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	Barcan formula - Wikipedia, the free encyclopedia
		In quantified modal logic, the Barcan formula and the converse Barcan formula state possible relationships between quantifiers and modalities.
		The Barcan formula is most often used when adding quantifiers to Clarence Irving Lewis's modal logic S5, and was first proposed by Ruth Barcan Marcus.
		It implies the converse condition of the Barcan formula regarding the existence of objects in the actual world and all accessible possible worlds--i.e.
	en.wikipedia.org /wiki/Barcan_formula (244 words)

	Barcan formula -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		In quantified (A system of logic whose formal properties resemble certain moral and epistemological concepts) modal logic, the Barcan formula and the converse Barcan formula state possible relationships between quantifiers and modalities.
		The formula tells us that if everything is quantifiable in all other worlds then it would have to be necessary that everything is quantifiable in our world as well.
		The Barcan formula is most often used when adding quantifiers to (additional info and facts about David Lewis) David Lewis's modal logic S5, and was first proposed by (additional info and facts about Ruth Barcan Marcus) Ruth Barcan Marcus.
	www.absoluteastronomy.com /encyclopedia/b/ba/barcan_formula.htm (229 words)

	Ruth Barcan Marcus - Wikipedia, the free encyclopedia
		Ruth Barcan Marcus (born 1921) is the philosopher and logician after whom the Barcan formula is named.
		Ruth Barcan Marcus is the daughter of Sam and Rose Barcan (Bronx, NY).
		Her father, Samual Barcan, had a promising career writing for the Jewish Yiddish Forward and was active in The Workman's Circle prior to his early death.
	en.wikipedia.org /wiki/Ruth_Barcan_Marcus (364 words)

	ipedia.com: Barcan formula Article (Site not responding. Last check: 2007-10-08)
		The Barcan Formula states: In English, the statement reads, "'For all x, it is necessary that A', implies, 'It is necessary that for all x, A'".
		The Barcan formula is used in S5 modal logic of the Kripke System.
		The formula was first proposed by Ruth Barcan Marcus.
	www.ipedia.com /barcan_formula.html (222 words)

	Ruth Barcan Marcus Bibliography
		Copeland, B.J. "A Note on the Barcan Formula and Substitutional Quantification." Logique et Analyse (March 1982), 25 [97]:353-364.
		"Truthmakers and the Converse Barcan Formula." / Timothy Williamson.
		"Ruth Barcan Marcus and the Barcan Formula." / Terence Parsons
	sun3.lib.uci.edu /eyeghiay/Philosophy/Faculty/Visiting/marcus.html (1504 words)

	Guidelines for the final exam (Site not responding. Last check: 2007-10-08)
		If a test by tree rules shows that a formula or argument is invalid, construct a counter-example from an open path in its tree, and prove that it is a counter-example using the valuation rules for the logical constants in the formula or argument.
		State the Barcan formula and its converse, in each of its two versions.
		Demonstrate using tree rules that the Barcan formula and its converse are each valid in any normal modal extension of classical first-order logic but invalid in any normal modal extension of free logic.
	www.humanities.mcmaster.ca /~hitchckd/guidelines.htm (561 words)

	Re: SUO: Re: One Stone Fits All
		I would agree with your philosophical misgivings about the Barcan formula, but the fact is that S5+BF can be used to capture modal intuitions in a wide variety of domains.
		But fact is, for a lot of applications, that's ok. It means that "possible" objects (whatever that might mean in the context) are distinguished from actually existing objects.
		If the modal operators are used for temporal logic, the Barcan > formula would imply that no entity can come into existence, pass out > of existence, or be absorbed into some other entity (when it is > eaten, for example).
	grouper.ieee.org /groups/suo/email/msg10470.html (715 words)

	Modal Logic
		However, the provability of such formulas as (Aand~A) B in such logics seems at odds with concern for the paradoxes.
		In provability logics, □p is interpreted as a formula (of arithmetic) that expresses that what p denotes is provable in PA. Using this notation, sentences of provability logic express facts about provability.
		Note however, that actualists may respond that they need not be commited to the actuality of possible worlds so long as it is understood that quantifiers used in their theory of language lack strong ontological import.
	plato.stanford.edu /entries/logic-modal (7308 words)

