
	Where results make sense

Topic: Axiom S5

Related Topics

Ontological argument

Yamato weapon

SNMP

IBM

Disaster

Bessus

928

Letizia Ortiz

Cothen

Dalriada

Lucky

Caiphas

Bremen, Maine

Tilton, Illinois

Saigo Takamori

	Axiom S5 - Wikipedia, the free encyclopedia
		Axiom S5 is the distinctive axiom of the S5 system of modal logic and says that if possibly necessarily p, then necessarily p.
		Axiom S5 is also at the heart of Plantinga's ontological argument.
		In terms of Kripke semantics, S5 describes sets of possible worlds on which the accessibility relation is symmetric, transitive, and reflexive--that is, an equivalence relation.
	en.wikipedia.org /wiki/Axiom_S5 (269 words)

	Modal Logic (Stanford Encyclopedia of Philosophy)
		Note that the characteristic axiom of modal logic, (M): □A→A, is not acceptable for either H or G, since A does not follow from ‘it always was the case that A’, nor from ‘it always will be the case that A’.
		Density corresponds to the axiom (C4): □□A→□A, the converse of (4), so for example, the system KC4, which is K plus (C4) is adequate with respect to models where the frame is dense, and KDC4, adequate with respect to models whose frames are serial and dense, and so on.
		The relationship between conditions on frames and corresponding axioms is one of the central topics in the study of modal logics.
	plato.stanford.edu /entries/logic-modal (7297 words)

	Re: modal logic (Site not responding. Last check: 2007-10-11)
		Axiom S5 corresponds to the policy that all databases must have exactly the same set of laws or constraints.
		Axiom S4 corresponds to the policy that the accessibility of (L2,F2) from (L1,F1) requires that all laws of L2 must also be facts in F1.
		Axiom S4 is a more realistic policy that would allow a database administrator to change a constraint, but only if it doesn't invalidate the current database.
	grouper.ieee.org /groups/suo/email/msg00118.html (349 words)

	Chapter 12: The Systems of Complete Modalization - Alternative Formulations
		Axiom L4 is formula 10.6; the rest of the basis of the present S3° is clearly contained in the original S3°.
		Axiom L7 is clearly a thesis of S5.
		One immediate result of the fact that S3, S4, and S5 are able to be formulated as above is that the deduction theorem is provable for them in these formulations exactly as it was for the systems containing the positive implicational calculus in Chapter 2.
	www.clas.ufl.edu /users/jzeman/modallogic/chapter12.htm (3723 words)

	The Annual Modal Logic $100 Challenge (Site not responding. Last check: 2007-10-11)
		In modal logics, the lattice of relationships between the Kripke based logics up to S5 is a well known structure.
		Theorems of the logic are the axioms, and any theorems that can be derived from prior theorems using the inference rules.
		The syntactic representation of the axioms and rules can be anything reasonable (use of the TPTP syntax is encouraged).
	www.cs.miami.edu /~tptp/HHDC (525 words)

	Modal Logic Axiom 5 (Mp>LMp) (Site not responding. Last check: 2007-10-11)
		This axiom is also called axiom "E" by Hughes and Cresswell.
		The strict form of this axiom is called M10 by Zeman.
		S5 = Axiom K: L(p>q) > (Lp>Lq) + Lp>p + Axiom 5 [Mp>LMp] [Hughes and Cresswell, 1996, p58]
	www.cc.utah.edu /~nahaj/logic/structures/axioms/CMpLMp.html (122 words)

	Review of Subsystems of Second Order Arithmetic by Stephen G. Simpson (Site not responding. Last check: 2007-10-11)
		On the one hand, there are philosophers who think the question of what are the appropriate axioms and rules of logic for mathematics to be one that it is appropriate and important for philosophers to address, and among the philosophers in this first group there are many who actually sympathize with the heretics.
		There is no such axiom in the system, and a proof of a universal statement in the system really does constitute an orthodox proof that all sets X of natural numbers, not just the recursive ones, have the property expressed by the formula
		Such proving of axioms from theorems is called ``reverse mathematics'', and is a main theme of the first part of the book.
	www.math.psu.edu /simpson/sosoa/burgess/burgess.html (2350 words)

