Academic literature on the topic 'Predicate calculus'

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Journal articles on the topic "Predicate calculus"

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LANZET, RAN. "A THREE-VALUED QUANTIFIED ARGUMENT CALCULUS: DOMAIN-FREE MODEL-THEORY, COMPLETENESS, AND EMBEDDING OF FOL." Review of Symbolic Logic 10, no. 3 (May 8, 2017): 549–82. http://dx.doi.org/10.1017/s1755020317000053.

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AbstractThis paper presents an extended version of the Quantified Argument Calculus (Quarc). Quarc is a logic comparable to the first-order predicate calculus. It employs several nonstandard syntactic and semantic devices, which bring it closer to natural language in several respects. Most notably, quantifiers in this logic are attached to one-place predicates; the resulting quantified constructions are then allowed to occupy the argument places of predicates. The version presented here is capable of straightforwardly translating natural-language sentences involving defining clauses. A three-valued, model-theoretic semantics for Quarc is presented. Interpretations in this semantics are not equipped with domains of quantification: they are just interpretation functions. This reflects the analysis of natural-language quantification on which Quarc is based. A proof system is presented, and a completeness result is obtained. The logic presented here is capable of straightforward translation of the classical first-order predicate calculus, the translation preserving truth values as well as entailment. The first-order predicate calculus and its devices of quantification can be seen as resulting from Quarc on certain semantic and syntactic restrictions, akin to simplifying assumptions. An analogous, straightforward translation of Quarc into the first-order predicate calculus is impossible.
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Friedman, Harvey M., and Andrej Ščedrov. "On the quantificational logic of intuitionistic set theory." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 1 (January 1986): 5–10. http://dx.doi.org/10.1017/s0305004100063854.

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Formal propositional logic describing the laws of constructive (intuitionistic) reasoning was first proposed in 1930 by Heyting. It is obtained from classical pro-positional calculus by deleting the Law of Excluded Middle, and it is usually referred to as Heyting's (intuitionistic) propositional calculus ([9], §§23, 19) (we write HPP in short). Formal logic involving predicates and quantifiers based on HPP is called Heyting's (intuitionistic) predicate calculus ([9], §§31, 19) (we write HPR in short).
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Ruitenburg, Wim. "Basic Predicate Calculus." Notre Dame Journal of Formal Logic 39, no. 1 (January 1998): 18–46. http://dx.doi.org/10.1305/ndjfl/1039293019.

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BEN-YAMI, HANOCH. "THE QUANTIFIED ARGUMENT CALCULUS." Review of Symbolic Logic 7, no. 1 (January 22, 2014): 120–46. http://dx.doi.org/10.1017/s1755020313000373.

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AbstractI develop a formal logic in which quantified arguments occur in argument positions of predicates. This logic also incorporates negative predication, anaphora and converse relation terms, namely, additional syntactic features of natural language. In these and additional respects, it represents the logic of natural language more adequately than does any version of Frege’s Predicate Calculus. I first introduce the system’s main ideas and familiarize it by means of translations of natural language sentences. I then develop a formal system built on these principles, the Quantified Argument Calculus or Quarc. I provide a truth-value assignment semantics and a proof system for the Quarc. I next demonstrate the system’s power by a variety of proofs; I prove its soundness; and I comment on its completeness. I then extend the system to modal logic, again providing a proof system and a truth-value assignment semantics. I proceed to show how the Quarc versions of the Barcan formulas, of their converses and of necessary existence come out straightforwardly invalid, which I argue is an advantage of the modal Quarc over modal Predicate Logic as a system intended to capture the logic of natural language.
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Liusti, Siti Ainim. "ANALISIS KALIMAT BERDASARKAN POLA KALIMAT DASAR DAN KALKULUS PREDIKAT." Adabiyyāt: Jurnal Bahasa dan Sastra 15, no. 2 (December 25, 2016): 157. http://dx.doi.org/10.14421/ajbs.2016.15203.

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This study aims to analyze the sentences based on the basic sentence patterns of Indonesian and predicate calculus. These approaches put the predicate as a core component in the sentence structure. The object of study is focused on declarative sentences of Indonesian. The data analysis consists of several stages. Basic sentence patterns of Indonesian consist of identifying the type of sentences, identifying the elements forming sentences, and putting on elements which are based on basic sentence patterns of Indonesian. Predicate calculus consists of identifying atomic or compound propositions, determining the predicate and other components, defining a form of expression predicate calculus, and making a notation function. The results showed that the basic sentence pattern analysis only identifies the internal elements in a single sentence, while the predicate calculus can as well identifies the internal elements of a single or compound sentence.
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Andjelkovic, Danica. "Aristotle's syllogistic and modern logic." Theoria, Beograd 48, no. 3-4 (2005): 155–66. http://dx.doi.org/10.2298/theo0504155a.

