
	Where results make sense

Topic: Interpretability logic

Related Topics

mathematical logic

logic gate

logical positivism

symbolic logic

intuitionistic logic

fuzzy logic

Combinatory logic

modal logic

logical argument

Logical disjunction

first order logic

In the News (Mon 13 Oct 08)

Arizona Cardinals

Beverly Hills

Reggie Bush

Shane Watson

Morgan Tsvangirai

Bank of America 500

Jeff Burton

Kimi Raikkonen

Robert Mugabe

Zaheer Khan

	Lecture Notes in Logic - LNL 10
		This thoroughly revised second edition of a classic book on the main ideas and results of general meta-mathematics contains new results and simplified proofs, as well as an up to date bibliography.
		In addition to the standard results of Gödel and others on incompleteness, (non) finite axiomatizability, interpretability, etc., it contains a thorough treatment of partial conservativity and degrees of interpretability.
		The reader should be familiar with the widely used method of arithmetization and with the elements of recursion theory.
	www.aslonline.org /books-lnl_10.html (80 words)

	Logic article - Logic reasoning epistemology knowledge cognitive psychology philosophy - What-Means.com (Site not responding. Last check: 2007-10-21)
		Aristotelian logic has principally been 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 own right, and so logic is studied at a more abstract level.
		The boldest attempt to apply to logic to mathematics was undoubtedly the logicism pioneered by philosopher-logicians such as Gottlob Frege and Bertrand Russell: the idea was that mathematical theories were logical tautologies, and the programme was to show this by means to a reduction of mathematics to 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.
	www.what-means.com /encyclopedia/Logic (1922 words)

	CONK! Encyclopedia: Provability_logic (Site not responding. Last check: 2007-10-21)
		Provability logic is a modal logic where the box (or "necessity") operator is interpreted as 'it is provable that', capturing the notion of a proof predicate of a reasonably rich formal theory such as Peano arithmetic.
		There are a number of provability logics, some of which are covered in the literature mentioned in the References section.
		Interpretability logics present natural extensions of provability logic.
	www.conk.com /search/encyclopedia.cgi?q=Provability_logic (193 words)

	Logic
		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.
		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.brainyencyclopedia.com /encyclopedia/l/lo/logic_1.html (1472 words)

	Logic - Open Encyclopedia (Site not responding. Last check: 2007-10-21)
		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 the study of logic as used in natural language arguments.
	open-encyclopedia.com /Logic (2307 words)

	Interpretability - Wikipedia, the free encyclopedia
		The concept of interpretability is one in mathematical logic.
		This concept, together with weak interpretability, was introduced by Alfred Tarski in 1953.
		Three other related concepts are cointerpretability, logical tolerance, and cotolerance, introduced by Giorgi Japaridze in 1992-1993.
	en.wikipedia.org /wiki/Interpretability (73 words)

	Interpretability logic (Site not responding. Last check: 2007-10-21)
		Interpretability logics comprise a family of modal logic s that extend provability logic to describe interpretability and/or various related metamathematical properties and relations such as weak interpretability, Π
		Computational Isomorphisms in Classical Logic Article by V. Danos, J. Joinet and H. Schellinx examining the categorical semantics of classical logic from a persepctive inspired by linear logic.
		Logic is the basis of many principles including the scientific method.
	www.serebella.com /encyclopedia/article-Interpretability_logic.html (380 words)

	Lunch Abstracts (Site not responding. Last check: 2007-10-21)
		This notion has been used in a technical way to develop the semantics of modal logics, and it can be viewed as a major impetus behind the growth of (formal) modal logic.
		Interpretability Logic is a modal logic designed for deriving principles valid for the notion of interpretability between finite extensions of a given (arithmetical) theory.
		Interpretability logic is an extension of provability logic.
	www-logic.stanford.edu /Abstracts/Lunch/Winter02.html (696 words)

	Weak interpretability - Wikipedia, the free encyclopedia
		This concept, together with interpretability, was introduced by Alfred Tarski in 1953.
		Weak interpretability is a special case of the concept of tolerance introduced by Giorgi Japaridze in 1992.
		G.Japaridze, A generalized notion of weak interpretability and the corresponding logic.
	en.wikipedia.org /wiki/Weak_interpretability (84 words)

	An overview of Interpretability Logic - Visser (ResearchIndex)
		5: The interpretability logic of Peano arithmetic (context) - Berarducci - 1990
		8 The interpretability logic of Peano arithmetic (context) - Berarducci - 1990 DBLP
		2 The logic of linear tolerance (context) - Dzhaparidze - 1992 DBLP
	citeseer.ist.psu.edu /visser97overview.html (1012 words)

	Introduction
		The subject of study in provability logic as with interpretability logic is formal theories.
		As these two logics are different, it seems very natural to ask for the core logic, that is the interpretability logic of all reasonable arithmetical theories.
		The primary aim of this paper is to contribute to the quest for the interpretability logic of all reasonable arithmetical theories.
	www.phil.uu.nl /~jjoosten/final/node1.html (795 words)

