Multi-valued logic

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Topic: Multi-valued logic

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	Logic - LearnThis.Info Enclyclopedia
		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.
		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.
		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.
	encyclopedia.learnthis.info /l/lo/logic_1.html (1449 words)

	Paraconsistent logic - Wikipedia, the free encyclopedia
		There are several motivations for paraconsistent logic, all of which arise out of a dissatisfaction with the consistency of classical logic, which seems to lead to results which are counter to intuition.
		Graham Priest, proponent of the paraconsistent logic dialetheism, offers the example of a man who is standing in a doorway in such a way that precisely half of his molecules are in the room and half of them not.
		A paraconsistent logic is a logic which attempts to deal with contradictions.
	en.wikipedia.org /wiki/Paraconsistent_logic (639 words)

	Value Solids
		Of perhaps deeper significance, however, these value solids for simple classical systems also show a striking resemblance to a very different type of solid that can be drawn for connectives within multi- valued or infinite-valued logics.
		Using similar binary decimals for the values of sentences in an infinite-valued logic, on the other hand, a statement with the value.1000 would be half true.
		In one standard treatment of infinite-valued connectives, for example, the value of a conjunction of sentences p and q is the minimum value of the two, represented as:
	www.sunysb.edu /philosophy/fractal/Solids.html (1101 words)

	A Multi-valued Epistemic Logic for Web-based Information Retrieval
		This research formulates a multi-valued epistemic logic (MEL) which combines the features of both multi-valued logic and epistemic logic, allowing the various notions of self-belief, meta-belief, degree of belief and degree of meta-belief to be represented.
		This research considers a unifying logic that subsumes the semantics of various existing epistemic logics such asthe logic of implicit and explicit belief, the logic of awareness, the Cadoli-Schaerf epistemic model, Non-standard epistemic logic, the logic of local reasoning,Epistemic structures, the logic of implicit and explicit propositions and Fusion epistemic models.
		In outline, this thesis presents a logic that not only has a sound and complete axiomatization and is decidable, but also (i) has a unifying semantics for representing belief, (ii) provides a means to represent degree of belief and (iii) adopts both the deductive-theoretic and the model-theoretic approach for characterizing belief.
	www.iis.sinica.edu.tw /%7Ekmsim/epistemic.htm (1030 words)

	COURSE OUTLINE
		modal and deontic logics), and non-classical logics (e.g.
		Knowledge of the syntax of classical propositional and predicate logic, including the ability to symbolize the sentences of natural languages in the notation of first-order logic.
		The course is divided into three units as follows: (1) Propositional logic, (2) Predicate logic, and (3) Extensions to and departures from classical logic.
	libarts.wsu.edu /philo/faculty-staff/shier/401Syll.html (685 words)

	Many-Valued Logic
		A philosophical application of 3-valued logic to the discussion of paradoxes was proposed by the Russian logician Bochvar (1938), and a mathematical one to partial function and relations by the American logician Kleene (1938).
		They are similar to classical logic because they accept the principle of truth-functionality, namely, that the truth of a compound sentence is determined by the truth values of its component sentences (and so remains unaffected when one of its component sentences is replaced by another sentence with the same truth value).
		And A is logically valid or a tautology iff it is valid under all valuations.
	plato.stanford.edu /entries/logic-manyvalued (4979 words)

	multi-valued logic: an introduction
		The focus is on extending the notion of binary logic as the description of electronic switching between two states (in general given as '1' and '0', or 'on' and 'off' or 'true' and 'false') to multi-value logic.
		In case of 3 valued logic the term ternary or trinary logic is used.
		the logic '1' is assumed to be identical to the arithmetical '1' and the logical '0' is assumed to be identical to the arithmetical '0'.
	www.multivaluelogic.com (4227 words)

	TP.doc
		We do not use a particular multi-valued logic but a family of logics, and each viewpoint has a specify logic associated with it.
		The family of multi-valued logics that have these properties are called quasi-boolean logics.
		Note that the symmetry of the lattice diagram across its horizontal axis is a sufficient condition for quasi-boolean logic, where the negation of each element is defined to be its image through horizontal symmetry.
	www.geocities.com /sien_huay/TP.doc (1850 words)

	F. C. S. Schiller Bibliography
		Logic cannot be independent of psychology, and truth is the recognition of a practical value.
		Logic should consist of aids to actual reflective thinking and hence is a normative science of the evaluation of truth-claims.
		Given these considerations, the proper criteria of truth cannot be found in formal logic, since that logic only deals with the formal truth-claim made by every proposition, and hence is unable to distinguish the actual truth from error.
	www.pragmatism.org /schiller/schiller_bib.htm (8236 words)

	itinerary3
		This collaboration has resulted in a number of interesting publications about different systems of many-valued logic and their relation to main uncertainty calculi, such as probability theory or possibilistic logic.
		A complete analysis of the relations between this logic and the fragment of necessity-valued possibilistic logic and fuzzy-truth-valued logic was also achieved.
		A very recent application of Fuzzy Logic undertaken in our Institute within the framework of the PhD work of Maite López is applied to the problem of the acquisition of maps of unknown environments by means of a troup of autonomous mini-robots (the ANTs project).
	www.iiia.csic.es /History/itinerary3.html (2108 words)

