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	Relevance logic - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-21)
		Relevance logic aims to capture aspects of implication, or entailment, which are ignored by the "material implication" operator in classical truth-functional logic.
		Entailment: the logic of relevance and necessity, vol.
		Relevance logic at the Stanford Encyclopaedia of Philosophy.
	en.wikipedia.org /wiki/Relevant_logic (435 words)

	Peter Suber, "Non-Standard Logics"
		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.
		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.
		Belnap, N.D., Jr., "Modal and Relevance Logics: 1977," in Agazzi, 131-151.
	www.earlham.edu /~peters/courses/logsys/nonstbib.htm (2695 words)

	Paraconsistent Logic
		A logic is said to be paraconsistent iff its relation of logical consequence is not explosive.
		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.
		Relevant logics were pioneered by Anderson and Belnap.
	plato.stanford.edu /entries/logic-paraconsistent (2629 words)

	Relevance Logic (Site not responding. Last check: 2007-10-21)
		Relevance logicians claim that what is unsettling about these so-called paradoxes is that in each of them the antecedent seems irrelevant to the consequent.
		The theory of relevance that is captured by at least some relevant logics can be understood by how the corresponding natural deduction system understands a real use of a premise and how the rules are allowed to access premises.
		Linear logic is, in fact, a weak relevant logic with the addition of two operators.
	www.science.uva.nl /~seop/archives/sum1999/entries/logic-relevance (2523 words)

	Classical and Nonclassical Logics
		Classical logic is adequate for the needs of mathematics, but it bears little resemblance to the "implications" of everyday nonmathematical English; it disregards causality, relevance, and other ingredients of everyday reasoning.
		Constructive logic is known in some of the literature by the less descriptive term "intuitionistic logic." It is the type of reasoning used by constructivists, mathematicians who feel mathematics is (or should be) a collection of procedures, not just statements.
		The logics that are developed in the book were selected not for their appealing algebraic structures, but for their philosophical and psychological motivation, their connections to the premathematical experience of students, who may have very little previous mathematical training.
	www.math.vanderbilt.edu /~schectex/logics (1648 words)

	A Strong Relevant Logic Model of Epistemic Processes in Scientific Discovery - Cheng (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		12: Entailment: The Logic of Relevance and Necessity (context) - Anderson, Belnap - 1975
		146 Entailment: The Logic of Relevance and Necessity (context) - Anderson, Jr - 1975
		71 Relevance Logic and Entailment (context) - Dunn - 1986
	citeseer.ist.psu.edu /317295.html (731 words)

	whatislogic
		To be acceptable as proof, a logical argument must be both valid (the premises are relevant to the conclusion and the conclusion is therefore relevant to the premises) and true (the premises have been verified by physical evidence).
		In logic, the series of arguments based on the rules of inference of that logic which are used to derive that conclusion from the premises.
		Logic, Deductive: The systematic attempt (a) t formulate rules of inference that are consistent and complete, (b) to apply them to formally presented arguments, and (c) to determine whether or not their conclusions cane validly inferred from the premises.
	www.bobkwebsite.com /whatislogic.html (3775 words)

	Husserl: Logic and Formal Ontology
		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 important to logic not merely in providing an account of notions such as unity and (in)compatibility, however, but also because it can be used as the basis of an account of the cognitively and logically relevant dimensions of variation in those mental acts of whose ideal structures logic ultimately treats.
		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)

	Paraconsistent Logic Page
		The logic fde of first degree entailments is shown to arise naturally out of the deeper concerns of relevant logic.
		The relevant refusal to validate these inferences is defended, and finally it is suggested that more needs to be done towards a satisfactory theory of when they may nonetheless safely be used.
		The main result is that the Abelian logic A is rejection-complete; i.e., that each formula B is either a theorem of A or else leads in the style of Lukasiewicz to a proof of the variable p.
	users.rsise.anu.edu.au /~jks/paraconsistency.html (651 words)

	Universal Logic
		But a new type of weak relevant logic may prove itself to be better equipped to present new solutions to persisting paradoxes.
		Universal Logic conceptualizes a new weak quantified relevant logic where the main inference connective is understood as `meaning containment'.
		The volume begins with an overview of classical logic and relevant logic, and discusses the limitations of both types of logic in analyzing certain paradoxes.
	csli-publications.stanford.edu /site/1575862565.html (155 words)

	Substructural Logics
		In addition, techniques from substructural logics are useful in the study of traditional logics such as classical and intuitionistic logic.
		While the relevant logic R has a proof system more complex than the substructural logics such as linear logic, which lack distribution of (extensional) conjunction over disjunction, its semantics is altogether more simple.
		A Routley-Meyer model for the relevant logic R is comprised of a set of points P with a three-place relation R on P.
	www.science.uva.nl /~seop/archives/win2004/entries/logic-substructural (2919 words)

