Extension (predicate logic)

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Topic: Extension (predicate logic)

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	Predicate Logic and Tree Automata with Tests - Treinen (ResearchIndex)
		Predicate Logic and Tree Automata with Tests (2000)
		@article{ treinen00predicate, author = "Ralf Treinen", title = "Predicate Logic and Tree Automata with Tests", journal = "Lecture Notes in Computer Science", volume = "1784", pages = "329--??", year = "2000", url = "citeseer.ist.psu.edu/article/treinen00predicate.html" }
		Our rst insight is that there is no generalization of tree automata with tests that has a decidable emptiness problem and that is equivalent to the full class of formulae in some extension of WS2S, at least not when we are asking for an conservative extension of the classical...
	citeseer.ist.psu.edu /288512.html

	First-order logic - Wikipedia, the free encyclopedia
		The predicate calculus is an extension of the propositional calculus.
		Nevertheless, first-order logic is strong enough to formalize all of set theory and thereby virtually all of mathematics.
		First-order logic is mathematical logic that is distinguished from higher-order logic in that it does not allow quantification over properties; i.e.
	www.wikipedia.org /wiki/First-order_predicate_calculus

	predicate logic
		<logic> (Or "predicate calculus") An extension of propositional logic with separate symbols for predicates, subjects, and quantifiers.
		For example, where propositional logic might assign a single symbol P to the proposition "All men are mortal", predicate logic can define the predicate M(x) which asserts that the subject, x, is mortal and bind x with the universal quantifier ("For all"):
		Higher-order predicate logic allows predicates to be the subjects of other predicates.
	www.linuxguruz.com /foldoc/foldoc.php?predicate+logic

	Predication I: Simple Predications
		Predicate logic is an extension of sentential logic which studies why those additional arguments are valid.
		That's important in defining a wff in predicate logic: an n-place predicate letter followed by exactly n names is a wff, but if it is followed by more or fewer than n names it's not a wff.
		You might put it this way: a predicate expression is something that becomes a sentence when its blank space (or spaces) is (or are) filled in with names; a name is a word that can be used to fill in a blank in a predicate expression.
	aristotle.tamu.edu /~rasmith/Courses/Logic/predication.1.html

	Binary Decision Diagrams for First Order Predicate Logic (ResearchIndex)
		Abstract: We present an extension of Binary Decision Diagrams (BDDs) such that they can be used for predicate logic.
		Binary Decision Diagrams for First Order Predicate Logic
		Binary Decision Diagrams for First Order Predicate Logic (ResearchIndex)
	citeseer.ist.psu.edu /179.html (410 words)

	First-order predicate calculus - Wikipedia, the free encyclopedia
		Predicate calculus is an extension of propositional calculus.
		First-order predicate calculus or first-order logic( FOL) is a theory in symbolic logic that permits the formulation of quantified statements such as "there is at least one X such that..." or "for any X, it is the case that...", where X is an element of a set called the domain of discourse.
		A first-order theory is a theory that can be axiomatised as an extension of first-order logic by adding a recursive set of first-order sentences as axioms.
	en.wikipedia.org /wiki/Predicate_calculus (410 words)

	2000-November.txt
		The semantics of the generalized head extension should be specified by something like the mapping (?R X Y) and (?F X Y) to (apply-predicate ?R X Y) and (apply-function ?F X Y).
		hard to ensure that this was preserved in every extension, and (1) is the real killer, since I think that in order to be viable, KIF needs to be able to describe the syntax of other languages as well as its own.
		hard to ensure that this >was preserved in every extension, and (1) is the real killer, since I >think that in order to be viable, KIF needs to be able to describe the >syntax of other languages as well as its own.
	grimpeur.tamu.edu /pipermail/kif/2000-November.txt (410 words)

	Predication I: Simple Predications
		Predicate logic is an extension of sentential logic which studies why those additional arguments are valid.
		In passing, we should note that there are also zero -place predicate letters: these are just the propositional variables we used in sentential logic.
		Sentential logic can't see any structure inside atomic statements.
	aristotle.tamu.edu /~rasmith/Courses/Logic/predication.1.html (410 words)

	predicate
		<logic> (Or "predicate calculus") An extension of propositional logic with separate symbols for predicates, subjects, and quantifiers.
		For example, where propositional logic might assign a single symbol P to the proposition "All men are mortal", predicate logic can define the predicate M(x) which asserts that the subject, x, is mortal and bind x with the universal quantifier ("For all"):
		Higher-order predicate logic allows predicates to be the subjects of other predicates.
	www.linuxguruz.com /foldoc/foldoc.php?predicate (119 words)