	RMG_7 (Site not responding. Last check: 2007-10-11)
		Axiom R1: The most basic rhythm is a regularly repeating beat.
		Axiom R2: Rhythms are constructed by variations on the most basic rhythm.
		Axiom S5: A subscale of the 12-note chromatic scale is the 7-note major scale, formed by steps of {2, 2, 1, 2, 2, 2, 1} from the 12-note scale.
	pace.pace.net /rmg/presentation/RMG_7.htm (63 words)

	The Prosblogion: Modal Logic axioms 4 and 5
		Axiom four says that for any iterated string of the same modal operator we can collapse the string to a single operator.
		Whether one of them corresponds to the correct logic of necessity is a pretty important philosophical matter, though certainly S5 is often spoken of as the logic of necessity.
		One good reason to worry about S5 being the correct logic of necessity is that, given the strength of the logic, lots of important distinctions can't be made in it.
	prosblogion.ektopos.com /archives/2006/03/modal_logic_axi.html (1719 words)

	Robert C. Koons: Phl 356 Lecture #9
		The principles K, S5 and T are all standard axioms of the simplest and most powerful systems of modal logic, the so-called S5 system.
		A defender of the cosmological argument is committed to accepting that all of the premises (and, of course, the conclusion as well) are true (with the possible exception of the S5 axiom).
		This logical axiom is true because we always begin, in thought, with an ideal object that possesses all positive properties, and form our ideas of particular things by a process of negation.
	www.leaderu.com /offices/koons/docs/lec9.html (3002 words)

	Citations: A guide to the modal logics of knowledge and belief - Halpern, Moses (ResearchIndex)
		....in S5 models When formalizing tests as we did in definition 3.6, it was assumed that the knowledge of agents is modelled by a KT axiomatization.
		For example, knowledge and weak common knowledge satisfy the axioms and rules of the modal system S5 Strong common knowledge also satisfies S5, unless the relation ; is not symmetric, in which case it satisfies only the axioms of the weaker modal system S4.
		A useful tool for thinking about E m S and C S is an undirected graph whose nodes are the points of the system, in which two points (ae; k) and (ae 0 ; k) are connected by an edge iff the points are....
	citeseer.ist.psu.edu /context/100932/0 (2751 words)

	Welcome To Axiom Online (Site not responding. Last check: 2007-10-11)
		Axiom Automotive Technologies is the world’s largest supplier of OEM and aftermarket replacement parts to transmission professionals.
		Axiom is the industry leader in the availability, quality and distribution of transmission products.
		Customers of Axiom may use the Part Numbers for purposes of placing orders with Axiom, or otherwise operating their business, but no permission is granted to any customer or other individual or entity to make use of the Part Numbers to compete with Axiom in any way.
	www.axiom.com (277 words)

	[No title]
		Axiom ax_1Axiom = new Axiom("ax-1", "wi $1 wi $2 $1", "Axiom of simplification (propositional calculus)"); axiomVec.addElement(ax_1Axiom); // ax-2 $a - ((P -> (Q -> R)) -> ((P -> Q) -> // (P -> R))) $.
		Axiom ax_2Axiom = new Axiom("ax-2", "wi wi $1 wi $2 $3 wi wi $1 $2 wi $1 $3", "Axiom of distribution (propositional calculus)"); axiomVec.addElement(ax_2Axiom); // ax-3 $a - ((-.
		Axiom df_exAxiom = new Axiom("df-ex", "wb wex $1 $2 wn wal $1 wn $2", "Definition of existential quantifier"); axiomVec.addElement(df_exAxiom); // df-sub $a - [ x / y ] P
	us.metamath.org /mmsolitaire/mm.java (3670 words)

	New Elegant Axiomatizations of Some Logics
		Meredith [18] claims to have ``almost completed a proof that no single axiom of (C,O) can contain less than 19 letters.'' As far as we know, no such proof was ever completed (that is, until now...).
		4 The Implicational Fragment (C5) of the Modal Logic S5 In their classic paper [6], Lemmon, Meredith, Meredith, Prior, and Thomas present several axiomatizations (assuming only the rule of condensed detachment) of the system C5, which is the strict implicational fragment of the modal logic S5.
		Bases for C5 containing 4, 3, 2, and a single axiom are presented in [6].
	fitelson.org /ar.html (2082 words)