	Relevant Logic Page
		The extension to relevant logic, however, is nontrivial and so far has been secured only for the one fragment.
		On the Structure of De Morgan Monoids, with Corollaries on Relevant Logic and Theories.
		The paper concludes with some applications to the relevant logic R and particularly to the arithmetic R#.
	users.rsise.anu.edu.au /~jks/relevant.html (649 words)

	Ernst Mally's Deontik (1926) (Site not responding. Last check: 2007-10-21)
		We show that the strangeness of Mally's system is not so much due to his informal deontic principles as to the fact that he formalized those principles in terms of the propositional calculus.
		If they are formalized in terms of relevant logic rather than classical logic, one obtains a system which is related to Anderson's relevant deontic logic and not nearly as strange as Mally's own system.
		A logic of the doubtful: On optative and imperative logic.
	www.tbm.tudelft.nl /webstaf/gertjanl/deontik.html (769 words)

	Logical Pluralism \| Log
		Thus logical consequence is the intersection of truth-prservation and relevance.
		Relevance is no separable ingredient in the analysis of logical consequence, but a necessary condition of it.
		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)

	“To Pee and not to Pee
		In such circumstances, The Dog argued, idealizations of epistemic subjectivity according to which we are completely consistent, logically omniscient, etc are irrelevant to epistemology, and the adoption of a logic suited to inferential angels would be irrational.
		Logic, then, if it is to play its proper epistemological role, must not only get us from truth to truth but also prevent our going from truth to falsehood, and even more importantly, from unavoidable, justifiedly believed falsehood to spurious falsehood.
		This will disturb those who believe that the subject matter of logic is logical truth and logical falsehood, and that there is lots of it around—that is, that besides entailments, there are sentences that are logically true or false.
	www.smith.edu /philosophy/jgarfieldpee.htm (4318 words)

	Temporal Relevant Logic as the Logic Basis for Reasoning about Dynamics of Concurrent Systems - Cheng (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		The logic system that is widely used in the current approaches to specifying, reasoning, and proving properties of a concurrent system is temporal classical logic.
		The important advantages of using temporal relevant logics rather than temporal classical logics as the logical basis of autonomous...
		4: Entailment: The Logic of Relevance and Necessity (context) - Anderson, Belnap - 1975
	citeseer.ist.psu.edu /cheng98temporal.html (575 words)

	Ed Mares’s Web Page
		Centre for Logic, Language and Computation, which has members from our maths, philosophy, computer science, and linguistics programmes.
		There is a lot of interesting work going on here on modal logic, non-classical logics, model theory, algebraic logic, recursion theory, complexity theory, and set theory.
		My current research is on relevant logic, Bertrand Russell, and on the logic of belief revision.
	www.vuw.ac.nz /phil/ed.html (1016 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)

	Amazon.ca: Books: Relevant Logic: A Philosophical Interpretation (Site not responding. Last check: 2007-10-21)
		The defining feature of relevant logic is that it forces the premises of an argument to be really used and thus become "relevant" in deriving its conclusion.
		This book introduces the reader to relevant logic and provides it with a philosophical interpretation.
		The logic is analyzed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles (especially implication and negation) and natural language conditionals.
	www.amazon.ca /exec/obidos/ASIN/0521829232 (207 words)

	Deontic (Site not responding. Last check: 2007-10-21)
		Others would more broadly say the subject of deontic logic is the logic of legal or moral discourse (or both), and some like to extend it to the use of imperatives even in scientific discourse ("Let alpha equal zero!").
		Metaphorically speaking, stan-dard dyadic deontic logic as represented by G is the logic of a snap shot picturing the deontic relations between world courses in a DTL+-model at any point of time.
		Though deontic logic is regarded as the logic of normative reasoning, norms - as entities lacking truth values - are usually represented neither in its language nor its semantics.
	www.hh.shuttle.de /win/Joerg.Hansen/Deontic.html (1354 words)

	AJL: Volume 3, 2005
		This is a simpler case of the difficult problem of providing a sound and complete axiomatisation for constant-domain quantified relevant logics, which can be seen as a kind of modal logic with a two-place modal operator, the relevant conditional.
		The completeness proof is adapted from a proof for classical modal predicate logic (I follow James Garson’s 1984 presentation of the completeness proof quite closely), but with an important twist, to do with the absence of Boolean negation.
		We start with a concise introduction to epistemic logic, through the example of one, two and finally three players holding cards; and, mainly for the purpose of motivating the dynamics, we also very summarily introduce the concepts of general and common knowledge.
	www.philosophy.unimelb.edu.au /ajl/2005 (889 words)