	Provability Logic (Stanford Encyclopedia of Philosophy)
		Provability logic is a modal logic that is used to investigate what arithmetical theories can express in a restricted language about their provability predicates.
		The logical language of propositional provability logic contains, in addition to propositional atoms and the usual truth-functional operators as well as the contradiction symbol ⊥, a modal operator □ with intended meaning “is provable in T,” where T is a sufficiently strong formal theory, let us say Peano Arithmetic (see section 4).
		Even though propositional provability logic is a modal logic with a kind of “necessity” operator, it withstands Quine's (1976) critique of modal notions as unintelligible, because of its clear and unambiguous arithmetic interpretation.
	plato.stanford.edu /entries/logic-provability (5019 words)

	AMCA: The interpretability logic and generalized Veltman models by Mladen Vukovic (Site not responding. Last check: 2007-10-21)
		The interpretability logic IL is the natural extension of the provability logic GL (Gödel-Löb).
		A. Visser, An overview of interpretability logic, in: M. Kracht, M. de Rijke, and H. Wansing (eds.), Advances in modal logic '96, CSLI Publications, Stanford, 307-359
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/e/x/08.htm (192 words)

	Interpretability (Site not responding. Last check: 2007-10-21)
		This concept together with weak interpretability was by Alfred Tarski in 1953.
		Faulkner's Absalom Absalom and Interpretability the Inexplicable Unseen (Europaische Hochschulschriften.
		Interpretability studies of electronic flight instruments (Saab technical notes, 61)
	www.freeglossary.com /Interpretability (129 words)

	Interpretability logic (Site not responding. Last check: 2007-10-21)
		Interpretability logics comprise a family of modal logics that extend provability logic to describe interpretability and/or various related metamathematical properties and such as weak interpretability Π
		Logic is not just for Spock; deduction (which, if you read this book, you'll discover is rather different) is not just for Sherlock Holmes.
		I quit taking guitar lessons long ago because I was frustrated with the lack of system, despite my teacher being an excellent blues and rock player and a good man. He did his best to provide some systematic learning by combining rudimentary music theory w...
	www.freeglossary.com /Interpretability_logic (543 words)

	International Journal of Hybrid Intelligent Systems (Site not responding. Last check: 2007-10-21)
		The study revisits the existing categories of logic neurons, provides with their taxonomy, helps understand their functional features and sheds light on their behavior when being treated as computational components of any neurofuzzy architecture.
		The two main categories of aggregative and reference neurons are deeply rooted in the fundamental operations encountered in the technology of fuzzy sets (including logic operations, linguistic modifiers, and logic reference operations).
		As the network takes advantage of various logic neurons, this imposes an immediate requirement of structural optimization, which in this study is addressed by utilizing various mechanisms of genetic optimization (genetic algorithms).
	www.cs.okstate.edu /~ijhis/abs1.html (384 words)

	Proof Theory (Site not responding. Last check: 2007-10-21)
		Based on the axioms and rules of inference of such a system, derivations of logical statements are constructed.
		As such, proof theory is related to syntax in logic; model theory correspondingly relates to semantics.
		For example, one may state that there is no proof theory for second-order logic, meaning that there is no syntactical calculus for this logic that simultaneously (1) is sound, and (2) is complete, and (3) is decidable (admits a proof-checking algorithm).
	www.wikiverse.org /proof-theory (475 words)

	Read about Interpretability logic at WorldVillage Encyclopedia. Research Interpretability logic and learn about ... (Site not responding. Last check: 2007-10-21)
		Interpretability logics comprise a family of modal logics that extend provability logic to describe
		interpretability and/or various related metamathematical properties and relations such as weak interpretability, Π
		Giorgi Japaridze (http://www.csc.villanova.edu/~japaridz/) and Dick de Jongh, The Logic of Provability.
	encyclopedia.worldvillage.com /s/b/Interpretability_logic (104 words)

	5 What else?
		We see that provability logic can be helpful in studying and understanding the properties of self-referential equations and sentences.
		An immediate consequence of proposition 9 is that GL has the finite model property and is decidable, which are properties shared by many modal logics.
		In the proof of proposition 9 we have tried to point out a phenomenon called alternation by theoretical computer scientists: in some cases a node is positive iff all successors of it are positive, while in other cases it is positive iff some successor of it is positive.
	www.hf.uio.no /filosofi/njpl/vol4no2/provlog/node5.html (823 words)

	List of topics in logic (Site not responding. Last check: 2007-10-21)
		Paraconsistent logics -- Paradox -- Pierce's law -- [Plural quantification]] --Polish notation -- Polylogic -- Polysyllogism --Predicate -- Principia Mathematica -- Principle of bivalence -- Proof theory -- Proposition -- Propositional calculus -- Provability logic
		There is a list of fallacies on the logical fallacy page.
		Modern mathematical logic is at the list of mathematical logic topics page.
	www.factsite.co.uk /en/wikipedia/l/li/list_of_topics_in_logic.html (501 words)