	Axiom S5 queen latifah Axiom S5
		Axiom S5 queen latifah Axiom S5 Home
		Axiom S5 queen latifah Axiom S5 Axiom S5 Axiom S5 is the distinctive axiom of the S5 system of modal logic and says that if possibly necessarily p, then necessarily p.
		If the modality here is what Alvin Plantinga calls "broadly logical" necessity and possibility, then an argument for the axiom can be given as follows.
	www.find-ask.com /Encyclopedia/Axiom_S5/Axiom_S5.html (318 words)

	Modal Logic
		The system B (for the logician Brouwer) is formed by adding axiom (B) to M. It is interesting to note that S5 can be formulated equivalently by adding (B) to S4.
		Let a 4-model be any model whose frame is such that R is a transitive relation on W. Then an argument is 4-valid iff any 4-model whose valuation assigns T to the premises at a world also assigns T to the conclusion at the same world.
		A, the converse of (4), so for example, the system KC4, which is K plus (C4) is adequate with respect to models where the frame is dense, and KDC4, adequate with respect to models whose frames are serial and dense, and so on.
	www.seop.leeds.ac.uk /archives/spr2003/entries/logic-modal (6981 words)

	Proof Explorer - Home Page - Metamath
		An axiom (example: ax-1) is a wff that we postulate to be true no matter what (within the constraints of the syntax rules) we substitute for its variables.
		The somewhat bizarre axiom C10' was shown to be equivalent to the simpler ax-9 after the paper was submitted; see theorem ax9.
		The first three are the axiom and rule schemes for traditional predicate calculus, and the last two are the axiom schemes for the traditional theory of equality.
	us.metamath.org /mpegif/mmset.html (8716 words)

	Chapter 11: The Systems of Complete Modalization - S4°, S4, and S5
		It is clear that S4° is a system of complete modalization in the sense discussed in Chapter 10, and that metatheorems 10.4 and 10.5 hold in S4° when complete modalization is as it was defined for S4 in the statement of *10.6.
		The reason that there is no S5° is that the addition of M10 to S1° makes axiom M6 immediately derivable, giving the system S5; this was first mentioned by Sobocinski 1962.
		It is clear, therefore, that a formula is completely modalized in S5 (M-modalized as well as L-modalized) provided every one of its propositional variables is in the scope of a modal operator.
	www.clas.ufl.edu /users/jzeman/modallogic/chapter11.htm (1474 words)

	The left's real argument against God - Page 7 - Sean Hannity Discussion
		axiom S5 says that if a proposition is possibly necessarily true, then it is necessarily true.
		axiom S5 and the "possibility premise" that a maximally great being is possible.
		The more controversial of these two is the "possibility premise" since S5 is widely but by no means universally accepted.
	www.hannity.com /forum/showthread.php?t=3511&page=7 (1442 words)

	CSCI2408 Type Stack: Algebraic Specification
		We will refer to a particular stack axiom by prefixing its number with the letter S. Axiom S4 describes the characteristic behaviour of a stack.
		It is possible to simplify the last three examples by applying the stack axioms to reduce the stack expressions.
		You should indicate which axiom you are using at each stage of the reduction.
	www.cse.dmu.ac.uk /~drs/csci2408/java4/web/notes/theories/stack_algebra.htm (371 words)

	Contexts (Site not responding. Last check: 2007-10-11)
		System T combined with axioms S4, S5, and BF is one of the strongest versions of modal logic, but it is often too strong.
		The axioms of System T would permit such modifications to the laws, but System S4 would prohibit them because earlier laws could not be deleted.
		Similar analysis would be required to derive the axioms and theorems for all possible combinations of the five kinds of possibility with the five kinds of necessity.
	www.jfsowa.com /pubs/contexts.htm (14781 words)

	The Ontological Arguments - Catholic Answers Forums
		S5 is an axiom from S5 modal logic which states that is something is possibly necessarily true then it is necessarily true.
		If this axiom does not click in your mind further research into modal logic is suggested.
		Now, that is a respectable axiom if you want to take that to be true.
	forums.catholic.com /showthread.php?p=1348191 (4323 words)

	[No title]
		With an axiom system we minimise the number of rules of inference and add a number of basic principles — the axioms — which serve as the foundation for our system.
		Everything we prove rests on these axioms, so if our axioms are false we have no guarantee that what we have proved from them is true.
		An axiom system must have some rules of inference, for otherwise there is no way to manipulate the axioms, and hence no way to prove anything at all.
	ahpc-jp30.st-and.ac.uk /~ahwiki/pub/Trash/TrashAttachment/LogicLecture8.doc (704 words)

