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Topic: Arities

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	IFF-FOL Language Grammar
		The arity of a tuple of terms is the union of the term arities.
		The arity of a conjunction is the union of the arities of the conjunct expressions.
		The arity of a negation is the arity of the expression being negated.
	suo.ieee.org /IFF/metalevel/lower/ontology/fol/grammar.html (1397 words)

	Arity - Enpsychlopedia (Site not responding. Last check: 2007-10-19)
		In linguistics, arity is sometimes referred to as valency, not to be confused with valency in mathematics.
		For example, rather than saying "the arity of the addition operation is 2" or "addition is an operation of arity 2" one usually says "addition is a binary operation".
		Sometimes, it is useful to consider a constant as an operator or function of arity 0, and hence call it nullary (or sometimes anary).
	psychcentral.com /psypsych/wiki/Arity (432 words)

	Intermediate MUF Tutorial - Understanding Arities (Site not responding. Last check: 2007-10-19)
		("Arity" is a generalization of "unary", "binary", "trinary"...) The arity of a function is a synopsis of how many values it accepts and returns on the stack.
		Muq expects each function to have a fixed arity (to always consume and return the same number of arguments), and it normally computes this arity for each function as it compiles it, and saves the result for future reference.
		This is sometimes useful in cases which MUF is not smart enough to analyse itself.
	www.muq.org /~cynbe/muq/muf2_14.html (582 words)

	[KIF] Re: SUO: tuples
		Implementations > > of theorem-proving and logic-programming systems often assume that the > > arity of a term is invariant under substitution, which is false when > > sequence variables are used.
		It wouldn't be accurate to say that arities are ambiguous or underspecified in CL. There just aren't any arities.
		In the case of (2), as I've noted several times, you can add arity constraints such as in the standard language of FOL and still be compliant with CL. In these cases, one simply provides a recursive specification of the relevant restrictions.
	philebus.tamu.edu /pipermail/kif/2002-July/001215.html (611 words)

	JTP API Documentation: Uses of Package jtp.disp
		This interface represents backward-chaining reasoners whose goals are literals that can be dispatched based on their relation symbols, polarities and arities.
		This interface represents forward-chaining reasoners whose goals are reasoning steps proving literals, each such reasoning step can be dispatched based on the literal's relation symbol, polarity and arity.
		This is the base interface for all reasoners that have their goals dispatched according to basic literal properties: relation symbol, polarity and arity.
	www-ksl.stanford.edu /software/jtp/old-api/jtp/disp/package-use.html (239 words)

	[No title]
		The details of the new logic are given by introducing new classes, new types with their arities, constants and rules.
		Consequently, the arity declaration for this type is just the class term to which this type is defined to belong.
		Once types, together with their arities, are defined, constants can be declared to build elements of those types.
	www.di.unipi.it /~semprini/isabelle.htm (1919 words)

	[KIF] Re: SUO: tuples (Site not responding. Last check: 2007-10-19)
		Being able to represent (r ?a), (r ?b ?c), >and (r ?d ?e ?f) (the same relation symbol used with different >arities) is pretty unproblematic, since instantiating the arguments >doesn't change the number of arguments in each expression.
		Variadic does not mean just 'one of some particular number of fixed arities'.
		This was Mike Genesereth's argument at the TAMU meeting, by the way, and one that I found convincing (and still do).
	grimpeur.tamu.edu /pipermail/kif/2002-July/001239.html (328 words)

	Primitive Recursive Indices
		The arity of the outer function is lh(d(x, 1)) and the arity of the inner functions is taken to be k, so that the resulting composition has the required arity.
		Notice how nicely having the arity given as an input together with our convention that constants are 0-ary functions allows us to steer past the restrictions on the domains of C and R without including them as special conditions.
		The arities of the embedded functions are recovered from the given k.
	www.andrew.cmu.edu /user/kk3n/recursionclass/2prindex.html (1069 words)

	HUT / Digital Systems Laboratory: Research Report A18 (Site not responding. Last check: 2007-10-19)
		They have the property that all words in the space are within a given Hamming distance, called the covering radius, from some codeword.
		Traditionally, mainly spaces where all coordinates have the same arity (usually 2 or 3, that is, they are binary or ternary) have been discussed.
		The approach is very general, no restrictions are set upon m and the arities q_i.
	www.tcs.hut.fi /old/reports/A18abstract.html (201 words)

	Glossary
		"Arity" is the number of arguments of a function.
		Arity of a function can be 0, 1, 2,...
		Such functions can have any arity larger or equal to a certain minimum arity (the number of non-optional arguments).
	homepage.mac.com /yacas/manual/refprogchapter8.html (970 words)

	Re: primitive-generics are limited in their arities
		Mikael Djurfeldt writes: > The arity of primitive generics is restricted to the arity of their > primitive methods.
		When primitive-generics are unrestricted in terms of arity, they would be more similar to the regular generics, which would be nice, I think...
		Re: primitive-generics are limited in their arities, Mikael Djurfeldt,
	lists.gnu.org /archive/html/guile-devel/2003-07/msg00049.html (93 words)

