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Topic: First-order predicate calculus


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In the News (Sat 25 May 19)

  
 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.
The statistical estimation of provability in the first order predicate calculus
Predicate calculus is an extension of propositional calculus.
encyclopedia.worldsearch.com /predicate_calculus.htm

  
 Foundations of Mathematics
A Brief Introduction to The Intuitionistic Propositional Calculus - by Stuart A. Kurtz
Introduction to Lambda Calculus [compressed PS] - by Henk Barendregt, Erik Barendsen
Formal theories, propositional and predicate logic, the completeness theorem, automatic theorem proving, other predicate theories
sakharov.net /foundation_rt.html

  
 first-order predicate calculus - a Whatis.com definition - see also: first-order logic
First-order logic is also known as first-order predicate calculus or first-order functional calculus.
first-order predicate calculus - a Whatis.com definition - see also: first-order logic
In first-order logic, a predicate can only refer to a single subject.
whatis.techtarget.com /definition/0,,sid9_gci835674,00.html

  
 First-order predicate calculus - Wikipedia, the free encyclopedia
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.
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

  
 Search Results for predicate - Encyclopædia Britannica
A predicate calculus in which the only variables that occur in quantifiers are individual variables is known as a lower (or first-order) predicate calculus.
Discusses the Aristotelean logic, predicate calculus, geometry of Euclid, formal theories of mathematics, and Plato and Aristotle’s philosophy of mathematics.
The problem of consistency for the predicate calculus is relatively simple.
www.britannica.com /search?query=predicate&submit=Find&source=MWTEXT   (537 words)

  
 Constructivity03
We base omega-PA on a modified first order predicate calculus where we replace the strong Generalisation rule of inference I(ii) by a weaker omega-Constructivity rule of inference I(iii).
PA is based on a particularisation of the general first order predicate calculus K whose primitive symbols are (Mendelson p57):
Arithmetic, as specified in §3.4, added to a first order predicate calculus A(i) to A(iii), as specified in §3.4, with both the
alixcomsi.com /Constructivity03.htm   (1622 words)

  
 mbox
Because propositional calculus (no quantifiers) is decidable unary function-free predicate calculus is decidable first-order predicate calculus is *semi*-decidable second-order predicate calculus is *un*-decidable in general.
my second book states that we are only using first order predicate logic in prolog.
The point is that the second version can be executed in bounded (and rather small) memory space, while the first version cannot.
www.csci.csusb.edu /dick/cs320/prolog/mbox   (1976 words)

  
 Frege's Logic, Theorem, and Foundations for Arithmetic
Again, these are essentially the same as the rules for the first-order predicate calculus, except for the addition of new rules for the second-order quantifiers that correspond to the generalization and instantiation rules (i.e., introduction and elimination rules) for the first-order quantifiers.
These are essentially the same as the axioms for the first-order predicate calculus, except for the addition of laws for the second-order quantifiers ∀F and ∃F which correspond to the laws governing the first-order quantifiers ∀x and ∃x.
In his Begriffsschrift of 1879, he developed a second-order predicate calculus and used it both to define interesting mathematical concepts and to state and prove mathematically interesting propositions.
www.science.uva.nl /~seop/archives/win2004/entries/frege-logic   (15131 words)

  
 EMail Msg <9402171237.AA10497@rodin.wustl.edu>
To put things in a nutshell, his work shows stat we need second >order logic and that the usual second order predicate calculus is precisely >one of the above mentioned intrinsically inadequate framework.
But is "the usual _second_ order predicate calculus...
(Or in some other form like order-sorted n-adic n-order predicate calculus.) My main point was the "potentially useful".
www-ksl.stanford.edu /email-archives/srkb.messages/233.html   (1681 words)

  
 First Order Predicate Logic
One such artificial language is the first order predicate calculus, also known as FOL, first order logic.
First order logic is very well understood, and has a sound mathematical foundation.
Logic was first studied in the 4th century B.C. its invention is attributed to the Greek philosopher Aristotle.
www.ryerson.ca /~dgrimsha/courses/cps721/FOLIntro.html   (271 words)

  
 First Order Predicate Logic
One such artificial language is the first order predicate calculus, also known as FOL, first order logic.
First order logic is very well understood, and has a sound mathematical foundation.
Logic was first studied in the 4th century B.C. its invention is attributed to the Greek philosopher Aristotle.
www.ryerson.ca /~dgrimsha/courses/cps721/FOLIntro.html   (271 words)