	Frege's Logic, Theorem, and Foundations for Arithmetic
		It will soon become clear that the language and logic of his predicate calculus are ‘second-order’.
		His axioms included familiar axioms of propositional logic, second-order predicate logic, and the logic of identity.
		Despite the failure of Basic Law V, Frege validly proved a rather deep fact about the natural numbers, namely, that the Dedekind/Peano axioms for number theory could be derived in second-order logic with the help of a single additional principle.
	plato.stanford.edu /entries/frege-logic (119 words)

	Predicate calculus - Wikipedia, the free encyclopedia
		In mathematical logic the predicate calculus, predicate logic or calculus of propositional functions is a formal system used to describe mathematical theories.
		The predicate calculus is an extension of propositional calculus, which is inadequate for describing more complex mathematical structures.
		A subject is a name for a member of a given group of individuals (a set) and a predicate is a relation on this group.
	en.wikipedia.org /wiki/Predicate_logic (119 words)

	Mind: Why higher-order vagueness is a pseudo-problem - Symposium: Higher-Order Vagueness
		The apparent lack of a sharp boundary to the predicate's extension is typically explained by the presence of border (borderline, or penumbral) cases for the predicate in question: cases which jointly constitute the border region (borderline region or penumbra) for the vague predicate.
		Even given qualifications to the notion of a border case in order to exclude cases of inexactness, meaninglessness, ambiguity, context sensitivity, etc. the notion of a border case still appears too broad to properly characterise the phenomenon of vagueness.
		I want to argue that the iterative conception captures a feature of vagueness that is real enough--the phenomenon of higher orders of vagueness--but that this phenomenon is ultimately an echo of a more basic feature of border cases.
	www.dynomind.com /p/articles/mi_m2346/is_n409_v103/ai_14916928 (1414 words)

	The Neural Basis of Predicate-Argument Structure
		The idea of zero-place predicates has generally been sidelined in logic (despite their obvious applicability to weather phenomena); and the extension of predicate-argument notation to include event variables is relatively recent.
		Logical binding is not a relationship between a predicate and its argument, but a relationship between all predicates in the scope of a particular quantifier which take the bound variable as argument.
		The canonical fillers of the argument slots in predicate logic formulae are constants denoting individuals, corresponding roughly to natural language proper names.
	www.ling.ed.ac.uk /~jim/newro.htm (1414 words)

	IFIP Working Group 2.1 -- Meeting #58 Details
		Exemplarily, we present the integration of a logic language with constraint systems, and the extension of a functional logic language with constraints.
		By formal calculation using a functional predicate calculus, weakest precondition and strongest postcondition semantics are derived as theorems.
		Right from the start, all calculations were guided by the "shape of the formulas", and went very smoothly where intuition was uncertain; afterwards one could "sit back and enjoy" the intuitive interpretation of the intermediate and final results.
	web.comlab.ox.ac.uk /oucl/work/jeremy.gibbons/wg21/meeting58 (975 words)

	Predicate transformer semantics - Wikipedia, the free encyclopedia
		Predicate transformer semantics is an extension of Floyd-Hoare Logic invented by Dijkstra and extended and refined by other researchers.
		A predicate transformer is a total function mapping between two predicates on the state space of a program.
		It is a method for defining the semantics of an imperative programming language by assigning to each command in the language a corresponding predicate transformer.
	en.wikipedia.org /wiki/Predicate_transformer_semantics (975 words)

	First-order logic - Wikipedia, the free encyclopedia
		The predicate calculus is an extension of the propositional calculus that defines which statements of first order logic are provable.
		Most of these logics are in some sense extensions of first order logic: they include all the quantifiers and logical operators of first order logic with the same meanings.
		First-order predicate calculus (FOPC) or first-order logic (FOL) is a system of mathematical logic, extending propositional logic (equivalently, sentential logic) and in turn extended by second-order logic.
	en.wikipedia.org /wiki/First-order_predicate_calculus (2903 words)

	First-order predicate calculus - Encyclopedia.WorldSearch
		First-order predicate calculus or first-order logic (FOL) is a theory in symbolic logic that permits the formulation of quantified statements such as "there is at least one X such that..." or "for any X, it is the case that...", where X is an element of a set called the domain of discourse.
		Predicate calculus is an extension of propositional calculus.
		If propositional calculus is defined with eleven axioms and one inference rule (modus ponens), not counting some auxiliary laws for the logical equivalence operator, then predicate calculus can be defined by appending four additional axioms and one additional inference rule.
	encyclopedia.worldsearch.com /predicate_calculus.htm (2903 words)

