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Lindström Quantifier
In mathematical logic, a Lindström quantifier is a generalized polyadic quantifier. Lindström quantifiers generalize first-order quantifiers, such as the existential quantifier, the universal quantifier, and the counting quantifiers. They were introduced by Per Lindström in 1966. They were later studied for their applications in logic in computer science and database query languages. Generalization of first-order quantifiers In order to facilitate discussion, some notational conventions need explaining. The expression : \phi^=\ for ''A'' an ''L''-structure (or ''L''-model) in a language ''L'', ''φ'' an ''L''-formula, and \bar a tuple of elements of the domain dom(''A'') of ''A''. In other words, \phi^ denotes a ( monadic) property defined on dom(A). In general, where ''x'' is replaced by an ''n''-tuple \bar of free variables, \phi^ denotes an ''n''-ary relation defined on dom(''A''). Each quantifier Q_A is relativized to a structure, since each quantifier is viewed a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lexicographical Order
In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements. Another variant, widely used in combinatorics, orders subsets of a given finite set by assigning a total order to the finite set, and converting subsets into increasing sequences, to which the lexicographical order is applied. A generalization defines an order on a Cartesian product of partially ordered sets; this order is a total order if and only if all factors of the Cartesian product are totally ordered. Motivation and definition The words in a lexicon (the set of words used in some language) have a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanford Encyclopedia Of Philosophy
The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. Each entry is written and maintained by an expert in the field, including professors from many academic institutions worldwide. Authors contributing to the encyclopedia give Stanford University the permission to publish the articles, but retain the copyright to those articles. Approach and history As of August 5th, 2022, the ''SEP'' has 1,774 published entries. Apart from its online status, the encyclopedia uses the traditional academic approach of most encyclopedias and academic journals to achieve quality by means of specialist authors selected by an editor or an editorial committee that is competent (although not necessarily considered specialists) in the field covered by the encyclopedia and peer review. The encyclopedia was created in 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lecture Notes In Computer Science
''Lecture Notes in Computer Science'' is a series of computer science books published by Springer Science+Business Media since 1973. Overview The series contains proceedings, post-proceedings, monographs, and Festschrifts. In addition, tutorials, state-of-the-art surveys, and "hot topics" are increasingly being included. The series is indexed by DBLP. See also *''Monographiae Biologicae'', another monograph series published by Springer Science+Business Media *''Lecture Notes in Physics'' *''Lecture Notes in Mathematics'' *''Electronic Workshops in Computing ''Electronic Workshops in Computing'' (eWiC) is a publication series by the British Computer Society. The series provides free online access for conferences and workshops in the area of computing. For example, the EVA London Conference proceeding ...'', published by the British Computer Society References External links * Publications established in 1973 Computer science books Series of non-fiction books Springer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Symbolic Logic
The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by '' Mathematical Reviews'', Zentralblatt MATH, and Scopus. Its 2009 MCQ was 0.28, and its 2009 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... was 0.631. External links * Mathematics journals Publications established in 1936 Multilingual journals Quarterly journals Association for Symbolic Logic academic journals Logic journals Cambridge University Press academic journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE Symposium On Logic In Computer Science
The ACM–IEEE Symposium on Logic in Computer Science (LICS) is an annual academic conference on the theory and practice of computer science in relation to mathematical logic. Extended versions of selected papers of each year's conference appear in renowned international journals such as Logical Methods in Computer Science and ACM Transactions on Computational Logic. History LICS was originally sponsored solely by the IEEE, but as of the 2014 founding of the ACM Special Interest Group on Logic and Computation LICS has become the flagship conference of SIGLOG, under the joint sponsorship of ACM and IEEE. From the first installment in 1988 until 2013, the cover page of the conference proceedings has featured an artwork entitled ''Irrational Tiling by Logical Quantifiers'', by Alvy Ray Smith. Since 1995, each year the '' Kleene award'' is given to the best student paper. In addition, since 2006, the ''LICS Test-of-Time Award'' is given annually to one among the twenty-year-old LIC ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Pure And Applied Logic