	Oxford University Press
		It can certainly serve as an information and reference source as well as a source of problems to work on.
		This book principally concerns the rapidly growing area of what might be termed "Logical Complexity Theory", the study of bounded arithmetic, propositional proof systems, length of proof, etc and relations to computational complexity theory.
		Also included is an extended abstract of J P Ressayre's new approach concerning the model completeness of the theory of real closed expotential fields.
	www.oup.com /ca/isbn/0-19-853690-9 (400 words)

	Arithmetical hierarchy - Wikpedia (Site not responding. Last check: 2007-10-21)
		In mathematical logic, the arithmetical hierarchy (also known as the arithmetic hierarchy) classifies the set of all formulas (or functions) according to their degree of solvability.
		The polynomial hierarchy is a "feasible resource-bounded" version of the arithmetical hierarchy, in which polynomial length bounds are placed on the strings involved, or equivalently, polynomial time bounds are placed on the Turing machines involved.
		G.Japaridze (http://www.csc.villanova.edu/~japaridz/), The logic of the arithmetical hierarchy.
	www.bostoncoop.net /~tpryor/wiki/index.php?title=Arithmetical_hierarchy (271 words)

	Vitezslav Svejdar (Site not responding. Last check: 2007-10-21)
		Assistant professor at the Department of Logic of the Philosophical Faculty of Charles University, since Nov 1990.
		Dissertation self-Reference and Modal Logic, 1982, supervisor Petr Hajek.
		Interpretability of axiomatic theories, arithmetization, related modal logics, complexity of non-classical logics.
	www.cuni.cz /%7Esvejdar/svpage/svejdar.html (145 words)

	Bi-Unary Interpretability Logic - de Rijke (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		In [6] the system ILP is shown to be the interpretability logic of all \Sigma 0 1 -sound finitely axiomatised sequential theories that extend I\Delta 0 +SupExp; in [1] it is shown that ILM is the interpretability logic of PA. Montagna...
		1 The Interpretability Logic of Peano Arithmetic (context) - Berarducci - 1989 DBLP
		1 ILM is the Logic of \Pi 0 1 -Conservativity (context) - H'ajek, Montagna - 1989
	citeseer.ist.psu.edu /derijke90biunary.html (295 words)

	Computer Science Colloquium - May 25
		Since then several extension of this idea are formulated and one of these is interpretability logic.
		In general the advantage is that modal logic makes reasoning about formalized arithmetic a lot easier and we will see one particular example of this.
		The first half of the talk will be an overview of provability and interpretability logic, using a knowledge interpretation of the box in order to simplify matters a bit.
	web.gc.cuny.edu /Computerscience/cs_cllqm/workshop_2004_06/evan_goris.html (115 words)

	Atlas: The interpretability logic and generalized Veltman models by Mladen Vukovic (Site not responding. Last check: 2007-10-21)
		It is (non-standard) propositional modal logic with two modal operators.
		We study generalized Veltman models as defined by D. de Jongh.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-08.
	atlas-conferences.com /c/a/e/x/08.htm (194 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		The many faces of interpretability Evan Goris, Joost J. Joosten Abstract: In this paper we discus work in progress on interpretability logics.
		In particular we falsify the conjecture about the nature of the interpretability logic of all reasonable arithmetical theories.
		With this apparatus, the rather wild behavior of the different interpretability logics are nicely formulated in a single notion that expresses their differences in a uniform way.
	www.science.uva.nl /pub/theory/illc/ResearchReports/PP-2005-15.abstract.txt (131 words)

	Vitezslav Svejdar, Publications (Site not responding. Last check: 2007-10-21)
		Poznamka o vztahu vyplyvani v klasicke predikatove logice (A Note on the Consequence Relation in Classical Predicate Logic).
		Logika: neúplnost, složitost a nutnost (Logic: Incompleteness, Complexity, and Necessity), Academia Praha, 2002.
		From propositional and predicate logic to metamathematics of Peano Arithmetic and some non-classical logics, with an emphasis on connections to theoretical computer science, 464 pages.
	www.cuni.cz /~svejdar/papers/publications.html (211 words)

	The Principles of Interpretability, Mladen Vuković
		A generalized Veltman semantics developed by de Jongh is used to investigate correspondences between several extensions of intepretability logic
		[7] Visser, A., ``The formalization of interpretability,'' Studia Logica, vol.
		[10] Vuković, M., ``Interpretability logic and generalized Veltman models,'' abstract, The Bulletin of Symbolic Logic, vol.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.ndjfl/1038949538 (219 words)

	Science: Mathematics: Logic: Proof Theory: Interpretability logic - Open Site
		Interpretability logic is a family of modal logics that extend provability logic to describe various metamathematical properties and relations such as provability, interpretability, conservativity, cointerpretability, tolerance, cotolerance, arithemtic complexities.
		Being inspired by the success achieved in provability logic, the study of interpretability logics began at the late 1980s Main contributors to the field: Alessandro Berarducci, Konstantin Ignatiev, Giorgi Japaridze, Vladimir Shavrukov, Rineke Verbrugge, Albert Visser, Domenico Zambella.
		Giorgi Japaridze and Dick de Yongh, The Logic of Provability.
	open-site.org /Science/Mathematics/Logic/Proof_Theory/Interpretability_logic (113 words)

Try your search on: Qwika (all wikis)