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Topic: Paraconsistent logics

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	Paraconsistent logic - Wikipedia, the free encyclopedia
		Paraconsistent logic makes it possible to distinguish between inconsistent theories, and to reason with them in a way that may help to determine how they ought to be revised to regain consistency.
		Paraconsistent logic has signficant overlap with many-valued logic; however, not all paraconsistent logics are many-valued (and, of course, not all many-valued logics are paraconsistent).
		Paraconsistent logic has been proposed as means of providing a simple and intuitive formal account of truth that does not fall prey to paradoxes such as the Liar.
	en.wikipedia.org /wiki/Paraconsistent_logics (2053 words)

	Paraconsistent logics (Site not responding. Last check: 2007-10-08)
		A paraconsistent logic is then a logical system in which ECQ does not hold.
		Paraconsistent logic can be used in modelling belief systems which are inconsistent, and yet from which not anything can be inferred.
		In standard logics, care has to be taken to not allow such statements as the liar paradox to be formed; paraconsistent logics can be much simplified in that they do not have to excise such statements (though they still have to excise Curry's paradox).
	ccc.domaindlx.com /kazenoouji/paraconsistent_logics.htm (143 words)

	Peter Suber, "Non-Contradiction and Excluded Middle"
		Because the PEDC is logically equivalent to the conjunction of the PNC and PEM, that is, because PEDC
		Rescher and Brandom, Logic of Inconsistency, Rowman and Littlefield, 1979.
		If standard logic insists that contradictions are nothing but false, then it must justify this or else beg the question against dialetheism; but as we have seen, it is difficult to produce such a justification that is not viciously circular by presupposing the standard PEDC and hence the PNC that dialetheism has rejected.
	www.earlham.edu /~peters/courses/logsys/pnc-pem.htm (1662 words)

	Peter Suber, "Non-Standard Logics" (Site not responding. Last check: 2007-10-08)
		Logics in which the set of implications determined by a given group of premises does not necessarily grow, and can shrink, when new wffs are added to the set of premises.
		Paraconsistent logics can be "lived" if one vows to accept all truths, but does not insist on rejecting all falsehood.
		Logics in which the times at which propositions bear certain truth-values can be indicated, in which the "tense" of the assertion can be indicated, and in which truth-values can be affected by the passage of time.
	www.earlham.edu /~peters/courses/logsys/nonstbib.htm#combinatory (2695 words)

	Paraconsistency Everywhere, Greg Restall (Site not responding. Last check: 2007-10-08)
		Paraconsistent logics are, by definition, inconsistency tolerant: In a paraconsistent logic, inconsistencies need not entail everything.
		In this paper I distinguish {contradictions} from {other inconsistencies}, and I show that several different logics are, in an important sense, "paraconsistent" in virtue of being inconsistency tolerant without thereby being contradiction tolerant.
		Given this fact, a widespread view—that traditional paraconsistent logics are especially repugnant because they countenance inconsistencies—is undercut.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.ndjfl/1074290713 (528 words)

	Bibliography on Adaptive Logics / references
		This paper concerns some connections between paraconsistent logics, modal logics (mainly S5), and Ambiguity Logic AL (Classical Logic applied to a language in which all letters are indexed and in which quantifiers over such indices are present).
		This paraconsistent logic seems especially useful as a lower limit logic for inconsistency-adaptive logics that are suitable for mathematical contexts.
		We consider the very weak paracomplete and paraconsistent logics that are obtained by a straightforward weakening of Classical Logic, as well as some of their maximal extensions that are a fragment of Classical Logic.
	logica.rug.ac.be /adlog/ref.html (598 words)

	M-TH: Dialectics and Paraconsistent Logic (Site not responding. Last check: 2007-10-08)
		A logic is said to be paraconsistent iff its relation of logical consequence is not explosive.
		If an underlying paraconsistent logic is used to formalise the arithmetic, and the theory therefore allowed to be inconsistent, the Gödel sentence may well be provable in the theory (essentially by the above reasoning).
		So a paraconsistent approach to arithmetic overcomes the limitations of arithmetic that are supposed (by many) to follow from Gödel's theorem.
	lists.econ.utah.edu /pipermail/marxism-thaxis/1998-March/007115.html (2667 words)