	letozadeh.text
		Just as is the case for fuzzy logic's relation to multi-valued logic, MVL can be shown to take us a certain distance, but a qualitative leap is needed to achieve real open texture (by the way, the concept seems to have originated in jurisprudence).
		While the correct path, I believe, is to formalize the processes of argumentation -- counterargument, rebuttal, defeat, etc. -- that are appropriate, a multi-valued logic reduction seeks to reduce the convention to something that it is not.
		Some, for example, have tried to reduce the non-demonstrative reasoning on which open-texture depends to various kinds of multi-valued logics.
	www.cs.wustl.edu /~loui/letozadeh.text (712 words)

	Ternarylogic LLC
		This "second" advantage will generally only show up when true multi-valued logic is applied.
		The validity of multi-valued logic (MVL) is well established.
		Binary logic may be considered to be a subset of a higher valued logic.
	www.ternarylogic.com (1134 words)

	Home page of Giangiacomo Gerla (fuzzy logic, fuzzy control, multi-valued logic, approximate reasoning, pointfree geometry)
		Boolean Fuzzy Logic and generalized Capacities (Capacity measure as valued theories in a Boolean fuzzy logic).
		A fuzzy logic is a continuous operators, we call "immediate consequence operator" in the class of all fuzzy subsets of the set of sentences of a given language.
		(Envelopes as theories of a fuzzy logic whose models are the probabilities: the theories are the envelopes, the models are the probabilities).
	www.dmi.unisa.it /people/gerla/www (846 words)

	RESEARCHERS IN MULTI-VALUED LOGIC.
		Most of the multiple valued logics work done at RMC is with respect to clone theory and AI applications.
		This structure supports any 'r'-valued logic function of 'n'-places, (where: 'r' is an integer >1, and 'n' is an integer >0), as well as the memory elements required by "Sequential" and "Clocked Sequential" logic.
		Polyvalued Logic "Boolean algebra" for truth values between 0 and 1.
	www.ee.pdx.edu /~mperkows/ISMVL/%3Dhomes.html (1062 words)

	Multivalued Logic
		v is a multivalued logic with a range of values such as is found on a five point preference scale.
		The challange for infinite valued logics if to find a way to determine the value of a proposition.
		v is infinite valued and is suitable for use in a probabilistic, fuzzy and other continuous logics.
	cs.wwc.edu /~aabyan/Logic/MultiValued.html (529 words)

	Report on Grant GACR 401/01/00218
		Jirkù, Petr - palek Martin: On Interrelations Among Extensional Three-Valued Logics.
		Logic Colloquium 2001, Vienna, August 6-11, In Collegium Logicum (Annals of the Kurt Goedel-Society, Vol.
		Jirkù, Petr: Racionalita a logika (Rationality and Logic).
	www.cuni.cz /~jirkup/logika/gacr0218.htm (97 words)

	Re: M Physics 21: What constituted the Space of Multi-valued Logics?
		In Reply to: M Physics 21: What constituted the Space of Multi-valued Logics?
		I hope that you continue with this thread, especially somehow including reference to Pavel Hajek's Metamathematics of Fuzzy Logics, Kluwer: Dordrecht 1998, who was the first to organize what had been a really disorganized field and contributed much research of his own.
		I never cared much for Zadeh's writings, for example, although he was early if not earliest in one branch at least of fuzzy logic.
	superstringtheory.com /forum/dualboard/messages12/365.html (409 words)

	Fuzzy archive: Re: multi-valued logic vs. fuzzy-logic
		Fuzzy logic is one of an infinite number of multi-valued logics, ranging
		Maybe in reply to: mark@infosys.agrenv.mcgill.ca: "multi-valued logic vs. fuzzy-logic"
		Lukasiewicz logic (a AND b = max(0, 1 - (a + b)), a OR b = min(1, a + b)).
	www.dbai.tuwien.ac.at /marchives/fuzzy-mail95/0581.html (270 words)

	The 'Definitive' Critique of General Semantics
		Since he views logic and mathematics as forms of human behavior involving semantic reactions, he reinterprets the '=' as indicating equivalency, which is a function of agreement by humans to ignore differences.
		Aristotle's formulation of logic accentuates this use of "to be" and thus encourages us to treat the classifications and qualities we ascribe to the world as self-evident givens rather than abstractions we create.
		The propositions of logic have long been recognized as being "necessary" and so nonempirical; and this view of the nature of logic is held almost without exception by logicians and philosophers.
	www.driveyourselfsane.com /gsarticles/maxblack.html (10110 words)

	Implementing a Multi-Valued Symbolic Model Checker - Chechik, Devereux, Easterbrook (ResearchIndex)
		Abstract: Multi-valued logics support the explicit modeling of uncertainty and disagreement by allowing additional truth values in the logic.
		In this paper, we present an implementation of a symbolic model checker for multi-valued temporal logics.
		The model checker works for any multi-valued logic whose truth values form a quasiboolean lattice.
	citeseer.lcs.mit.edu /chechik01implementing.html (570 words)