This is a list of scientific, technical and general interest periodicals published by Elsevier or one of its imprints or subsidiary companies. Both printed items and electronic publications are included in this list. A B C D E F G H * ''Heart Rhythm'' * ''Historia Mathematica'' * ''Human Immunology'' I J L M N O P R S T U * '' Ultramicroscopy'' * ''Urology'' V * '' Veterinary Microbiology'' W Z * '' Zeitschrift für Evidenz, Fortbildung und Qualität im Gesundheitswesen'' See also References {{RELX Periodicals Elsevier Elsevier () is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell'', the ScienceDirect collection of electronic journals, '' Trends'', th ... ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoria (philosophy Journal)
''Theoria: A Swedish Journal of Philosophy and Psychology'' is a peer review, peer-reviewed academic journal publishing research in all areas of philosophy established in 1935 by Åke Petzäll (:sv:Åke Petzäll, sv). It is published quarterly by Wiley-Blackwell on behalf of Stiftelsen Theoria. The current editor-in-chief is Sven Ove Hansson. ''Theoria'' publishes articles, reviews, and shorter notes and discussions. Editors Notable articles Among the contributions to philosophy, logic, and mathematics first published in ''Theoria'' are: * Carl Gustav Hempel, Le problème de la vérité, ''Theoria'' 3, 1937, 206–244. (Hempel's paradox, Hempel's confirmation paradoxes) * Ernst Cassirer, Was ist "Subjektivismus"?, ''Theoria'' 5, 1939, 111–140. * Alf Ross, Imperatives and Logic, ''Theoria'' 7, 1941, 53–71. (Ross' deontic paradox) * Georg Henrik von Wright, The Paradoxes of Confirmation, ''Theoria'' 31, 1965, 255–274. * Per Lindström, First Order Predicate Logic with Gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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) having both the (countable) compactness property and the (downward) Löwenheim–Skolem property. Lindström's theorem is perhaps the best known result of what later became known as abstract model theory, the basic notion of which is an abstract logic; the more general notion of an institution was later introduced, which advances from a set-theoretical notion of model to a category-theoretical one. Lindström had previously obtained a similar result in studying first-order logics extended with Lindström quantifiers. Jouko VäänänenLindström's Theorem/ref> Lindström's theorem has been extended to various other systems of logic, in particular modal logics by Johan van Benthem and Sebastian Enqvist. Notes References * Per L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Löwenheim–Skolem Theorem
In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf Skolem. The precise formulation is given below. It implies that if a countable first-order theory has an infinite model, then for every infinite cardinal number ''κ'' it has a model of size ''κ'', and that no first-order theory with an infinite model can have a unique model up to isomorphism. As a consequence, first-order theories are unable to control the cardinality of their infinite models. The (downward) Löwenheim–Skolem theorem is one of the two key properties, along with the compactness theorem, that are used in Lindström's theorem to characterize first-order logic. In general, the Löwenheim–Skolem theorem does not hold in stronger logics such as second-order logic. Theorem In its general form, the Löwenheim–Skolem Theorem states that for every signature ''σ'', every infinite ''σ''-structure ''M'' and e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compactness Theorem
In mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important tool in model theory, as it provides a useful (but generally not effective) method for constructing models of any set of sentences that is finitely consistent. The compactness theorem for the propositional calculus is a consequence of Tychonoff's theorem (which says that the product of compact spaces is compact) applied to compact Stone spaces, hence the theorem's name. Likewise, it is analogous to the finite intersection property characterization of compactness in topological spaces: a collection of closed sets in a compact space has a non-empty intersection if every finite subcollection has a non-empty intersection. The compactness theorem is one of the two key properties, along with the downward Löwenheim–Skolem theorem, that is used in Lindström's theorem to characterize first-order logic. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henkin Quantifier
In logic a branching quantifier, also called a Henkin quantifier, finite partially ordered quantifier or even nonlinear quantifier, is a partial ordering :\langle Qx_1\dots Qx_n\rangle of quantifiers for ''Q'' ∈ . It is a special case of generalized quantifier. In classical logic, quantifier prefixes are linearly ordered such that the value of a variable ''ym'' bound by a quantifier ''Qm'' depends on the value of the variables : ''y''1, ..., ''y''''m''−1 bound by quantifiers : ''Qy''1, ..., ''Qy''''m''−1 preceding ''Qm''. In a logic with (finite) partially ordered quantification this is not in general the case. Branching quantification first appeared in a 1959 conference paper of Leon Henkin. Systems of partially ordered quantification are intermediate in strength between first-order logic and second-order logic. They are being used as a basis for Hintikka's and Gabriel Sandu's independence-friendly logic. Definition and properties The simplest Henkin quant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