	Issue 124 - Arities for built=in functions are ignored? (Site not responding. Last check: 2007-10-19)
		I am not sure how the arity checking is supposed to be done, but the arities provided in the Omake_builtin.builtin_funs are clearly ignored - for example, "getenv" is listed there with arity 0, but the real arity is 1 or 2...
		The policy is that if the arity is zero, then the function takes a variable number of arguments (and the arity is not checked).
		The arity is checked iff the number is positive.
	cvs.cs.cornell.edu:12000 /bugzilla/show_bug.cgi?id=124 (163 words)

	ARITIES (Site not responding. Last check: 2007-10-19)
		"ARITIES" is a common misspelling or typo for: amities, rarities.
		In mathematics, the arity of a function or an operator is the number of arguments or operands it takes,
		A function or operator can thus be described as unary, binary, ternary,etc. Terms such as 7-ary or n-ary are also used.
	www.websters-online-dictionary.org /definition/ARITIES (72 words)

	Nuprl - KBDCMDkbd absadjust (Site not responding. Last check: 2007-10-19)
		The arities of free vars from the rhs supercede the arities of free vars on the left with the same name.6.
		The bindings of the lhs are adjusted to match the arities of the var instances in their scope.The rhs will also be adjusted when it seems that a recursive definition is desired.7.
		command, build the fake to contain the vars of the various arities and the op-parms and level-exprs you want in the operator, put the opid you want in the lhs, then use the adjuster.
	www.cs.cornell.edu /Info/People/sfa/Nuprl/EditorDoc/XKBDCMDkbd_absadjust.html (264 words)

	ipedia.com: Free object Article (Site not responding. Last check: 2007-10-19)
		An example for that is the way a free magma on X turns out to be the magma of binary trees labelled at the leaves by X.
		That construction generalises (from a single binary operation to any collection of 'arities') in a way the free object concept makes much more palatable.
		In general, the setting for a free object is like this: a category C of algebraic structures (sets plus operations, obeying some laws) has a functor F to Sets, the category of sets and functions, that simply ignores the operations.
	www.ipedia.com /free_object.html (489 words)

	[Uuu-devel] VMs and such (Site not responding. Last check: 2007-10-19)
		In particular, the area used to store program instructions is garbage collected.
		We recommend to avoid as much as possible dynamically creating atoms (with String.toAtom or VirtualString.toAtom) or records with new arities (for example, with Record.filter).
		Tuples do not have entries in the arity table, so they are not subject to this restriction.
	unununium.org /pipermail/uuu-devel/2004-October/000363.html (330 words)

	Practical Foundations of Mathematics
		As for induction on closure conditions, it is a distortion of the theory to restrict the arities to be finite in advance.
		But we insisted there that the arities were finite, since Theorem 5.6.9 fails for infinitary operations.
		For example the set in Exercise 2.16 with two ``overlapping'' elements is not finite in the strong sense required by Theorem 5.6.9.
	www.cs.man.ac.uk /~pt/Practical_Foundations/html/s61.html (1959 words)

	[Inquiry] Re: Blocks On The Road Of Inquiry -- Discussion
		peirce appears to distinguish this from both arities and modalities.
		i think i can see that modalities are a special case under arities, as reflected in alpha, beta, gamma graphs, and this is related to the synthesis of (a) intension and (b) extension under (c) information, but this is all very tentative.
		at present, the only place where we see anything like proof of three categories being necessary and sufficient is with regard to relation arities.
	stderr.org /pipermail/inquiry/2004-April/001324.html (1044 words)

	[No title]
		In conjunction with products arising from the use of this ;material, there shall be no use of my name in any advertising, ;promotional, or sales literature without prior written consent in ;each case.
		args) (require 'printf) (apply fprintf (current-error-port) args) (newline (current-error-port))) (define (parameter-list->getopt-usage comname optnames arities types aliases.
		(define (getopt->arglist optnames positions arities types defaulters checks aliases.
	www.mit.edu /afs/athena/software/scm_v5d9/slib/getparam.scm (978 words)

	Demo Verification and Specication of web services
		The specification uses 19 page schemas, 4 database relations of arities between 2 and 7, 10 state relations of arities between 0 and 5, 6 input relations of arities between 1 and 5, 5 actions relations of arities between 0 and 5, and 29 constants.
		The specification models 22 pages using 12 database relations (arities up to 10), 11 state relations (arities up to 5), 1 action relation (arity 1) and 31 constants.
		It models 35 pages using 22 database relations (arities up to 14), 7 state relations (arities up to 6) and 22 constants.
	www.cs.ucsd.edu /~lsui/project/examples.html (920 words)

