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Topic: Functional predicate

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	Equality (mathematics) article - Equality (mathematics) equality mathematics binary predicate equivalence relation ... (Site not responding. Last check: 2007-11-07)
		Note that it may be impractical to compute with equivalence classes: one solution often used is to look for a distinguished normal form representative of a class.
		Predicate logic contains standard axioms for equality that formalise Leibniz's law, put forward by the philosopher Gottfried Leibniz in the 1600s.
		This axiom schema, valid for any predicate P in one variable, takes care of only one direction of Leibniz's law; if x and y are equal, then they have the same properties.
	www.what-means.com /encyclopedia/Equals (767 words)

	Functional predicate -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		In a (A representative form or pattern) model, a function symbol will be modelled by a (A mathematical relation such that each element of one set is associated with at least one element of another set) function.
		Note that P will itself be a relational ((logic) what is predicated of the subject of a proposition; the second term in a proposition is predicated of the first term by means of the copula) predicate involving both X and Y.
		Many treatments of predicate logic don't allow functional predicates, only relational ((logic) what is predicated of the subject of a proposition; the second term in a proposition is predicated of the first term by means of the copula) predicates.
	www.absoluteastronomy.com /encyclopedia/f/fu/functional_predicate.htm (1157 words)

	Axiom schema of replacement - Wikipedia, the free encyclopedia
		Indeed, if one formalises the language of predicate logic to allow the use of derived functional predicates in axiom schemas, then the axiom schema may be rewritten as:
		For example, suppose that f is a function from a set S to a set T.
		Then we may construct a functional predicate F such that F(x) = f(x) whenever x is a member of S, letting F(x) be anything we like otherwise (it won't matter for this application).
	en.wikipedia.org /wiki/Axiom_schema_of_replacement (1088 words)

	[No title]
		The functional structure, or f-structure, is a hierarchy of finite functions that assigns values to the subject, predicate, object, and other primitive grammatical relations of a sentence.
		What differs is the functional organization: just as in English, the dependency is unacceptable when the initial phrase must be interpreted as an adjunct but permissible when it is an argument of the subsequent predicate.
		The problem, of course, is that this is an infinite family of equations, and hence impossible to enumerate in a finite disjunction appearing on a particular rule of grammar.
	www-csli.stanford.edu /Archive/monthly/month7 (4526 words)

	Gottlob Frege
		In these functional expressions, ‘()’ is used as a placeholder for what Frege called the arguments of the function; the placeholder reveals that the expressions signifying function are, on Frege's view, incomplete and stand in contrast to complete expressions such as those in (a), (b), and (c).
		Thus, a simple predication is analyzed in terms of falling under a concept, which in turn, is analyzed in terms of functions which map their arguments to truth values.
		Frege's functional analysis of predication coupled with his understanding of generality freed him from the limitations of the ‘subject-predicate’ analysis of ordinary language sentences that formed the basis of Aristotelian logic and it made it possible for him to develop a more general treatment of inferences involving ‘every’ and ‘some’.
	www.science.uva.nl /~seop/archives/win2004/entries/frege (10226 words)

	Predicate Colloquium (Site not responding. Last check: 2007-11-07)
		Participants in the Conference are cordially invited to attend, free of charge, a one-day Colloquium on the Predicate in Functional Grammar on Saturday 4 July, from 9.30 a.m.
		This Colloquium is co-organized by the Institute for Functional Research into Language and Language Use (IFOTT), an inter-university institute comprising researchers from the University of Amsterdam, the University of Leiden and the Vrije Universiteit, and by the CNRS Institute Langues -- Discourse -- Cognition (LanDisCo) of the Université Nancy 2, France.
		ONE-DAY COLLOQUIUM ON THE PREDICATE IN FUNCTIONAL GRAMMAR
	www.mis.coventry.ac.uk /FGIS/collo.html (2133 words)