	The Neural Basis of Predicate-Argument Structure
		The idea of zero-place predicates has generally been sidelined in logic (despite their obvious applicability to weather phenomena); and the extension of predicate-argument notation to include event variables is relatively recent.
		Logical binding is not a relationship between a predicate and its argument, but a relationship between all predicates in the scope of a particular quantifier which take the bound variable as argument.
		The canonical fillers of the argument slots in predicate logic formulae are constants denoting individuals, corresponding roughly to natural language proper names.
	bbsonline.cup.cam.ac.uk /Preprints/Hurford/Referees (2903 words)

	predicate logic from FOLDOC
		<logic> (Or "predicate calculus") An extension of propositional logic with separate symbols for predicates, subjects, and quantifiers.
		For example, where propositional logic might assign a single symbol P to the proposition "All men are mortal", predicate logic can define the predicate M(x) which asserts that the subject, x, is mortal and bind x with the universal quantifier ("For all"):
		Higher-order predicate logic allows predicates to be the subjects of other predicates.
	foldoc.doc.ic.ac.uk /foldoc/foldoc.cgi?predicate+logic (2903 words)

	First-order logic - Wikipedia, the free encyclopedia
		The predicate calculus is an extension of the propositional calculus.
		Nevertheless, first-order logic is strong enough to formalize all of set theory and thereby virtually all of mathematics.
		First-order logic is Mathematical logic that is distinguished from higher-order logic in that it does not allow quantification over properties; i.e.
	en.wikipedia.org /wiki/Predicate_logic (2903 words)

	First-order predicate calculus - Wikipedia, the free encyclopedia
		A first-order theory is a theory that can be axiomatised as an extension of first-order logic by adding a recursive set of first-order sentences as axioms.
		There are two types of axioms: the logical axioms which embody the general truths about proper reasoning involving quantified statements, and the axioms describing the subject matter at hand, for instance axioms describing sets in set theory or axioms describing numbers in arithmetic.
		Its restriction to quantification over individuals makes it difficult to use for the purposes of topology, but it is the classical logical theory underlying mathematics.
	en.wikipedia.org /wiki/First-order_predicate_calculus (2903 words)

	Specifications in Temporal Logic
		RTTL is an extension of the Manna-Pnueli temporal logic [11].
		Temporal logic studies the structure or topology of time [13].
		In more recent years, temporal logic has been successfully applied in various areas of computer science, especially software verification.
	rutcor.rutgers.edu /~pinzon/papers/rrr1/node13.html (245 words)

	Constraint Simplification Rules - Fruhwirth (ResearchIndex)
		1 Termination Proofs for Logic Programs based on Predicate Ine..
		We are investigating the use of logic programs to define and implement constraint solvers 1.
		The representation of constraint evaluation in the same formalism as the rest of the program greatly facilitates the prototyping, extension, specialization and combination of constraint solvers.
	citeseer.ist.psu.edu /fruhwirth92constraint.html (245 words)

	15-818A4 Separation Logic
		Separation logic is an extension of Hoare logic for reasoning about programs that use shared mutable data structures.
		We will survey the current development of this logic, including extensions that permit unrestricted address arithmetic, dynamically allocated arrays, recursive procedures, and shared-variable concurrency.
		PREREQUISITES: Some knowledge of predicate logic and Hoare logic.
	www-2.cs.cmu.edu /afs/cs.cmu.edu/project/fox-19/member/jcr/www15818A4s2004/cs818A4-04.html (130 words)

	cs-disproving.abstract.txt
		First-Order Dynamic Logic is an extension of First-Order Predicate Logic that enables propositions about programs to be made in a natural way.
		We consider a dynamic logic for \Java\ and describe an approach for proving formulas invalid that works by reduction to the validity problem.
		The adherence of a program to certain properties---like preserving invariants or compliance with pre-/postconditions---can be translated into the statement that a particular formula of Dynamic Logic is valid, which can be proved mechanically using calculi.
	www.cs.chalmers.se /~philipp/publications/cs-disproving.abstract.txt (118 words)

	The Use of Mathematical Logic
		Particular logical languages are determined by a particular choice of concepts and the predicate and function symbols to represent them.
		One important extension was the development of modal logic starting in the 1920s and using it to treat modalities like knowledge, belief and obligation.
		We need to distinguish the actual use of logic from what Allen Newell, [Newell, 1981] and [Newell, 1993], calls the logic level and which was also proposed in [McCarthy, 1979].
	www-formal.stanford.edu /pub/jmc/human/node3.html (555 words)

	McDermott & Doyle 1990: Non-Monotonic Logic I
		Defines a broad array of terms relating to non-monotonic logic, concentrating on the notion of a ``fixed point'' which is an extension of a notion from monotonic logic.
		Keywords: Non-Monotonic Logic Systems: TMS (Truth Maintenance System) Summary: Introduces the notion of non-monotonic logic, a logical system in which new information may be added to invalidate old conclusions.
		McDermott and J. Doyle, Non-Monotonic Logic I. Artificial Intelligence, 13 (1\&2), 1980.
	www.cc.gatech.edu /~jimmyd/summaries/mcdermott1980-1.html (251 words)

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Topic: Extension (predicate logic)

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