	Mosses98CafeOBJ -- 4.3 Models (Site not responding. Last check: 2007-10-19)
		Note that CASL still allows models where the embedding is actually a set inclusion.
		The binary transition relation of rewriting logic can used together with pairing to represent relations of greater arities (analogously to representing functions of n arguments as unary functions on products).
		But CASL does not have rewriting logic transitions built-in, so there is no reason to restrict the arities of relations.
	www.csl.sri.com /users/mosses/CoFI/Documents/Tentative/Mosses98CafeOBJ/index_18.html (253 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		Together with the notion of sets provided by the feature label theory, this yields a first-class status of arities.
		If the feature label theory is the theory of infinitely many constants and finite sets over infinitely many constants, we obtain an extension of the feature theory CFT, giving first-class status to arities.
		As an another application, we obtain decidability of the theory of feature trees, where the feature labels are words, and where the language includes the successor function on words, lexical comparison of words and first-class status of arities.
	www.ps.uni-sb.de /papers/abstracts/FeatArbStruct.bib (302 words)

	The Journal of Philosophy Vol (Site not responding. Last check: 2007-10-19)
		General graph theory is the theory of structures induced by a single relation (two- or more place, symmetric or not, and so on) and integrally involves what we might think of as "relational combinatorics": the ways in which entities (here, vertices) may be connected by a relation.
		Reduction of arity (from 2 or higher to 1) of basic predicates in the world is thus possible only if one tolerates an explosion of the number of basic monadic predicates.
		This is artfully hidden from us by the casual assumption--in materialist metaphysics, for exampie--that entities are ultimately and simply distinguished by their locations in space, time, or space-time.
	www.neologic.net /rd/Papers/Structure%20J%20Phil.html (11028 words)

	[No title]
		In all cases, if unclaimed arguments remain after processing, a warning is signaled and #f is returned.
		@end defun @defun getopt->arglist optnames positions arities types defaulters checks aliases desc @dots{} Like @code{getopt->parameter-list}, but converts @var{argv} to an argument-list as specified by @var{optnames}, @var{positions}, @var{arities}, @var{types}, @var{defaulters}, @var{checks}, and @var{aliases}.
		If the options supplied violate the @var{arities} or @var{checks} constraints, then a warning is signaled and #f is returned.
	www.mit.edu /afs/athena/software/scm_v5d9/slib/getparam.txi (272 words)

	Module 3, part 1 (Site not responding. Last check: 2007-10-19)
		We have three different arities, even though we have represented only four nodes so far.
		It is possible to write Prolog programs that can handle structured objects with differing arities that represent the same kind of object, but it makes the program more complicated than necessary.
		Each path has one start node and one end node and thus we can immediately be certain that all path facts will have the same arity.
	www.csd.uu.se /kurs/datalogi/lp1/prolog_course/md3/md3_simple_net.html (308 words)

	A Complete Axiomatization of a Theory with Feature and Arity Constraints - Backofen (ResearchIndex) (Site not responding. Last check: 2007-10-19)
		Abstract: this paper are all first-order-logic formulae over a signature of binary and unary predicates called features and arities, respectively.
		We establish the theory CFT by means of seven axiom schemes and show its completeness.
		A complete axiomatization of a theory with feature and arity constraints.
	citeseer.lcs.mit.edu /backofen95complete.html (738 words)

	The Mercury Project: [m-dev.] for review: update of Aditi update changes
		Add predicate `adjust_func_arity' to convert between the arity
		of a function to its arity as a predicate.
		+ ; { Arities = [_] } ->
	www.cs.mu.oz.au /research/mercury/mailing-lists/mercury-developers/mercury-developers.9907/0149.html (909 words)

	The Mercury Project: Re: [m-rev.] for review: fix a bug caused by fake type_ctor arities
		The Mercury Project: Re: [m-rev.] for review: fix a bug caused by fake type_ctor arities
		Re: [m-rev.] for review: fix a bug caused by fake type_ctor arities
		Next in thread: Fergus Henderson: "Re: [m-rev.] for review: fix a bug caused by fake type_ctor arities"
	www.cs.mu.oz.au /research/mercury/mailing-lists/mercury-reviews/mercury-reviews.0303/0078.html (262 words)

	Extract.hs
		Adds type of variables from type declarations and primitive and foreign function definitions to symbol table of internal state (but not type declarations from classes).
		{- Adds arity of defined variable to symbol table of internal state (any old arity is overwritten).
		Adds error message, if equations of definition suggest different arities.
	www.cse.ogi.edu /~hallgren/Talks/LHiH/compiler98/Extract.hs (201 words)

	The Mercury Project: [m-rev.] for review: fix a bug caused by fake type_ctor arities (Site not responding. Last check: 2007-10-19)
		Fix a bug caused by the fake arities of the types defining typeinfos:
		+ The proper fix would be to avoid making their arities** lie.
		+% to have arity 1, when its true arity is variable, with the actual argument
	www.mercury.cs.mu.oz.au /mailing-lists/mercury-reviews/mercury-reviews.0303/0070.html (1089 words)

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