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# Topic: Predicate calculus

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 NationMaster - Encyclopedia: Predicate calculus The predicate calculus is an extension of the propositional calculus. If the propositional calculus is defined with eleven axioms and one inference rule (modus ponens), not counting some auxiliary laws for the logical equivalence operator, then the predicate calculus can be defined by appending four additional axioms and one additional inference rule. First-order predicate calculus or first-order logic (FOL) is a theory in symbolic logic that states quantified statements such as "there exists an object such that..." or "for all objects, it is the case that...". www.nationmaster.com /encyclopedia/Predicate-calculus   (1670 words)

 First-order logic - Wikipedia, the free encyclopedia It is important to note that the predicate calculus can be formalized in many equivalent ways; there is nothing canonical about the axioms and rules of inference given here, but any formalization will yield the same theorems of logic (and deduce the same theorems from any set of non-logical axioms). The predicate calculus is an extension of the propositional calculus that defines which statements of first order logic are provable. If the propositional calculus is defined with a suitable set of axioms and the single rule of inference modus ponens (this can be done in many different ways), then the predicate calculus can be defined by appending some additional axioms and the additional inference rule "universal generalization". en.wikipedia.org /wiki/Predicate_logic   (3184 words)

 [No title]   (Site not responding. Last check: 2007-10-31) 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. While the set of inference rules in first-order calculus is finite, the set of axioms may very well be and often is infinite. We are using the object constants 0 and 1, the function constants + and *, and the predicate constant =. www.wikiwhat.com /encyclopedia/f/fi/first_order_predicate_calculus.html   (1059 words)

 The predicate calculus   (Site not responding. Last check: 2007-10-31) However, Frege's account was defective in several respects, and notationally awkward to boot. Instead of Frege's system, we shall present a streamlined system known as first-order logic or the predicate calculus. The predicate calculus dates from the 1910's and 1920's. www.math.psu.edu /simpson/papers/philmath/node6.html   (107 words)

 E. Dubinsky & O. Yiparaki One role of predicate calculus in mathematics is as a tool for making sense of and analyzing mathematical statements which are not otherwise understood. But predicate calculus becomes important when dealing with concepts which are not well understood and for which analogies and mental pictures are hard to come by --- such as uniform continuity. They use the tool of predicate calculus (implicitly or explicitly) to convert these strange statements into familiar situations by building new images that may be fundamentally different from what is previously in their experience. www.cs.cornell.edu /Info/People/gries/symposium/dubinsky.htm   (6189 words)

 MATHS: Lower Predicate Calculus The lower predicate calculus (LPC) with equality is a standard logic that can be applied to a wide range of situations where we have objects or individuals to talk about. (principle_of_genericity): The lower predicate calculus with equality is a generic logic that applies to all types of objects. Some predicates remain true for all values of a variable, others are true for only one value, some are true for at least one value some are true for no value. www.csci.csusb.edu /dick/maths/logic_10_PC_LPC.html   (2131 words)

 Predicates and individuals   (Site not responding. Last check: 2007-10-31) In the predicate calculus, the subject/predicate distinction is drawn somewhat differently from the way it is drawn in Aristotelean logic. The main point here is that, in the predicate calculus, a subject is always an individual entity, never a class of entities. Since a subject in the predicate calculus is always an individual entity, it is usual to speak of individuals rather than subjects. www.math.psu.edu /simpson/papers/philmath/node7.html   (452 words)

 PREDICATE CALCULUS The actual interpretation of the predicate and its arguments, of course, depends entirely on the use to which the logician wants to put his calculus. Such a rule produces a predicate calculus that is recursive, which means that the logician may define a part in terms of the same part relationship. It is important to realize that when the logician defines a predicate, as I did in the examples of figure 1, one will always make a tacit assumption as to the type of its arguments. userpages.burgoyne.com /bdespain/grammar/gram043.htm   (576 words)