	Truth Values and Modal Logic: Philosophy Forums (Site not responding. Last check: 2007-10-08)
		Owen, both the Barcan and Converse Barcan formulas are valid only with respect to constant domain modal semantics.
		In a varying domain modal semantics, both formulas are invalid, and adding the Barcan corresponds to a condition on frames called anti-monotonicity while the Converse is called monotonicity.
		Also, depending on which modal logic you're using and which semantics you've chosen, the Barcan and Converse Barcan formulas may or may not be theorems.
	forums.philosophyforums.com /comments.php?id=13771&page=last (1738 words)

	Actualism
		If a formula is true in some possible world, then from the point of view of every possible world, the formula is true in some possible world.
		That all instances of BF are logically true is shown in the supplementary document The Barcan Formula is Logically True; that all instances are derivable in from the axioms and rules of SQML is shown in Proof of the Barcan Formula in S5.
		In the supplementary document, Proof of Barcan Formula Equivalent, it is shown that this proposition is indeed logically equivalent to BF in SQML.)
	plato.stanford.edu /entries/actualism (14027 words)

	Re: The Pure and The Logic (Site not responding. Last check: 2007-10-08)
		And you're right here, too: there are systems of quantified modal logic in which the Barcan formula is valid (a logical truth in one relevant sense); in others it doesn't attain that status.
		This is also irrelevant to the question of whether the proposition naturally expressed by the Barcan formula is true -- not in this or that logical system, but true as such.
		Santa Claus takes a dim view of that sort of thing, accounting it for nothing.) Oh, and as it happens, the Barcan formula is false, though it's converse, happily, is true.
	www.ccir.ed.ac.uk /~jad/vantil-list/archive-Dec-1999/msg00057.html (777 words)

	Re: Ex(~x=x), counterpart theory, and contingent identity
		I reject the latter formula, which is an instance of the combination of the Barcan Formula and the Converse Barcan Formula, because treating de dicto and de re necessities as equivalent has certain metaphysical implications I consider inacceptable.
		Kripke, for instance, has devised a modification of the standard system S5 such that the Barcan formulas are no longer derivable and no longer valid.
		A universally quantified formula is true just exactly when every actually existing individual satisfies (makes true) the formula preceded by the universal quantifier, and an existentially quantified formula is true just in case some existing individual satisfies (makes true) the formula preceded by the existential quantifier.
	www.usenet.com /newsgroups/sci.math/msg20694.html (1255 words)

	Ruth Barcan Marcus - Encyclopedia Glossary Meaning Explanation Ruth Barcan Marcus (Site not responding. Last check: 2007-10-08)
		Ruth Barcan Marcus - Encyclopedia Glossary Meaning Explanation Ruth Barcan Marcus.
		Here you will find more informations about Ruth Barcan Marcus.
		In his 1995 paper, Marcus, Kripke, and the Origin of The New Theory of Reference, Quentin Smith made the case that Saul Kripke had taken credit for several ideas without properly crediting Ruth Barcan Marcus.
	www.encyclopedia-glossary.com /en/Ruth-Barcan-Marcus.html (232 words)

	Labelled tableaux
		The inference rules are provided by the propositional system KE - a tableau-like analytic proof system devised to be used both as a refutation and a direct method of proof - enlarged with suitable elimination rules for the conditional connective.
		The basic inference rules are provided by the propositional system KE - a tableau-like analytic proof system devised to be used both as a refutation method and a direct method of proof - that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective.
		World-paths can be composed, decomposed and manipulated through unification algorithms and formulas in different worlds can be compared even if they are sub-formulas which do not depend directly on the main connective.
	www.itee.uq.edu.au /~guido/Papers/labels.html?print=1 (2008 words)

	Oxford Scholarship Online: Ways a World Might Be
		This paper examines two logical principles that combine modality with quantification and with identity: a weaker version of the converse Barcan formula, and the principle of the necessity, not of identity, but of distinctness.
		It is argued that there are conceptual assumptions that lie behind and help the independence of these principles, and a semantics with some conceptual interest that invalidates them.
		It is shown that the necessity of distinctness is an independent principle, even in a theory that includes the qualified converse Barcan formula.
	www.oxfordscholarship.com /oso/public/content/philosophy/0199251487/acprof-0199251487-chapter-9.html (170 words)