	Treatise On Many-Valued Logics; Author: Gottwald, Siegfried; Hardback; Book
		This book provides coverage of many multi-valued logics from theoretical foundations to latest results and applications, including theorem proving, approximate reasoning, program verification and generalized set theories.
		It covers the main areas of actual research interest, surveys the most important results and indicates the lines of actual research tendencies.This text provides comprehensive coverage of many-valued logic from theoretical foundations to results and applications: including theorem proving, approximate reasoning, program verification and generalized set theories.
		Treatise On Many-Valued Logics; Author: Gottwald, Siegfried; Hardback; Book
	www.netstoreusa.com /tabooks/086/0863802621.shtml (225 words)

	ACDCA 5th Summer Academy - Proceedings
		An obvious extension is to construct truth-tables in multi-valued logics.
		Constructing Truth-Tables in Propositional Multi-Valued Logics with DERIVE 4
		The implementation presented here deals with Kleene's style (min/max) p-valued logic (for any integer p>1) and it can build truth tables, check tautologies and check tautological consequences.
	www.acdca.ac.at /kongress/goesing/g_roanes.htm (108 words)

	Carles Sierra
		was devoted to the design of the MILORD language and environment that integrated several representation languages and allowed for different reasoning patterns by combining multi-valued logics and reflection mechanisms.
		Formal semantics based on Dynamic logic is another topic of interest.
		En: Fuzzy Logic for the Management of Uncertainty (L.A. Zadeh & J. Kacprzyk, eds.), 1992,John Wiley & Sons, pp.
	www.iiia.csic.es /People/Carles/Carles.html (1565 words)

	[No title]
		The meeting is called International Symposium on Multiple-Valued Logic, the proceedings are published by the IEEE Computer Society Press.
		Multiple-Valued Logic: an International Journal, published by Gordon and Breach.
		Klir and Yuan, 1996], which contain material on fuzzy logic in the narrow sense.
	www.cs.chalmers.se /~reiner/mvl-web (796 words)

	Citebase - Hypotheses Founded Semantics of Logic Programs for Information Integration in Multi-Valued Logics
		[3] Belnap, N. D., Jr, A Useful Four-Valued Logic, in:J. Dunn and G. Epstein (eds.), Modern Uses of Multiple-valued Logic, D. Reichel, Dordrecht, 1977.
		In such a setting incomplete information from a source or contradictory information from different sources necessitate the use of many-valued logics in which programs can be evaluated and hypotheses can be tested.
		The information consists of facts that a central server collects and tries to combine using (a) a set of logical rules, i.e.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:cs/0111059 (745 words)

	From Possibilistic Information To Kleene's Strong Multi-Valued Logics (ResearchIndex)
		Abstract: this paper, we look at a very particular aspect of possibilistic logic: we investigate how, under certain independence assumptions, the introduction of possibilistic uncertainty in classical propositional logic leads to the consideration of special classes of multi-valued logics, with a proper set of truth values and logical functions combining them.
		86 Possibilistic logic - Dubois, Lang et al.
		3 Towards a possibilistic logic - de Cooman - 1995
	citeseer.ist.psu.edu /61663.html (349 words)

	re: ICFRU utility (multi-valued logics)
		An axiomatic basis for a multi-valued logic is easy to construct, and this has been done, but such logics have not proved to be more than playthings for logicians: They haven't been consequential; nothing interesting has emerged from examining them.
		In the AAAP (Anglo-American-Austrian-Polish) analytic tradition there is only two-valued logic: ^(a & ^a), tertium non datur in antique language.
		If now you are talking about degrees of credibility, it is certainly true that o I believe that x o I believe strongly that x o I believe very strongly indeed that x have different imports/connotations, and these differences can even be mapped into various partially ordered (teilweise geordnete) representations.
	www.seriousliving.net /new-2078357-188.html (302 words)

	Constraint Solving over Multi-valued Logics (Author: F. Azevedo)
		In this dissertation we address such problems, developing models with multi-valued logics that we formalise and generalise to multiple faults.
		Constraint Solving over Multi-valued Logics (Author: F. evedo)
		Such logics extend Boolean logic by encoding dependencies on faults, thus allowing the modelling of an arbitrary number of diagnostic theories.
	www.iospress.nl /html/1586033042.php (136 words)

	Efficient Bridging Fault Simulation of Sequential Circuits Based on Multi-Valued Logics
		We present the concept of a multi-valued logic simulator for bridging faults in sequential circuits.
		32nd International Symposium on Multiple-Valued Logic (ISMVL'02) p.
		Different models for the handling of intermediate values in flip-flops on the digital design level can be integrated and result in an Expected realistic behavior area for bridging faults.
	csdl.computer.org /comp/proceedings/ismvl/2002/1462/00/14620216abs.htm (160 words)

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