	Return to conference page
		Alexiadou 1999, Davis and Matthewson 1999, Marantz 1995), which explore the idea that functional heads are involved in determining lexical category, the predicate fronting analyses might predict that predicate-initial languages do not exhibit the same sorts of categorical distinctions as V-fronting or INFL-lowering languages.
		In this paper I will outline the properties of lexical categories in Niuean, and I will argue that these characteristics are consistent with the predicate fronting analysis, and that they lend support to this analysis, as well as to theories of word classes which appeal to relations between functional heads and lexical heads.
		Related issues will also be discussed, such as the nature of the predicate in Niuean (which can freely be noun-like, adjective-like, or verb-like), the absence of infinitives, and the isolating morphology of the language.
	www.ling.hawaii.edu /afla/AbMassamD.htm (402 words)

	Functional programming in the Java language
		A higher order function is able to take another function (indirectly, an expression) as its input argument, and in some cases it may even return a function as its output argument.
		From a functional programming standpoint, the expression is not yet a general piece of logic; that is, it cannot be passed around and asked to execute whenever you want, without regard to the current position of execution control.
		That is, you need to compose a function that internally calls the first functor and streams the output of that evaluation as input into the evaluation of the second functor.
	www-128.ibm.com /developerworks/library/j-fp.html?ca=dnt-528 (4910 words)

	"Practical Predicate Dispatch" (Site not responding. Last check: 2007-11-07)
		Predicate dispatch is an object-oriented (OO) language mechanism for determining the method implementation to be invoked upon a message send.
		With predicate dispatch, each method implementation includes a predicate guard specifying the conditions under which the method should be invoked, and logical implication of predicates determines the method overriding relation.
		Predicate dispatch naturally unifies and generalizes several common forms of dynamic dispatch, including traditional OO dispatch, multimethod dispatch, and functional-style pattern matching.
	www.cs.ucla.edu /~todd/research/oopsla04.html (256 words)

	ACM OOPS Messenger 4, 4 (Oct 1993), 2-27 (Site not responding. Last check: 2007-11-07)
		Functional arrays are known to have performance problems, because a succession of single-element updates may convert a problem of linear complexity into one of quadratic complexity [Bloss89].
		For example, the comparison of (functional) rational numbers would be performed by comparing their numerators and denominators; this comparison would only work correctly for pairs with no common divisors in which the sign appeared uniformly in either the numerator or the denominator.
		Since these functional dependencies can all be viewed as immutable attributes of the object (whether direct attributes or transitive attributes dependent upon an immutable direct attribute), the inclusion of all of these attributes as part of the object cannot cause an inconsistency.
	evil-wire.luvfeed.org /cache/3826 (15312 words)

	Gottlob Frege
		In the modern predicate calculus, the symbols ‘∀’ (‘every’) and ‘∃’ (‘some’) are called the ‘universal’ and ‘existential’ quantifier, respectively, and the variable ‘x’ in the sentence ‘∀xMx’ is called a ‘quantified variable’, or ‘variable bound by the quantifier’.
		In the notation of the modern predicate calculus, this is formalized as:
		One may consistently suppose that the concept denoted by the former predicate maps John to The True whereas the the concept denoted by the latter predicate does not.
	plato.stanford.edu /entries/frege (10319 words)

	PAL Constraint Statements
		A PAL statement is composed of a set of embedded predicate and functional expressions that involve variables ranging over a set of values (range definitions), and that ultimately return true or false on each particular instantiation of variables.
		To write those sentences, PAL supports a number of predefined predicates and functions, that can be used in constraint statements to test or compute properties of variables.
		The slot responsible_for is used as a predicate, to test whether the employee in question is under the responsibility of the editor in question.
	protege.stanford.edu /plugins/paltabs/pal-documentation/lang_const.htm (569 words)

	preface
		Abstract discussions such as what a constituent is are largely avoided (in fact, the term constituent is since it is a stumbling block), and the structure of the NP and AP is brought in line with that of the VP: NPs and APs have complements as well as modifiers.
		Lexical categories project to phrases and these phrases have functions at sentence level (subject, predicate, object).
		Functional categories (the determiner, auxiliary, coordinator, and complementizer) do not project to phrases and have no function at sentence level (they function exclusively inside a phrase and connect clauses and phrases).
	www.public.asu.edu /~gelderen/314text/preface.htm (771 words)