  
 Directory - Computers: Programming: Languages: Logic-based: Functional Logic
They are hybrid languages, based on (higher-order) predicate calculus extended with characteristics of the lambda-calculus which allows introducing elements such as (strong(er)) typing.
ALF  · cached · Foundation: Horn clause logic with equality which consists of predicates and Horn clauses for logic programming, and functions and equations for functional programming.
LPG  · Generic functional logic language: functions defined by conditional rewrite rules, predicates defined by Horn clauses whose bodies may contain equations, disequations, or classical atomic formulae.
www.incywincy.com /default?p=509318   (400 words)

  
 BotSpot's Secret Agent Man
Lenat's company, Cycorp, is attempting to give CYC a conceptual understanding of the world by using second order predicate calculus to create hundreds of knowledge bases or microtheories.
However, in a more recent conversation, Lenat told me that CYC was still unable to communicate in natural language (i.e., conversations much be carried on in second order predicate calculus - talk about a party stopper!).
Regardless of whether or not Lenat meets his latest self-imposed deadline, it is clear that understanding is the key to Natural Language Processing (NLP) and the way to achieve understanding is through knowledge.
www.botspot.com /pcai/article8.htm   (1106 words)

  
 CVonline: Predicate Calculus
First Order Predicate Calculus (PDF, Section 12.1, page 2) (Computer Vision, Dana Ballard and Christopher Brown)
Predicate Calculus: Tableaux (Hugh Rice, The Logic Web project)
A Description Classifier for the Predicate Calculus (Robert M. MacGregor)
www.homepages.informatics.ed.ac.uk /cgi/rbf/CVONLINE/entries.pl?TAG849   (1106 words)

  
 First-Order Predicate Logic
The "first-order" bit says that we consider predicates (or relations) on the one hand, and individuals on the other; that atomic sentences are constructed by applying the former to the latter; and that quantification is permitted only over the individuals.
Though predicates are one of the features which distinguish first-order logic from propositional logic, these are really just a bit of extra structure necessary to permit the study of quantifiers.
The two important features of natural languages whose logic is captured in the predicate calculus are the terms "every" and "some" and their synonyms, whose analogues in formal logic are called the universal and existential quantifiers.
www.rbjones.com /rbjpub/logic/log019.htm   (521 words)

  
 First-order logic - Wikipedia, the free encyclopedia
Unlike the propositional calculus, first-order logic is undecidable.
First-order logic is mathematical logic that is distinguished from higher-order logic in that it does not allow quantification over properties.
(logical or), → (logical conditional), ↔ (logical biconditional).
en.wikipedia.org /wiki/First-order_logic   (884 words)

  
 First-order predicate calculus
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...".
First-order logic is distinguished from higher-order logic in that it does not allow statements such as "for every property, it is the case that..." or "there exists a set of objects such that...".
We are using the object constants 0 and 1, the function constants + and *, and the predicate constant =.
usapedia.com /f/first-order-predicate-calculus.html   (1079 words)

  
 TDAN Engle - Data Modeling Left Right
The fact is that the meanings of the predicate letters of [basic first-order] predicate logic vary from problem to problem: Unlike quantifiers, truth-functional operators, and the identity predicate, they do not have fixed meanings.
For these reasons (and others), left-wing data modeling requires the use of “non-standard” logics, such as semantically dependent logic, higher-order predicate logic, frame logic (F-logic), three-valued logic, and/or probability-calculus logic.
This approach seems to me to be unrealistic: In order to logically model deeply layered, fully extensible type hierarchies, you must use a higher-order predicate logic.
www.tdan.com /i024hy03.htm   (2752 words)

  
 The predicate calculus
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.
However, Frege's account was defective in several respects, and notationally awkward to boot.
www.math.psu.edu /simpson/papers/philmath/node6.html   (107 words)

  
 First Order Predicate Calculus
The grammar of first-order predicate calculus defines the legal expressions associated with a given vocabulary.
Theorem: This theorem also holds for first-order predicate calculus, provided that there are no existential quantifiers (and there are no occurrences of equality).
Theorem: The size of the Herbrand universe for a first-order language with function constants is infinite.
logic.stanford.edu /classes/cs157/prev_years/functions.html   (751 words)