	[No title]
		Linear logic is tightly connected with the so-called structural rules of sequent calculus and it had a key role in the emergence of the new research field of substructural logics.
		Priest thinks that paraconsistent logic is the most important event in logic in the XXth century because it is kicking out a principle which was taken as the basis of reasoning during more than two thousands years.
		All this shows that paraconsistent logic has played a fundamental role towards universal logic, by dismissing the last and the more sacred principles of logic, showing that logic is grounded at a more abstract level, where no principles hold.
	www.sorites.org /Issue_12/beziau.htm (10029 words)

	Edwin Mares
		The central idea behind relevant logic is that there needs to be a tighter connection in arguments considered valid than we find in many arguments that are deemed valid by standard (or 'classical') logic.
		Paraconsistent logics are logical systems that do not allow the derivation of every formula from every contradiction.
		These logics are useful in formalizing theories of how people do or should reason about fictional stories, scientific theories, and their own beliefs.
	www.vuw.ac.nz /phil/staff/mares.aspx (528 words)

	No Title
		The importance of paraconsistent logic also follows if, more contentiously, but as some people have argued, there are true contradictions (dialetheias), i.e., there are sentences, A, such that both A and ~A are true.
		Paraconsistent logic is motivated not only by philosophical considerations, but also by its applications and implications.
		Perhaps the simplest way of generating a paraconsistent logic, first proposed by Asenjo, is to use a many-valued logic, that is, a logic with more than two truth values.
	www.webspawner.com /users/angelaspersonalfi/orangela.html (10060 words)

	Logical Pluralism \| Log
		This situation has the absurd consequence that one might concede that the conclusion of an argument was true (since the argument had true premises and was truth-preserving); yet should refuse to infer the conclusion from the premises, in the absence of demonstration of the relevance of the premises to the conclusion.
		His paper on the role of logic in AI is very clear, and contains an excellent discussion of the role of logic as a determiner of valdi inference, as opposed to logic as a tool for constructing or analysing derivations.
		Different logics are given by choosing different syntactic units (is identity one of them? is necessity?) or by choosing different fixed interpretations of the syntactic units so chosen.
	pluralism.pitas.com (9922 words)

	Reductio ad absurdum and Lukasiewicz’s modalities (Site not responding. Last check: 2007-10-08)
		Our goal is not only to construct a logic with more appropriate paraconsistent properties, but also an attempt to find a new approach to a formalization of intuitionistic logic (only approach, not a final formalization).
		Note that paraconsistent logics without mentioned paradoxical property are well known, e.g., Sette’s maximal paraconsistent logic [5] Da Costa’s logics [6], and many others, but there is no connection between these logics and minimal logic.
		C(q) hold in L. The logic L is a C-presentation of a suitable extension of minimal logic.
	www.mathematik.tu-darmstadt.de /~mahofmann/teerunde/2002/7.6.2002.html (1461 words)

	Logical Studies No.2 (1999). A.Karpenko (Site not responding. Last check: 2007-10-08)
		L is an atomic paraconsistent logic if there is a formula B, such that it does not follow from p and
		Precise notion of paraconsistent logic seems to be important also when we consider the formula (Luk).
		On the other hand, E.K.Voishvillo suggests to generalize the notion of paraconsistency: A logic is paraconsistent, if there is no finite set of formulae from which an arbitrary formula B is derivable in this logic.
	www.logic.ru /LogStud/02/No2-02.html (298 words)

	Logics of Formal Inconsistency - Carnielli, Coniglio, Marcos (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Abstract: In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory entails all possible consequences) are assumed inseparable, granted that negation is available.
		This is an effect of an ordinary logical feature known as `explosiveness': According to it, from a contradiction `$\alpha$ and $ eg\alpha$' everything is derivable.
		26 Paraconsistent Logic: essays on the inconsistent (context) - Priest, Routley et al.
	citeseer.ifi.unizh.ch /631455.html (1214 words)