	Introduction to Mathematical Logic - From Monitor-Data.com Store
		Called predicate calculi in today's parlance, the author first defines the pure functional calculus of first order, and shows that the theorems of the propositional calculus also follow when considered as part of this system.
		In chapter 4, the author gives an alternative formulation of pure functional calculus of first order, wherein rules of substitution are used and axiom schemata are replaced by instances, making the number of axioms finite.
		In the last chapter of the book the author considers functional (predicate) calculi of second order, which is distinguished from the first order case by allowing the variables to range over what its predicates and subjects represent.
	www.monitor-data.com /books/0691029067.html (1252 words)

	symbolic logic -> The Predicate Calculus on Encyclopedia.com 2002 (Site not responding. Last check: 2007-11-07)
		Socrates is a man. Therefore Socrates is mortal.” The syllogism and many other more complicated arguments are the subject of the predicate calculus, or quantification theory, which is based on the calculus of classes.
		The predicate calculus of monadic (one-variable) predicates, also called uniform quantification theory, has been shown to be complete and has a decision procedure, analogous to truth tables for truth-functional analysis, whereby the validity or invalidity of any statement can be determined.
		The general predicate calculus, or quantification theory, was also shown to be complete by Kurt Gödel, but Alonso Church subsequently proved (1936) that it has no possible decision procedure.
	www.encyclopedia.com /html/section/symbolic_thepredicatecalculus.asp (384 words)

	Translation Strategies for Monadic Predicate Logic
		Statements in predicate logic will either be a singular statement (or a truth functional combination of singular statements) or a quantified statement (or, at worst, a truth functional statement that contains a quantified statement as a component).
		For example, the singular statement 'Jane is married' might use the predicate letter 'M' for the attribute of being married and the individual constant 'j' for Jane.
		So, the quantifier is existential, the propositional function is a conjunction, the subject term 'talented actors' is the left hand conjunct, and the predicate phrase 'are not famous' is the right hand conjunct.
	www.hu.mtu.edu /~wsewell/hu250/monadic_tips.htm (1626 words)

	Systemic functional grammar (Site not responding. Last check: 2007-11-07)
		Systemic functional grammar is a grammar model developed by Michael Halliday.
		It is functional in the sense that it attempts to explicate the communicative implications (function) of a selection within one of these systems.
		In general, functional approaches to grammar can be differentiated from formal or generative approaches to grammar by their focus on the communicative, as opposed to cognitive, aspect of language.
	www.kiwipedia.com /systemic-functional-grammar.html (125 words)

	Solution Strategies, Transfer, and Computational Resources II: Move Pattern Strategy
		Basic perceptual predicates are assumed to be part of the problem independent perceptual predicates possessed by the problem solver.
		In contrast, functional predicates are assumed to be perceptual predicates that have been developed as a result of understanding and solving a particular problem - they are problem dependent.
		This predicate is defined as true if 'a disk X that is on the peg of disk Y and X is a larger disk than disk Y. The functional predicate in row 4, FREE(A,X), has a relatively complex definition involving a universal quantifier.
	www.rci.rutgers.edu /~cfs/472_html/ProblemSolving/TOH_Strategies/TOH_MovePattern.html (629 words)

	ipedia.com: Mapping Article (Site not responding. Last check: 2007-11-07)
		In formal logic, it is sometimes used for a functional predicate.
		In mathematics and related technical fields, it is some kind of function: see map (mathematics).
		In computer science, it is usually a computable function, a procedure, or a table, e.g.
	www.ipedia.com /mapping_1.html (181 words)

	Axiom schema of specification : Axiom schema of comprehension (Site not responding. Last check: 2007-11-07)
		This is much the same trick as was used in the NBG axioms of the previous section, where the predicate was replaced by a class that was then quantified over.
		In the New Foundations[?] approach to set theory pioneered by W.V.O. Quine, the axiom of comprehension for a given predicate takes the unrestricted form, but the predicates that may be used in the schema are themselves restricted.
		The predicate (C isn't in C) is forbidden, because the same symbol C appears on both sides of the membership symbol; thus, Russell's paradox is avoided.
	www.wordlookup.net /ax/axiom-schema-of-comprehension.html (1296 words)

