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# Topic: Formal logic

###### In the News (Tue 25 Jun 19)

 Logic - Wikipedia, the free encyclopedia The ambiguity is that "formal logic" is very often used with the alternate meaning of symbolic logic as we have defined it, with informal logic meaning any logical investigation that does not involve symbolic abstraction; it is this sense of 'formal' that is parallel to the received usages coming from "formal languages" or "formal theory". Mathematical logic really refers to two distinct areas of research: the first is the application of the techniques of formal logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of formal logic. Logic is extensively applied in the fields of artificial intelligence, and computer science, and these fields provide a rich source of problems in formal logic. en.wikipedia.org /wiki/Logic   (3434 words)

 Logic - Encyclopedia.WorldSearch   (Site not responding. Last check: 2007-11-06) Formal logic (sometimes called "symbolic logic") attempts to capture the nature of logical truth and inference in formal systems, which consist of a formal language, a set of rules of derivation (often called "rules of inference"), and sometimes a set of axioms. For instance, propositional logic and predicate logic are a kind of formal logic, as well as temporal logic, modal logic, Hoare logic, the calculus of constructions, etc. Higher-order logics are logical systems based on a hierarchy of types. Informal logic is also more difficult because the semantics of natural language assertions is much more complicated than the semantics of formal logical systems, due to the presence of such phenomena as defeasibility. encyclopedia.worldsearch.com /formal_logic.htm   (2407 words)

 Learn more about Logic in the online encyclopedia.   (Site not responding. Last check: 2007-11-06) Logic is traditionally divided into deductive reasoning, concerned with what follows logically from given premises, and inductive reasoning, concerned with how we can go from some number of observed events to a reliable generalization. Mathematical logic is the use of formal logic to study mathematical reasoning. Logics such as fuzzy logic have since been devised with an infinite number of "degrees of truth", e.g., represented by a real number between 0 and 1. www.onlineencyclopedia.org /l/lo/logic_1.html   (1848 words)

 Logic   (Site not responding. Last check: 2007-11-06) More formally, logic is the study of valid inference, which is the process of reaching a conclusion from a set of assumptions in a systematic and valid way. Aristotelian logic is sometimes referred to as formal logic because it specifically deals with forms of reasoning, but is not formal in the sense we use it here or as is common in current usage. Mathematical logic refers to two distinct areas of research: The first, primarily of historical interest, is the use of formal logic to study mathematical reasoning, and the second, in the other direction, the application of mathematics to the study of formal logic. www.sciencedaily.com /encyclopedia/logic_1   (1441 words)

 Formal logic Article, Formallogic Information   (Site not responding. Last check: 2007-11-06) Aristotelian logic has principallybeen concerned with teaching good argument, and is still taught with that end today, while in mathematical logic and analytical philosophy much greater emphasis is placed on logic as an object of study in its ownright, and so logic is studied at a more abstract level. Mathematical logic really refers to two distinct areas of research: the first is the application of the techniques of formallogic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematicaltechniques to the representation and analysis of formal logic. Logic is extensively applied in the fields of artificial intelligence, and computerscience, and these fields provide a rich source of problems in formal logic. www.anoca.org /mathematical/reasoning/formal_logic.html   (1850 words)

 Formal Logic and Dialectics   (Site not responding. Last check: 2007-11-06) Formal logic, which was logic prior to Hegel, saw its field of study as restricted to the laws by means of which the truth of one proposition followed from that of another. Logic, is the science of the operations of the understanding which are subservient to the estimation of evidence: both the process itself of advancing from known truths to unknown, and all other intellectual operations in so far as auxiliary to this. Formal logic is at its most powerful, not at all when it is treated as something of little use to be violated at will, but on the contrary, when it is utilised with the maximum consistency and thoroughness, but with consciousness of its immanent limits and an understanding of when and how it supersedes itself. www.marxists.org /reference/archive/hegel/help/mean05.htm   (3804 words)

 The History of Formal Logic However Boole's logic was limited to propositional reasoning, and it was not until the much later development of quantifiers that formal logic was ready to be applied to general mathematics. Given this, the idea of a practical project to formalize mathematics completely, or even to use formal logic at all, seemed a dubious one. Increasingly, formal logic came to be seen as a theoretical device, rather than as a practical tool. www.rbjones.com /rbjpub/logic/jrh0103.htm   (1094 words)

 Information Headquarters: Logic Logos: some words about logic Logic is traditionally divided into deductive reasoning, concerned with what follows logically from given premises, and inductive reasoning, concerned with how we can go from some number of observed events to a reliable generalization. Formal logic Formal logic, also called symbolic logic, is concerned primarily with the structure of reasoning. Philosophical logic Philosophical logic is essentially a continuation of the traditional discipline that was called "Logic" before it was supplanted by the invention of Mathematical logic. www.informationheadquarters.com /Philosophy/Formal_logic.shtml   (2014 words)