	Phil 45.MV Spg 03 ESet#2 (Site not responding. Last check: 2007-10-21)
		Even if relevant material has not been discussed in class, it has been assigned as material from the text(s) and, so, is fair game.
		Defend the position that logic is relevant to those who reason.
		Your textbook claims that logic is the study of reason, but in the sense that logic is the study of argumentation.
	home.gwu.edu /~stiv/p45p03e2.htm (814 words)

	Alasdair Urquhart Bibliography
		The leading idea is that just as in modal logic validity may be defined in terms of certain valuations on a binary relational structure so in entailment logics validity may be defined in terms of valuations on a semilattice-interpreted informally as the semilattice of possible pieces of information."
		Abstract: "A finite many-valued logic is exhibited which has the property that the consequence relation determined by its characteristic five-valued matrix is not equivalent to a consequence relation axiomatized by a finite set of basic sequents, together with the rules of weakening, substitution and cut."
		Abstract: "I prove in this paper that the propositional logics of relevant implication (R) and entailment (E) are undecidable.
	sun3.lib.uci.edu /~scctr/philosophy/urquhart.html (3015 words)

	Ernst Mally's (1926), Gert-Jan C. Lokhorst
		We show that the strangeness of Mally's system is not so much due to Mally's informal deontic principles as to the fact that he formalized those principles in terms of the propositional calculus.
		[3] Anderson, A. R., and N. Belnap, Jr., Entailment: The Logic of Relevance and Necessity, vol.
		[9] Menger, K., ``A logic of the doubtful: On optative and imperative logic,'' pp.
	projecteuclid.org /getRecord?id=euclid.ndjfl/1038949542 (312 words)

	Acta analytica 10 (Site not responding. Last check: 2007-10-21)
		In the introduction, a 'normal relevant logic' is defined, and the further discussion is limited to such systems.
		The central point of the paper is the proposed definition of (relevant) validity by the modal notion of consistency.
		This definition is argued to be intuitively plausible and formally correct from the relevantists' point of view, since it blocks the principal fallacies of relevance, especially the questionable ex falso quodlibet and related irrelevant consequences.
	filo3.pfmb.uni-mb.si /~suster/toc10.htm (627 words)

	Science Math Logic and Foundations Software (Site not responding. Last check: 2007-10-21)
		Gateway to Logic - A collection of web-based logic programs offering a number of logical functions: interactively or automatically build proofs, check theorems, and operate on propositional logic formulae.
		MUltlog - Takes as input the specification of a finitely-valued first-order logic and produces a sequent calculus, a natural deduction system, and clause formation rules for this logic.
		WinKE: A Proof Assistant for Teaching Logic - WinKE is an interactive proof assistant based on analytic tableaux, and designed for the teaching of deductive reasoning.
	www.iper1.com /iper1-odp/scat/id/Science/Math/Logic_and_Foundations/Software (661 words)

	Relevance Logic
		Instead, relevant logic is relevant in two ways: (1) Relevance logics do not force us to accept any irrelevances.
		On one hand there is Arnon Avron who has used semantic arguments to motivate logics stronger than R.
		Thus, this logic does not make valid any circular arguments.
	plato.stanford.edu /entries/logic-relevance (2543 words)

	CSLI Calendar, 11 May 1995, vol.10:27
		____________ INTENSIONAL LOGIC LECTURE on Wednesday, 10 May 1:15 p.m., Building 90, Room 92-Q Relevant Logic Phil Kremer Stanford Philosophy This is the second in a series of talks on recent developments in and around modal logic by some guest speakers, illustrating connections with linguistics, philosophy, computer science, and AI.
		The faithfulness of the encoding is obtained as an application of the soundness theorem for the phase semantics of linear logic, a technique introduced by Y. Lafont in the presence of additive connectives.
		My aim will be to explain in intuitive and nontechnical terms what an action-based logic is. I will start with a short overview of elementary logic, and then explain action-based logic primarily in terms of a couple of examples.
	www-csli.stanford.edu /Archive/calendar/1994-95/msg00026.html (2924 words)

	Brady, Ross: Universal Logic
		Throughout the twentieth century, the classical logic of Frege and Russell dominated the field of formal logic.
		But, as Ross Brady argues, a new type of weak relevant logic may prove to be better equipped to present new solutions to persistent paradoxes.
		Universal Logic begins with an overview of classical and relevant logic and discusses the limitations of both in analyzing certain paradoxes.
	www.press.uchicago.edu /cgi-bin/hfs.cgi/00/14436.ctl (152 words)

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