	The Invalid Results of Paul Davies
		You'll need to wait before I can answer this.) Now the symbol "a" below, represents a "variable" and, when the axioms or allowed "formal deduction" procedures are applied, then the name of the rule or procedure applied is stated in the second column.
		There are various formal axiom systems similar to S that yield the exact same formal theory.
		The notion of "cannot be formally established in PA" refers to the specifically defined methods for writing down a formal proof using the axioms of PA and first-order predict logic.
	www.serve.com /herrmann/davies.htm (3110 words)

	Teaching Informal Modal Logic in Critical Thinking/Informal Logic Classes
		There are actually a number of different systems of modal logic and it is somewhat controversial as to which is best, for different theorems hold in different systems.
		S5 is particularly interesting because, if it were correct, then a version of the ontological argument could be constructed that would appear to be sound.
		Thus, the soundness of an argument for the existence of God, it may be argued, depends on one's intuitions regarding a theorem of modal logic.
	www.apa.udel.edu /apa/archive/newsletters/v97n2/teaching/logic.asp (2454 words)

	Epistemic Logic (Stanford Encyclopedia of Philosophy)
		The truth-conditions for the doxastic operator are defined in a way similar to that of the knowledge operator and the model may also be expanded to accommodate the two operators simultaneously.
		Other axioms of epistemic import require yet other relational properties to be met in order to be valid in all frames.
		These axioms in proper combinations make up epistemic modal systems of varying strength depending on the modal formulas valid in the respective systems given the algebraic properties assumed for the accessibility relation.
	plato.stanford.edu /entries/logic-epistemic (4695 words)

	Ephilosopher :: Philosophy of Religion Forum :: The Ontological Argument for the Existence of God (Site not responding. Last check: 2007-10-11)
		Modal logic (axiom S5, more specifically) states that if something is possibly necessary, then it is necessary.
		It is a theorem of S5 that no contingent statement is derivable from a necessary truth.
		To use axiom S5, it must be realized that something possibly necessary is to say that something is necessary.
	www.ephilosopher.com /phpBB_14-action-viewtopic-topic-3140-start-0.html (2643 words)

	WHY TRADITIONAL COSMOLOGICAL ARGUMENT DO NOT WORK :
		As a consequence, his sense of necessity, unlike the absolute one, is not subject to system S5’s basic axiom that if it is possible that it is necessary that p, then it is necessary that p.
		Premise 1 is a substitution instance of the axiom of S5 that if it is possible that it is necessary that p, then it is necessary that p.
		Assuming that one is willing to grant the S5 axiom that underlies premise 1, the only possibly dubious premise is 2, and dubious it is indeed.
	www.pitt.edu /~rmgale/cosmo.htm (7780 words)

	Springer Online Reference Works
		For each propositional system of modal logic S it is possible to consider the corresponding predicate system, which is obtained by the addition of object variables, predicate symbols and the quantifiers
		(or one of these) to the language of S. The usual axiom schemes and derivation rules for quantifiers are added.
		On the other hand, every extension of S5 has a finite adequate matrix with one distinguished value.
	eom.springer.de /m/m064320.htm (1205 words)

	Brian F. Chellas's Curriculum Vitae (Site not responding. Last check: 2007-10-11)
		"The connective of necessity of modal logic S5 is metalogical", by Zdzislaw Dywan.
		Paper read at the meeting of the Society for Exact Philosophy, University of Pittsburgh, 5 June 1978, and at the meeting of the Western Canadian Philosophical Association, University of Saskatchewan, 28 October 1978.
		Read at a meeting of the Florida Philosophical Association, Florida Atlantic University, Boca Raton, 8 November 1991, and at a meeting of the Society for Exact Philosophy, University of Southwestern Louisiana, Lafayette, Louisiana, 16 May 1992.
	www.ucalgary.ca /~chellas/vita.html (1630 words)

	Peter Marton
		The same can be said—and later we will exploit this fact—about the modal system within which the zombist argues: He needs S5 for the success of his argument.
		Summarily, if either S5 or logical supervenience is denied, then MT is not inconsistent with the existence of a zombie world.
		The answer is in the negative, because this proposition collapses into ‘zombies are possible’, at least in S5.
	www.brown.edu /Departments/Philosophy/zombie.html (3128 words)

Try your search on: Qwika (all wikis)