 Classical Logic Formal languages, deductive systems, and model-theoretic semantics are mathematical objects and, as such, the logician is interested in their mathematical properties and relations. A regimented language is similar to a formal language regarding, for example, the explicitly presented rigor of its syntax and its truth conditions. Another view is that a formal language is a mathematical model of a natural language in roughly the same sense as, say, a collection of point masses is a model of a system of physical objects, and the Bohr construction is a model of an atom. plato.stanford.edu /entries/logic-classical   (11934 words)

 Husserl: Logic and Formal Ontology   (Site not responding. Last check: 2007-11-06) Logic arises when we treat those species which are meanings as special sorts of proxy objects (as 'ideal singulars'), and investigate the properties of these objects in much the same way that the mathematician investigates the properties of numbers or geometrical figures. The theory of dependence is of importance for logic as theory of science first of all because it is in the terms of this theory that the idea of unity is to be clarified. Logic as Husserl conceives it is a science of certain privileged species in the sphere of both meanings and objects and of the relations holding between these and between the ideal singulars which they comprehend. ontology.buffalo.edu /smith/articles/lfo.html   (11183 words)

 COMPUTABILITY LOGIC: a theory of interactive computation HOMEPAGE Technically CL is a game logic: it understands interactive computational problems as games played by a machine against the environment, their computability as existence of a machine that always wins the game, logical operators as operations on computational problems, and validity of a logical formula as being a scheme of "always computable" problems. The formalism used as a specification language for computational problems, called the universal language, is a non-disjoint union of the formalisms of classical, intuitionistic and linear logics, with logical operators interpreted as certain, --- most basic and natural, --- operations on problems. Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. www.cis.upenn.edu /~giorgi/cl.html   (3951 words)

 Glossary of Terms: Fo   (Site not responding. Last check: 2007-11-06) In Mathematics, Formalism is associated with David Hilbert and reduces mathematics solely to rules for the construction of valid sequences of symbols. However, a cavalier attitude towards the requirements of formal logic when they are relevant is the method of Voluntarism, not Dialectics. Formal Logic reflects the fact that in the world, for practicable purposes, there are things that in order for us to deal with them (in every day life for example), they must be stable and concrete. www.marxists.org.uk /glossary/terms/f/o.htm   (1533 words)

 Formal logic Formal logic is a set of rules for making deductions that seem self evident. Mathematical logic formalizes such deductions with rules precise enough to program a computer to decide if an argument is valid. Logic assumes something cannot be both true and not true. www.mtnmath.com /whatth/node20.html   (317 words)

 Logic Tutorial - Visual Interactive Formal, Propositional, or Symbolic Logic The logical combinations of such sentences make up propositional logic, as illustrated by the diagram further along on this web page. There's a rule about this in formal logic called the "Excluded Middle" - either a proposition (sentence) is true, or false. It might be noted that long before truth tables, formal propositional logic, or the diagrams shown above existed, Hindu and Buddhist philosophers were debating the nature of language. logictutorial.com   (1011 words)

 Logic & Formal Reasoning Logic has been developed over the centuries as a formal (that is, precise not obtuse) way of representing assumptions about a world and the process of deriving the consequences of those assumptions. Logic lecture slides and accompanying transcripts from Professors Tomás Lozano-Pérez and Leslie Kaelbling's Spring 2003 course, Artificial Intelligence. The Isaac Newton of logic - It was 150 years ago that George Boole published his classic The Laws of Thought, in which he outlined concepts that form the underpinnings of the modern high-speed computer. www.aaai.org /AITopics/html/logic.html   (1264 words)

 The World Wide Web Virtual Library: Formal Methods   (Site not responding. Last check: 2007-11-06) Formal methods are a fault avoidance technique that help in the reduction of errors introduced into a system, particularly at the earlier stages of design. TLA (Temporal Logic of Actions), a logic for specifying and reasoning about concurrent and reactive systems. Formal Verification Methods and Tools from the VERIMAG research group, France. www.afm.sbu.ac.uk   (1641 words)

 Core Concepts in Critical Thinking, Part I   (Site not responding. Last check: 2007-11-06) Nor is there any particular reason to suppose that the logic of these primitives was primitive logic-- that is, they probably drew logically correct conclusions from their data about as often as folks do nowadays (i.e. In a typical symbolic logic course, emphasis is placed on the precise symbolic representation of logical concepts, the study of the abstract relationships between these concepts, and the systematization of these relationships. The formal structure of an argument in the wild will be complicated by (a) compounded compound statements (which will need to be broken down), (b) nested arguments which result in secondary conclusions which support the main conclusion- these arguments will need to be assessed on their own merits for validity and soundness. www.kcmetro.cc.mo.us /longview/ctac/corenotes.htm   (7404 words)