	Contexts
		The CG maps to a typed formula that is equivalent to the untyped formula for the EG:
		This formula maps situations to contexts: for every situation s, there exists a context C, whose set of true propositions is the same as the set of propositions entailed by s.
		Since the Barcan formula requires the possible worlds to be partitioned in equivalence classes that have the same individuals, any NGM that satisfies it would require the nested NGMs to be partitioned in equivalence classes with the same labels on their boxes.
	users.bestweb.net /~sowa/ontology/contexts.htm (14781 words)

	Lumpy Pea Coat (Site not responding. Last check: 2007-10-08)
		Ruth Barcan Marcus has been long arguing for a substitution interpretation of quantification (known to others as "truth-value semantics" form Hugues Leblanc) and one of her arguments is the following.
		Maybe she forgot about the canonical domains lemma that states that only the cardinality of the domain matters and what actually constitutes the members of the domain is immaterial.
		Given a formula α of S4 we can construct a formula α' such that (1) if T ⊢ α' then S4 ⊢ α; (2) if α is S4-valid then α' is T-vaid.
	nortexoid.blogspot.com (3321 words)

	Actualism (Site not responding. Last check: 2007-10-08)
		BF, NE, and CBF are, respectively, the Barcan Formula, Necessary Existence, and the Converse Barcan Formula.
		The first is that the Barcan Formula is often discussed in the following equivalent form (indeed, this was the formulation that played a role in our discussion in the first section of the present essay):
		This interpretation, the new actualist argues, reveals that the problematic theorems of SQML -- most notably, the Barcan Formula (BF), the Converse Barcan Formula (CBF), and the Necessary Existence (NE) theorems -- do not contradict our modal intuitions, once those intuitions are understood in terms of a more subtle conception of the abstract/concrete distinction.
	www.seop.leeds.ac.uk /archives/win2003/entries/actualism (13716 words)

	- SHOP.COM
		Informed by her earlier ground-breaking axiomatizations of quantified modal logic, the papers collected here by the distinguished philosopher Ruth Barcan Marcus cover much ground in the development of her thought from 1961 to 1990.
		The first essay introduces themes initially viewed as iconoclastic, such as the necessity of identity, the directly referential role of proper names as tags, the Barcan Formula about the interplay of possibility and existence, and alternative interpretations of quantification.
		All other designated trademarks, copyrights and brands are the property of their respective owners.
	www.shop.com /op/aprod-p26271452 (253 words)

	Modality, Morality and Belief - Cambridge University Press (Site not responding. Last check: 2007-10-08)
		Modality, morality and belief are among the most controversial topics in philosophy today, and few philosophers have shaped these debates as deeply as Ruth Barcan Marcus.
		Inspired by her work, a distinguished group of philosophers explore these issues, refine and sharpen arguments and develop new positions on such topics as possible worlds, moral dilemmas, essentialism, and the explanation of actions by beliefs.
		This ‘state of the art’ collection honours one of the most rigorous and iconoclastic of philosophical pioneers.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521440823 (274 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-10-08)
		Encyclopedia : B : BA : BAR : Barcan formula
		The Barcan formula is most often used when adding quantifiers to David Lewis's modal logic S5, and was first proposed by Ruth Barcan Marcus.
		It implies that all objects which exist in this world (which the first [\forall x] is quantified over) must also exist in the sucessor states to this world (which the second [\forall x] is quantified over), so one interpretation is that no new objects can ever be created.
	www.alanaditescili.net /index.php?title=Barcan_formula (201 words)

	MARCUS' 1961 ARTICLE AS A TERMINATION OF RUSSELLIAN DOMINANCE IN ANALYTIC
		If one prefers, one could say that the ordered couples are members of a model whereas the individuals in the domain D are present or exist in a model (the "present/absent" terminology conforms to Marcus' later phraseology in [1993: 195].
		The "present in" or "exists in" terminology may be explained in part in terms of the fact that the quantifiers in each model range over the domain D, which is required for her derivation of the Barcan formula.
		Since the domain D is fixed, Marcus' worlds differ from one another in that her relation R holds between different individuals in different worlds (or does not hold between any individuals in her empty world).
	www.qsmithwmu.com /marcus'_1961_article_as_a_termination_of_russellian_dominance_in_analytic.htm (11264 words)