 Predicate calculus In the predicate calculus the logician decomposes a proposition further into two parts: a predicate () and a set of one or more argument s (). Predicate logic breaks a statement down into component parts, an object, object characteristic or some object assertion Predicate calculus uses variables and functions of... Related: predicate calculus :: predicate calculus examples :: predicate calculus tutorial :: predicate calculus symbols :: predicate calculus and program semantics :: predicate calculus example :: predicate calculus resolution :: predicate calculus unification :: predicate calculus in ai :: predicate calculus pdf www.logicjungle.com /wiki/Predicate_calculus   (295 words)

 The Epsilon Calculus The epsilon calculus is a logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics. The epsilon calculus is, in its most basic form, an extension of first-order predicate logic with an "epsilon operation" that picks out, for any true existential formula, a witness to the existential quantifier. The second epsilon theorem shows that any detour through the epsilon calculus used to derive a theorem in the language of the predicate calculus from axioms in the language of the predicate calculus can also be avoided. plato.stanford.edu /entries/epsilon-calculus   (6424 words)

 First order predicate calculus   (Site not responding. Last check: 2007-10-31) First-order predicate calculus or first-order logic (FOL) is a theory in symbolic logic that states quantified statements such as "there existsan object such that..." or "for all objects, it is the case that...." There are two types of axioms: the logical axioms which embody the general truths about proper reasoning involving quantifiedstatements, and the axioms describing the subject matter at hand, for instance axioms describing sets in set theory or axiomsdescribing numbers in arithmetic. While the set of inference rules in first-order calculus is finite, the set of axioms may very well be and often is infinite.However we require that there is a general algorithm which can decide for a givenwell-formed formula whether it is an axiom or not. www.therfcc.org /first-order-predicate-calculus-3442.html   (895 words)

 First-order predicate calculus   (Site not responding. Last check: 2007-10-31) 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 one X such that..." or "for any it is the case that..." where X an element of a set called the of discourse. There are two types of axioms: the axioms which embody the general truths about reasoning involving quantified statements and the axioms the subject matter at hand for instance describing sets in set theory or axioms numbers in arithmetic. While the set of inference rules in calculus is finite the set of axioms very well be and often is infinite. www.freeglossary.com /First-order_predicate_calculus   (1135 words)

 lec9Sept Propositional calculus only allows you to use any of these, but it they are embedded inside the propositions: President Regan was powerful. Predicate calculus separates out the refering expression from the rest of the proposition so that you can reason with the two separately: Every president of the US was powerful. In predicate calculus, the referring expressions are called "terms" and the rest of the sentence is called a "predicate." : "Regan was powerful" is represented as Powerful(Regan) where Regan is a term and Powerful(...) is a predicate. www.pitt.edu /~vanlehn/cs0441/lec9Sept.html   (602 words)

 predicate logic from FOLDOC   (Site not responding. Last check: 2007-10-31) (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. ftp.sunet.se /foldoc/foldoc.cgi?predicate+calculus   (89 words)

 Completeness of Predicate Calculus In light of the fact that there is no decision procedure for theoremhood in the predicate calculus this is a remarkable result that cannot be constructive for then there would be a decision procedure. A model is a set of objects and a map from the individual constants to the objects and a map that for each predicate, specifies for which tuples of the objects the predicate is true. In the predicate calculus a sentence is considered true if any interpretation of the constants of the language in any model turn out to be true for that model. www.cap-lore.com /MathPhys/Complete.html   (851 words)

 What is first-order logic? - a definition from Whatis.com - see also: first-order predicate calculus The predicate modifies or defines the properties of the subject. First-order logic is also known as first-order predicate calculus or first-order functional calculus. A sentence in first-order logic is written in the form Px or P(x), where P is the predicate and x is the subject, represented as a variable. whatis.techtarget.com /definition/0,,sid9_gci835674,00.html   (336 words)

 Home The reason [for the limitation] is that the statement calculus is limited to the structure of sentences in terms of component sentences, and the [example] requires an analysis of sentence structure along the subject-predict lines that grammarians describe. Symbols are used to represent both the subject and the predicate of a proposition. In predicate calculus, though, they're back again and have a prominent part, using universal and existential quantifiers. home1.gte.net /simres/k1-depre.htm   (1337 words)