 ASL Committee on Logic Education Logic Cafe, online courseware for symbolic logic, developed by John F. Halpin at Oakland University in Michigan. Logic Daemon, a web-based proof checker to accompany Logic Primer, MIT Press, 2000, by Colin Allen and Michael Hand, of Texas A&M. Graphical effects in learning logic: reasoning, representation and individual differences, by Cox, R., and Stenning, K., apparently from a 1994 Cognitive Science Conference; it reports on Hyperproof. www.math.ufl.edu /%7Ejal/asl/logic_education.html   (712 words)

 Philosophy in Cyberspace   (Site not responding. Last check: 2007-11-06) The Laboratory for Applied Logic is a research unit of the Department of Computer Science at Brigham Young University. The Logic, Language and Reasoning Web page is sponsored by the research group on Language and Reasoning Agents whose active research interests include logics of practical reasoning, natural language processing and multi-agent systems. The logic server, maintained by Christian Gottschall (chris@logik.phl.univie.ac.at), is a collection of logic-related resources including an introductory text on logic, exercises for the beginner logician, and access to a range of logic-related software. www-personal.monash.edu.au /%7Edey/phil/logic.htm   (1753 words)

 Philosophy 4150: Formal Logic: Syllabus he course is designed as an introduction to the theory of formal systems for students without any special training in mathematics or computer science. Primary emphasis will be placed on the role of formal analysis in the representation and evaluation of natural language arguments. Initially, students will learn to manipulate the apparatus of propositional and first-order predicate logics; subsequently, an introduction to the scope and limits of modal logic will be presented; finally, selected topics in the philosophy of logic will also be introduced. frank.mtsu.edu /~rbombard/RB/Sylab/syl415.html   (323 words)

 ABC News: Teaching Computers to Read No Simple Task   (Site not responding. Last check: 2007-11-06) Sentences must be converted into formal logic equations or other computer-friendly formats. Bringsjord and fellow RPI professor Konstantine Arkoudas want to create algorithms, or mathematical formulas, that allow their "Poised-for-Learning" machine to convert sentences into formal logic. The next step would be to create an additional set of algorithms that would allow the machine to use the information it takes in to figure things out. abcnews.go.com /US/wireStory?id=455767   (878 words)

 EpistemeLinks: Website results for Logic and Philosophy of Logic Description: Reasearch activity for the development of proof assistants and theorem-provers for various logics, the exploitation of various logics for problem specification or as programming languages and the investigation of their proof theory and semantics. Includes a massive index of logical fallacies of all kinds, along with helpful tips and examples to improve your critical thinking abilities. Description: a long and categorized listing of resources in critical thinking, formal logic, rhetoric, reasoning in specific contexts, and more. www.epistemelinks.com /Main/Topics.aspx?TopiCode=Logi   (755 words)

 The Reasoning Page This page does not solely focus on argumentation in natural language, but broadens the arena to address the issue of the nature and contexts of good reasoning. Thus, the page includes everything from formal logic resources (because in many contexts formal reasoning is good and appropriate reasoning) to resources in rhetoric (despite what Plato thought, persuasion is not inimical to reasoning). Logical Analysis and History of Philosophy/Philosophiegeschichte und logische Analyse pegasus.cc.ucf.edu /~janzb/reasoning   (441 words)

 A Modern Formal Logic Primer   (Site not responding. Last check: 2007-11-06) Austen Clark has Logic Software for both natural deduction systems and truth trees. Chapter 3, Logical Equivalence, Logical Truths, and Contradictions Austen Clark's Logic Software (useful for both natural deduction systems and truth trees) tellerprimer.ucdavis.edu   (415 words)

 Kurt Gödel Research Center for Mathematical Logic (former Institute for Logic — vormals Institut für Formale Logik) October 2005: The timetable for lectures this semester has stabilized, and can be found here. Koepke, An Elementary Approach to the Fine Structure of L, Bulletin of Symbolic Logic 3 (1997), pp. www.logic.univie.ac.at   (318 words)

 Home page "www.logic.at"   (Site not responding. Last check: 2007-11-06) CSL'03 and KGC (Annual Conference of the European Association for Computer Science Logic and 8th Kurt Gödel Colloquium) ESSLLI'03 (15th European Summer School in Logic, Language, and Information) LC'01 (Logic Colloquium - The 2001 ASL European Summer Meeting) www.logic.at   (107 words)

 The Logic Machine: Logic Software at Texas A&M University   (Site not responding. Last check: 2007-11-06) The Logic Machine at Texas AandM University hosts interactive logic software used for teaching introductory formal logic. The Daemon Proof Checker checks proofs and can provide hints for students attempting to construct proofs in a natural deduction system for sentential (propositional) and first-order predicate (quantifier) logic. The system and exercises are based on Logic Primer (MIT Press, 2000) but the exercises also suitable for use with other texts, such E.J. Lemmon's Beginning Logic. logic.tamu.edu   (116 words)

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