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Logical Graph
A logical graph is a special type of diagrammatic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic. 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 systems have branched out from what is abstractly the same formal base of graph-theoretic structures. See also * Charles Sanders Peirce bibliography * Conceptual graph * Propositional calculus * Truth table * Venn diagram A Venn diagram is a widely used diagram style that shows the logical relation between set (mathematics), sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple ... External links {{commonscat-inline, Logical graph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph (discrete Mathematics)
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a Set (mathematics), set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syntax (logic)
In logic, syntax is anything having to do with formal languages or formal systems without regard to any interpretation or meaning given to them. Syntax is concerned with the rules used for constructing, or transforming the symbols and words of a language, as contrasted with the semantics of a language which is concerned with its meaning. The symbols, formulas, systems, theorems, proofs, and interpretations expressed in formal languages are syntactic entities whose properties may be studied without regard to any meaning they may be given, and, in fact, need not be given any. Syntax is usually associated with the rules (or grammar) governing the composition of texts in a formal language that constitute the well-formed formulas of a formal system. In computer science, the term '' syntax'' refers to the rules governing the composition of well-formed expressions in a programming language. As in mathematical logic, it is independent of semantics and interpretation. Syntactic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Sanders Peirce
Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for thirty years, Peirce made major contributions to logic, a subject that, for him, encompassed much of what is now called epistemology and the philosophy of science. He saw logic as the formal branch of semiotics, of which he is a founder, which foreshadowed the debate among logical positivists and proponents of philosophy of language that dominated 20th-century Western philosophy. Additionally, he defined the concept of abductive reasoning, as well as rigorously formulated mathematical induction and deductive reasoning. As early as 1886, he saw that logic gate, logical operations could be carried out by electrical switching circuits. The same idea was used decades later to produce digital computers. See Also In 1934, the philosopher Paul W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qualitative Logic
An entitative graph is an element of the diagrammatic syntax for logic that Charles Sanders Peirce developed under the name of qualitative logic beginning in the 1880s, taking the coverage of the formalism only as far as the propositional or sentential aspects of logic are concerned. See 3.468, 4.434, and 4.564 in Peirce's ''Collected Papers''. Peirce wrote of this system in an 1897 ''Monist'' article titled "The Logic of Relatives", although he had mentioned logical graphs in an 1882 letter to O. H. Mitchell. The syntax is: * The blank page; * Single letters, phrases; * Dashes; * Objects (subgraphs) enclosed by a simple closed curve called a ''cut''. A cut can be empty. The semantics are: * The blank page denotes False; * Letters, phrases, subgraphs, and entire graphs can be True or False; * To surround objects with a cut is equivalent to Boolean complementation. Hence an empty cut denotes Truth; * All objects within a given cut are tacitly joined by disjunction. * A dash ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entitative Graph
An entitative graph is an element of the diagrammatic syntax for logic that Charles Sanders Peirce developed under the name of qualitative logic beginning in the 1880s, taking the coverage of the formalism only as far as the propositional or sentential aspects of logic are concerned. See 3.468, 4.434, and 4.564 in Peirce's ''Collected Papers''. Peirce wrote of this system in an 1897 ''Monist'' article titled "The Logic of Relatives", although he had mentioned logical graphs in an 1882 letter to O. H. Mitchell. The syntax is: * The blank page; * Single letters, phrases; * Dashes; * Objects (subgraphs) enclosed by a simple closed curve called a ''cut''. A cut can be empty. The semantics are: * The blank page denotes False; * Letters, phrases, subgraphs, and entire graphs can be True or False; * To surround objects with a cut is equivalent to Boolean complementation. Hence an empty cut denotes Truth; * All objects within a given cut are tacitly joined by disjunction. * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Existential Graph
An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on logical graph, graphical logic as early as 1882,Peirce, C. S., "[On Junctures and Fractures in Logic]" (editors' title for MS 427 (the new numbering system), Fall–Winter 1882), and "Letter, Peirce to O. H. Mitchell" (L 294, 21 December 1882), ''Charles Sanders Peirce bibliography#W, Writings of Charles S. Peirce'', v. 4, "Junctures" on pp. 391–393 (Googl preview and the letter on pp. 394–399 (Googl preview. See John F. Sowa, Sowa, John F. (1997), "Matching Logical Structure to Linguistic Structure", ''Studies in the Logic of Charles Sanders Peirce'', Nathan Houser, Don D. Roberts, and James Van Evra, editors, Bloomington and Indianopolis: Indiana University Press, pp. 418–444, see 420, 425, 426, 428. and continued to develop the method until his death in 1914. The graphs Peirce proposed three systems of existential graphs: * ''alpha'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal System
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined abstraction, system of abstract thought. The term ''formalism'' is sometimes a rough synonym for ''formal system'', but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. Background Each formal system is described by primitive Symbol (formal), symbols (which collectively form an Alphabet (computer science), alphabet) to finitely construct a formal language from a set of axioms through inferential rules of formation. The system thus consists of valid formulas built up through finite combinations of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called ''well-formed words'' or ''well-formed formulas''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational complexity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Sanders Peirce Bibliography
This Charles Sanders Peirce bibliography consolidates numerous references to the writings of Charles Sanders Peirce, including letters, manuscripts, publications, and . For an extensive chronological list of Peirce's works (titled in English), see the (Chronological Overview) on the (Writings) page for Charles Sanders Peirce. Abbreviations Click on abbreviation in order to jump down this page to the relevant edition information. Click on the abbreviation appearing with that edition information in order to return here. Main editions (posthumous) Other Primary literature Bibliographies and microfilms Other bibliographies of primary literature * Burks, Arthur W. (1958). "Bibliography of the Works of Charles Sanders Peirce." CP 8:260–321. * Cohen, Morris R. (1916). "Charles S. Peirce and a Tentative Bibliography of His Published Writings." ''The Journal of Philosophy, Psychology, and Scientific Methods'' 13(26):726–37. *Fisch, Max H. (1964). "A First Supplement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conceptual Graph
A conceptual graph (CG) is a formalism for knowledge representation. In the first published paper on CGs, John F. Sowa used them to represent the conceptual schemas used in database systems. The first book on CGs applied them to a wide range of topics in artificial intelligence, computer science, and cognitive science. Research branches Since 1984, the model has been developed along three main directions: a graphical interface for first-order logic, a diagrammatic calculus of logics, and a graph-based knowledge representation and reasoning model. Graphical interface for first-order logic In this approach, a formula in first-order logic (predicate calculus) is represented by a labeled graph. A linear notation, called the Conceptual Graph Interchange Format (CGIF), has been standardized in the ISO standard for common logic. The diagram above is an example of the ''display form'' for a conceptual graph. Each box is called a ''concept node'', and each oval is called a ''re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositional Calculus
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-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. Propositions that contain no logical connectives are called atomic propositions. Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or Quantifier (logic), quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-order logic. Explanation Logical connectives are found in natural languages. In English for example, some examples are "and" (logical conjunction, conjunction), "or" (lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