	WCP'2000: Abstract of contribution: ELIAS ALVES* and DANIEL VANDERVEKEN (Site not responding. Last check: 2007-10-08)
		Due to the complexity of many paraconsistent logics relative to classical logic, there are two practical concerns.
		One way of simplifying paraconsistent logic, for these purposes, is to focus on the core arguments it is likely to be used to formalize.
		We are also able to simplify the axiomatizations for those logics that are metacomplete, and even further for their first-degree fragment.
	www.cle.unicamp.br /wcp/Contributors/RossBrady.htm (290 words)

	Events
		Many systems of paraconsistent logics were already proposed using different methods and techniques.
		I examine the plurality of ways which can be used to create a paraconsistent logic: defining paraconsistent negations in the language (Beziau's argument showing how to generate paraconsistent logics from modal logics and vice-versa), by restrictions in the axioms (the example of some modal paraconsistent logics) and changing valuations (many-valued logics).
		I apply my methodology to some modal logics and many-valued logics in order to justify the paraconsistentization and, jumping into abstraction, the creation of a general theory of the combination of logics.
	logica.rug.ac.be /centrum/events/events.php?abstract_id=180 (182 words)

	Reasoning With Inconsistency in Structured Text - Hunter (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		There is a range of proposals for logics (called paraconsistent logics) for reasoning with inconsistency each with pros and cons.
		Selecting an appropriate paraconsistent logic for an application depends on the requirements of the application.
		Here we review paraconsistent logics for the potentially significant application area of technology for structured text.
	citeseer.ifi.unizh.ch /285081.html (882 words)

	Journal of Logic and Computation, Volume 10, Issue 5, pp. 677-703: Abstract. (Site not responding. Last check: 2007-10-08)
		A non-trivializable, or paraconsistent, logic is, by necessity, a compromise, or weakening, of classical logic.
		The compromises on QC logic seem to be more appropriate than other paraconsistent logics for applications in computing.
		Here we motivate the need for QC logic, present a proof theory, and semantics for the logic, and compare it to other paraconsistent logics.
	www.mi.sanu.ac.yu /~uros.m/logcom/hdb/Volume_10/Issue_05/100677.sgm.abs.html (135 words)

	LINGUISTIX&LOGIK, Tony Marmo's blog (Site not responding. Last check: 2007-10-08)
		A logic is paraconsistent if it disallows such presupposition, and allows instead for some inconsistent yet non-trivial theories to make perfect sense.
		The Logics of Formal Inconsistency, LFIs, form a particularly expressive class of paraconsistent logics in which the metatheoretical notion of consistency can be internalized at the object-language level.
		A formal abstract approach is proposed to all related definitions and an extended investigation is made into the logical principles and the positive and negative properties of negation.
	tonymarmo.tripod.com /linguistix-logik/index.blog?entry_id=620444 (412 words)

	On Partial and Paraconsistent Logics, Reinhard Muskens (Site not responding. Last check: 2007-10-08)
		In this paper we consider the theory of predicate logics in which the principle of bivalence or the principle of noncontradiction or both fail.
		Such logics are partial or paraconsistent or both.
		The paper shows that many techniques used for classical predicate logic generalize to partial and paraconsistent logics once the right setup is chosen.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.ndjfl/1022615616 (643 words)

	Talk:Paraconsistent logics - Wikipedia, the free encyclopedia
		There is a similar article with the name "Paraconsistent logic" (without the s)
		This article should definitely be merged with Paraconsistent logic (which should be the main article).
		I plan on merging it (no earlier than January 21, 2006), if no one protests.
	en.wikipedia.org /wiki/Talk:Paraconsistent_logics (79 words)

