is also used by the CASL extensions. Extensions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Logic
Common Logic (CL) is a framework for a family of logic languages, based on first-order logic, intended to facilitate the exchange and transmission of knowledge in computer-based systems. The CL definition permits and encourages the development of a variety of different syntactic forms, called ''dialects''. A dialect may use any desired syntax, but it must be possible to demonstrate precisely how the concrete syntax of a dialect conforms to the abstract CL semantics, which are based on a model theoretic interpretation. Each dialect may be then treated as a formal language. Once syntactic conformance is established, a dialect gets the CL semantics for free, as they are specified relative to the abstract syntax only, and hence are inherited by any conformant dialect. In addition, all CL dialects are comparable (i.e., can be automatically translated to a common language), although some may be more expressive than others. In general, a less expressive subset of CL may be translate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