	Lumpy Pea Coat: Quantification in Modal Logic (Site not responding. Last check: 2007-10-08)
		It's referenced all over the place and I had wanted to take a look at the completeness proofs for certain modal axiom systems for a while now—I had only thoroughly looked at completeness proofs for tableau systems (aside from Cresswell's Henkin-type proof) which are far more popular in the literature.
		Rigid terms, local predicates, fixed domains, fixed domains with the Barcan formula, varying domains with the Vulcan deathgrip formula,...it doesn't end.
		While on the topic, I don't see how anyone can argue that S4 is the right alethic modal logic when it has 14 inequivalent modalities.
	nortexoid.blogspot.com /2005/07/quantification-in-modal-logic.html (357 words)

	Find in a Library: Modality, morality, and belief : essays in honor of Ruth Barcan Marcus
		Modality, morality, and belief : essays in honor of Ruth Barcan Marcus
		by Ruth Barcan Marcus; Walter Sinnott-Armstrong; Diana Raffman; Nicholas Asher
		WorldCat is provided by OCLC Online Computer Library Center, Inc. on behalf of its member libraries.
	worldcatlibraries.org /wcpa/ow/94bc4a80311e018ba19afeb4da09e526.html (78 words)

	A proof-theoretic study of the correspondence of classical logic and modal logic , H. Kushida, M. Okada
		Mints extended this result to the quantified version of S5; using a purely proof-theoretic method he showed that the quantified S5 corresponds to the classical predicate logic with one-sorted variable.
		In this paper we extend Mints’ result to the basic modal logic S4; we investigate the correspondence between the quantified versions of S4 (with and without the Barcan formula) and the classical predicate logic (with one-sorted variable).
		We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.jsl/1067620195 (395 words)

	DIRECT, RIGID DESIGNATION AND A POSTERIORI
		The historical part of the paper mostly centers on the largely unknown contributions made by Peter Geach and Ruth Barcan Marcus (that is, contributions additional to the ones discussed in my [1995a] and [1995b] One of my main theses is that Geach [1969], not Donnellan [1970] originated the causal or “historical chain” theory of names.
		A formula “A is said to be universally valid if and only if A is valid in every non-empty domain”, [1959: 2].
		Since the domain D is fixed, Marcus’ worlds differ from one another in that her elation R holds between different individuals in different worlds (or does not hold between any individuals in her empty world).
	www.qsmithwmu.com /direct,_rigid_designation_and_a_posteriori.htm (16019 words)

	Institute of mathematics and Informatics. A. Pliuðkevièienë (Site not responding. Last check: 2007-10-08)
		Gentzen-type calculi for modal logic S4 with Barcan formula.
		On index method for modal logics with Barcan axiom.
		Cut-free indexed calculi for modal logics containing the Barcan axiom.
	www.mii.lt /mii_staff/pliuskai.htm (294 words)

	AUTHOR INDEX
		Although the filtration method for classical modal logics has been studied comprehensively, the method is not completely applied to intuitionistic modal logics yet.
		Let BF be the Barcan formula and T(K) the McKinsey-Tarski translation of Kuroda's formula.
		Θ in GK5 (GK5D) has a GK5-proof (GK5D-proof) such that every formula occurring in it is either a subformula of some formulas in Γ, Θ, or the formula L-LB or -LB, where LB occurs in the scope of some occurrence of L in some formulas of Γ, Θ.
	www.filozof.uni.lodz.pl /bulletin/v302.html (453 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Analytically, the onset of a predicating semem is due to a self-organization process as known from dynamic theory.
		Formalizing evolution of language in a "modal lower predicate calculus" (MLP) style (with restricted validity only of the Barcan formula), we were able to adopt that model also to stages of phyletic evolution of language by giving examples of writings from over three thousand years in ancient Egypt.
		Finally, discussion is triggered to what computer architecture may be needed to emulate language in a correct semantic manner.
	www.ling.ed.ac.uk /evolang2002/ABSTRACTS/krueger.txt (401 words)

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