	Some collected references to my work (Joao Marcos)
		In: J. Marcos, D. Batens, and W. Carnielli, organizers, Proceedings of the Workshop on Paraconsistent Logic (WoPaLo), held in Trento, Italy, 5—9 August 2002, as part of the 14th European Summer School on Logic, Language and Information (ESSLLI 2002), pp.121—129.
		In: J. Marcos, D. Batens, and W. Carnielli, organizers, Proceedings of the Workshop on Paraconsistent Logic (WoPaLo), held in Trento, Italy, 5—9 August 2002, as part of the 14th European Summer School on Logic, Language and Information (ESSLLI 2002), pp.90—102.
		Tutorial on "Propositional Paraconsistent Logics", presented at the Institut für Logik und Wissenschaftstheorie, Leipzig, Germany, 2001.
	www.geocities.com /jm_logica/References (1471 words)

	Paraconsistency - Dekker eBooks (Site not responding. Last check: 2007-10-08)
		This impressive compilation of the material presented at the Second World Congress on Paraconsistency held recently in Juquehy—São Sebastião, São Paulo, Brazil, represents an integrated discussion of all major topics in the area of paraconsistent logic—highlighting philosophical and historical aspects, major developments, and real-world applications.
		Covers most aspects of paraconsistency, including several systems of paraconsistent logic, philosophical aspects of paraconsistency, its relationships to other logics (modal, relevant, non-monotonic, fuzzy, substructural, and many-valued), and applications in logic programming, fault-tolerant systems, and geometry of impossible objects.
		Containing over 600 citations and the contributions of more than 30 internationally renowned experts, this comprehensive reference is essential reading for mathematical logicians, philosophers, computer scientists, and upper-level undergraduate and graduate students in these disciplines.
	www.ebooks.dekker.com /eBookCover.asp?eBookID=0824744233&type=ISBN (339 words)

	Abstract of invited talk to the WCP'2000: DIDERIK BATENS (Site not responding. Last check: 2007-10-08)
		and the logics cannot be defined from one another.
		One of the aims of the paper is to show that some paraconsistent logics are
		logic is useful for understanding (or regulating) the way in which people
	www.cle.unicamp.br /wcp/InvitedSpeakers/DiderikBatens.htm (247 words)

	Website OzsL
		History and Philosophy of Logic History and Philosophy of Logic 22:1 (for 2001, published August 2002), pp.
		In the Scope of Logic, Methodology and Philosophy of Science, Volume II of the 11th International Congress of Logic, Methodology and Philosophy of Science, Cracow, August 1999, Kluwer, Dordrecht, pp.
		Alberti, Balogh and Dekker (ed.) Proceedings of the Seventh Symposium on Logic and Language.
	www.ozsl.uu.nl /publications.shtml (9777 words)

	Journal of Applied Non-Classical Logics
		The Journal of Applied Non-Classical Logics is an international tribune, which aims at promoting the development of non-classical logics in Computer Science.
		Non-classical logics cover a large variety of formalisms such as: modal logics, temporal logics, epistemic logics, conditional logics, intermediate logics, non-monotonic logics, logics of vagueness, logics of uncertainty, relevance logics, paraconsistent logics, multivalued logics, logics of programs, etc.
		Contributions range from mathematical foundations of such logics to their applications in Computer Science.
	www.erraticimpact.com /philosophy/books/journals/journal_details.cfm?jID=267 (255 words)

	Table of contents for Library of Congress control number 2001095319
		Table of contents for Logic, artificial intelligence, and robotics : LAPTEC 2001 / edited by Jair Minoro Abe and Joäao Inâacio da Silva Filho.
		Bibliographic record and links to related information available from the Library of Congress catalog.
		Library of Congress Subject Headings for this publication: Artificial intelligence Congresses, Logic, Symbolic and mathematical Congresses, Robotics Congresses
	www.loc.gov /catdir/toc/fy041/2001095319.html (66 words)

	Amazon.ca: An Introduction to Paraconsistent Logics: Books (Site not responding. Last check: 2007-10-08)
		Look for books like An Introduction to Paraconsistent Logics by subject:
		Subjects > Nonfiction > Philosophy > Logic & Language
		Top of Page : An Introduction to Paraconsistent Logics
	www.amazon.ca /exec/obidos/ASIN/3631534132 (150 words)

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