  
 First Order Predicate Calculus Theorem Prover
THEOREM PROVER FOR THE FIRST ORDER PREDICATE CALCULUS.
THEOREMS IN THE FIRST ORDER PREDICATE CALCULUS THAT ARE TO BE PROVED ?
LET A FORMULA F BE IN PRENEX NORMAL FORM (Q1 X1).
www.frobenius.com /theorem.htm   (98 words)

  
 predicate
(Or "predicate calculus") An extension of propositional logic with separate symbols for predicates, subjects, and quantifiers.
Higher-order predicate logic allows predicates to be the subjects of other predicates.
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"):
www.linuxguruz.com /foldoc/foldoc.php?predicate   (119 words)

  
 Many Sorted and Higher Order Logic
Ordinary unsorted logic is often called   first order predicate calculus because one can think of its universe as consisting only of points, which are said to be first order.
This logic of points and sets is sometimes called     second order logic expressing the idea that sets have a   higher order than points.
If we were to include a third universe, sets of sets, the logic would have higher order.
www.math.psu.edu /melvin/logic/node9.html   (704 words)

  
 TDAN Engle - Data Modeling Left Right
The fact is that the meanings of the predicate letters of [basic first-order] predicate logic vary from problem to problem: Unlike quantifiers, truth-functional operators, and the identity predicate, they do not have fixed meanings.
For these reasons (and others), left-wing data modeling requires the use of “non-standard” logics, such as semantically dependent logic, higher-order predicate logic, frame logic (F-logic), three-valued logic, and/or probability-calculus logic.
This approach seems to me to be unrealistic: In order to logically model deeply layered, fully extensible type hierarchies, you must use a higher-order predicate logic.
www.tdan.com /i024hy03.htm   (2752 words)

  
 Citations: The semantics of second-order lambda calculus - Bruce, Meyer, Mitchell (ResearchIndex)
K.B. Bruce, A.R. Meyer, and J.C. Mitchell, The semantics of second order lambda calculus.
In Section 2 the syntax of the polymorphic lambda calculus is recalled and in Section 3 a modification of Bruce, Meyer and Mitchell s notion of a second order environment model is given which includes the case that types can be empty.
) Preprint submitted to Elsevier Preprint 3 August 1999 On the other hand, if a second order calculus has a function which is written by type case, it becomes non normalizing(Has94] Gir71] The author has studied, motivated by the study of object orientedness, polymorphic functions over a.
citeseer.ist.psu.edu /context/35051/0   (3236 words)

  
 BOOK OF INSTRUMENTS: SECOND-ORDER PREDICATES ON THE OBJECTUAL VIEW            
An example of a predicate expression which is taken to be second-order is < (-- is a) color > 'because green is a color' and green [] itself is a first-order predicate expression, 'because grass is green' and grass is chosen as an entity (or collection of entities) in the domain.
In the predicate calculus predicates of predicates are called "second-order".
Treating color simply as a second-order predicate expression therefore passes by the tendency in everyday language to treat phenomena of perception, or objects of experience, as basic entities of the or a domain of discourse.
www.trinp.org /MNI/BoI/1/3/3.HTM   (823 words)

  
 Atlas: Quasi-solvability of $\omega $-order Predicate Calculus by Andreas Schumann
I prove that \omega-order predicate calculus coincides with the \omega-order theory.
This approach permits to use solvable and recursively enumerable predicates, a well as predicates pointed to incompleteness of axioms system.
The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajy-29.
atlas-conferences.com /cgi-bin/abstract/cajy-29   (293 words)

  
 Peano axioms
See first-order predicate calculus for a way to rephrase these axioms to be first-order.
The objects of US are all ordered triples (X, x, f), where X is a set, x is an element of X, and f is a set map from X to itself.
This order is compatible with the arithmetical operations in the following sense: if a, b and c are natural numbers and a ≤ b, then a + c ≤ b + c and ac ≤ bc.
free-download-soft.com /info/college-arapahoe-college-community.html   (1818 words)

  
 The Modal Object Calculus and its Interpretation
The second-order modal object calculus is so-called to distinguish it from the second-order modal predicate calculus.
In the present paper, we focus on the second-order calculus.
Though the differences are slight, the extra expressive power of the object calculus significantly enhances its ability to resolve logical and philosophical concepts and problems.
mally.stanford.edu /abstracts/calculus.html   (306 words)

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