	Functional Grammar
		The conference was preceded by a one-day Colloquium on the Predicate in Functional Grammar organized jointly by the Institute for Functional Research into Language and Language Use (Amsterdam-Leiden) and the CNRS Institute Langues--Discourse--Cognition (LanDisCo) of the Université Nancy 2 (France) and funded by the Netherlands Organization for Scientific Research NWO.
		The 3rd International Conference on Functional Grammar was held in Amsterdam, The Netherlands, 20-24 June, 1988.
		Functional Grammar, which was held at the Universiteit van Amsterdam, Amsterdam, The Netherlands, 4-8 June 1984.
	home.hum.uva.nl /fg/conf_archives.html (487 words)

	Instance Based Function Learning - Ramon, Raedt (ResearchIndex)
		In IBFL one is given a set of positive examples of a functional predicate.
		The purpose is then to predict the output of the predicate given a new input.
		Further assumptions are that there is no background theory and that the inputs and outputs of the predicate consist of structured terms.
	citeseer.ist.psu.edu /ramon99instance.html (508 words)

	Cyc Fundamental Vocabulary
		#$Predicate is a collection of _relations_, and not a collection of expressions that represent or denote such relations.
		#$CommutativeRelation COMREL is a predicate or function that is commutative in all of its argument-places.
		That is, if COMREL is a predicate (function) that holds among (has the value VAL for) a given sequence of arguments, then COMREL also holds among (has the same value VAL for) any permutation of that sequence.
	www.cyc.com /cycdoc/vocab/fundamental-vocab.html (1311 words)

	Alex Winston's Blog: Functional objects made easy with tiger (Site not responding. Last check: 2007-11-07)
		Functional objects made even easier with tiger »
		predicates and closures as illustrated by the following code fragment.
		Your use of this web site or any of its content or software indicates your agreement to be bound by these Terms of Participation.
	weblogs.java.net /blog/alexwinston/archive/2005/01/functional_obje.html (1016 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		A ;;; natural operation is to extend this predicate to every element of ;;; a list, set, or other collection.
		Since ;;; we require that the collection function's first argument is ;;; the collection under examination, we simply need to write ;;; (lambda (?x) (actual-collection-P ?x [extra-args])), where the ;;; extra arguments are taken from the trigger we are looking at.
		The substitution for predicate ;;; is difficult, because we want to support very flexible ;;; predicates involving many arguments and various weird terms.
	www.cs.utexas.edu /users/jared/osets/osets-0.9/computed-hints.lisp (943 words)

	[No title]
		A predicate F is an element of Anti-Symmetric-Binary-Predicate if and only if F is a binary predicate and, if both (F X Y) and (F Y X) hold, then X=Y, for every X,Y within the domain and range of F. For example, Greater-Than-Or-Equal-To, Compatible-Blood-Types.
		A predicate F is an element of Anti-Transitive-Binary-Predicate if and only if F is a binary predicate and, for every X,Y,Z in the domain of F, (:not (:and (F X Y)(F Y Z)(F X Z))).
		A predicate F is an element of Asymmetric-Binary-Predicate if and only if F is a binary predicate and (F X Y) implies (:not (F Y X)).
	www-ksl.stanford.edu /onto-std/merged-ontology.ok (9915 words)

	English and Spanish Conjunctive Predicates
		This study provides a formal and functional account of a type of complex predicate which frequently occurs in English and Spanish conversation but has not been previously addressed in the literature.
		Regarding their function in discourse, conjunctive predicate constructions are found in particular junctures within conversational narrative sequences (Sacks 1974, Goodwin, 1984) and procedural sequences (Gallardo-Pauls 1993).
		The present study thus provides a formal and functional account of conjunctive predicate constructions as a special type of complex predicate that is commonly found in both English and Spanish conversation but has not received attention previously in the literature.
	www.unm.edu /~hdls/hdls-2/ivosanchez.html (728 words)

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