 Books on Predicate Calculus   (Site not responding. Last check: 2007-10-31) Arguments whose soundness cannot be proved by propositional calculus are discussed, and it is shown how formalization can reveal the logical form of arguments. The text's organization allows instructors to cover just statement logic, or statement logic combined with various extensions into predicate logic: monadic logic with or without identity, or the preceding plus relational logic with or without identity and with or without function symbols. This is the first book to provide a student-friendly introduction to propositional and Predicate Calculus, which is central to the broad field of mathematical logic. books.bankhacker.com /Predicate+Calculus   (772 words)

 Historical roots of logic programming (LP) For our purposes at the moment, it's important to note that the predicate calculus is the foundation of LP, because it provided, for the first time, a precise characterization of the concept of proof. Standard predicate logic is redundant in that there are often alternative ways to express the same thing: Two propositions may be syntactically distinct but semantically equivalent. While this might be an advantage for humans wanting to represent knowledge with predicate logic, it is a source of inefficiency for the automated procedures designed to manipulate these expressions in search of proofs. www.rpi.edu /~brings/LOG+AI/lai/node15.html   (761 words)

 predicate - Wiktionary In "The dog barked very loudly", "the dog" is the subject and the predicate is "barked very loudly". to predicate (third-person singular simple present predicates, present participle predicating, simple past predicated, past participle predicated) 1859: Charles Dickens, A Tale of Two Cities - There was a character about Madame Defarge, from which one might have predicated that she did not often make mistakes against herself in any of the reckonings over which she presided. en.wiktionary.org /wiki/Predicate   (200 words)

 Epsilon Calculi [Internet Encyclopedia of Philosophy] Leisenring took the epsilon calculus to be a better logic than the predicate calculus, but merely because of the Second Epsilon Theorem. This theorem, as before, states that an epsilon calculus proof of an epsilon-free theorem may be replaced by a predicate calculus proof of the same formula. It thus seems necessary, within the predicate calculus, that there be a 'model' for the quantifiers which restricts them to a certain 'domain', which means that they do not necessarily range over everything. www.iep.utm.edu /e/ep-calc.htm   (10009 words)

 More on Predicate Calculus Here is free textual content related to Predicate Calculusto utilize on your web site in accordance wi th the GNU license. First-order predicate calculus or first-order logic (FOL) permits the formulation of quantified statements such as "there exists an x such that..." (\exists x) or "for any x, it is the case that..." (\forall x), where x is a member of the domain of discourse. Simple and complex predicates If P is an n-adic (n ≥ 0) predicate, then Pa1,...,Pan is well-formed. www.artilifes.com /predicate-calculus.htm   (962 words)

 First-order predicate calculus   (Site not responding. Last check: 2007-10-31) It uses material from the Wiktionary page "Calculus". The part of the sentence (or clause) which says something about the subject, other than naming it. It uses material from the Wiktionary page "Predicate". www.serebella.com /encyclopedia/article-First-order_predicate_calculus.html   (1503 words)

 First Order Predicate Calculus The last two logical constants are additions to the logical connectives of propositional calculus ---they are known as quantifiers. A predicate with one argument is often used to express a property e.g. If there are no arguments then we can regard the `predicate' as standing for a statement à la the propositional calculus. www.oopweb.com /Prolog/Documents/prologbook/Volume/node18.html   (253 words)

 A Finitely Axiomatized Formalization of Predicate Calculus with Equality, Norman D. Megill We present a formalization of first-order predicate calculus with equality which, unlike traditional systems with axiom schemata or substitution rules, is finitely axiomatized in the sense that each step in a formal proof admits only finitely many choices. This formalization is primarily based on the inference rule of condensed detachment of Meredith. A closely related axiomatization of traditional predicate calculus is shown to be complete in a strong metamathematical sense. projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.ndjfl/1040149359   (556 words)

 predicate calculus - OneLook Dictionary Search Tip: Click on the first link on a line below to go directly to a page where "predicate calculus" is defined. Predicate Calculus : Eric Weisstein's World of Mathematics [home, info] Phrases that include predicate calculus: first order predicate calculus, second-order predicate calculus www.onelook.com /?w=predicate+calculus&ls=a   (209 words)

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