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Different understandings of Aristotle's syllogistic as a logical theory are reviewed. Leibniz offered a mathematical interpretation of syllogistic. Boole expressed all syllogistic relations by means of algebraic formulas. Lukasiewicz built a system of syllogistic as a logical theory separate and different from the predicate calculus Comparing syllogistic with other formal systems, its definitional equivalence with Boolean algebra is proven. Many systems of syllogistic are built, and their differences are due to recognizing the bearer of existential sense of categorical propositions. It is shown that these systems can be embedded in the predicate calculus, which means that syllogistic is not a separate and different theory from the predicate calculus.
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Shalack, Vladimir. "On Some Applied First-Order Theories which Can Be Represented by Definitions." Bulletin of the Section of Logic 44, no. 1/2 (January 1, 2015): 19–24. http://dx.doi.org/10.18778/0138-0680.44.1.2.03.

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In the paper we formulate a sufficient criterion in order for the first order theory with finite set of axioms to be represented by definitions in predicate calculus. We prove the corresponding theorem. According to this criterion such theories as the theory of equivalence relation, the theory of partial order and many theories based on the equality relation with finite set of functional and predicate symbols are represented by definitions in the first-order predicate calculus without equality.
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Konikowska, Beata, Andrzej Tarlecki, and Andrzej Blikle. "A Three-Valued Logic for Software Specification and Validation. Tertium tamen datur." Fundamenta Informaticae 14, no. 4 (April 1, 1991): 411–53. http://dx.doi.org/10.3233/fi-1991-14403.

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Different calculi of partial or three-valued predicates have been used and studied by several authors in the context of software specification, development and validation. This paper offers a critical survey on the development of three-valued logics based on such calculi. In the first part of the paper we review two three-valued predicate calculi, based on, respectively, McCarthy’s and Kleene’s propositional connectives and quantifiers, and point out that in a three-valued logic one should distinguish between two notions of validity: strong validity (always true) and weak validity (never false). We define in model-theoretic terms a number of consequence relations for three-valued logics. Each of them is determined by the choice of the underlying predicate calculus and of the weak or strong validity of axioms and of theorems. We discuss mutual relationships between consequence relations defined in such a way and study some of their basic properties. The second part of the paper is devoted to the development of a formal deductive system of inference rules for a three-valued logic. We use the method of semantic tableaux (slightly modified to deal with three-valued formulas) to develop a Gentzen-style system of inference rules for deriving valid sequents, from which we then derive a sound and complete system of natural deduction rules. We have chosen to study the consequence relation determined by the predicate calculus with McCarthy’s propositional connectives and Kleene’s quantifiers and by the strong interpretation of both axioms and theorems. Although we find this choice appropriate for applications in the area of software specification, verification and development, we regard this logic merely as an example and use it to present some general techniques of developing a sequent calculus and a natural deduction system for a three-valued logic. We also discuss the extension of this logic by a non-monotone is-true predicate.
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Monahan, Brian. "Predicate calculus and program semantics." Science of Computer Programming 17, no. 1-3 (December 1991): 259–62. http://dx.doi.org/10.1016/0167-6423(91)90048-3.

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Börger, Egon. "Predicate calculus and program semantics." Science of Computer Programming 23, no. 1 (October 1994): 91–101. http://dx.doi.org/10.1016/0167-6423(94)90002-7.

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Dissertations / Theses on the topic "Predicate calculus"

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Joshi, Rejeev. "Immediacy : a technique for reasoning about asynchrony /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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Florio, Salvatore. "Completeness of the Predicate Calculus in the Basic Theory of Predication." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1281927327.

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Hondet, Gabriel. "Expressing predicate subtyping in computational logical frameworks." Electronic Thesis or Diss., université Paris-Saclay, 2022. http://www.theses.fr/2022UPASG070.

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Le typage permet d'apporter de la sûreté dans la programmation, et il est utilisé au coeur de la majorité des systèmes de preuve. Plus un système de types est expressif, plus il est aisé d'y encoder des invariantsqui seront vérifiés mécaniquement lors du typage. Les types dépendants sont une extension des types simples dans laquelle les types peuvent dépendre de valeurs. Ils permettent par exemple de définir les vecteurs paramétrés par leur longueur. Le sous-typage par prédicat est une autre extension des types simples, dans laquelle les types peuvent être définis par des prédicats. Un sous-type défini par un prédicat, généralement noté { x : A | P(x) }, est habité par les éléments t de type A pour lesquels P(t) est vrai. Cette extension fournit un système de type très riche et intuitif, mais qui rend le typage indécidable.Cet ouvrage est dédié à l'encodage du sous-typage par prédicats dans Dedukti, un cadre logique avec des règles de calcul. On commence par encoder une version explicite du sous-typage par prédicats pour lequel un habitant de { x: A | P(x) } est syntaxiquement différent d'un habitant de A. On montre que tout jugement dérivable dans cette version du sous-typage par prédicat peut être encodé en un jugement dérivable du cadre logique.Le sous-typage par prédicat est souvent utilisé de manière implicite, sans différence syntaxique entre les habitants de A et les habitants de { x: A | P(x) }. On enrichit le cadre logique avec un système de raffinement des termes qui pourra ajouter ces marqueurs syntaxiques. Ce raffineur peut traduire des jugements typables avec du sous-typage par prédicat implicite en des jugements typable avec du sous-typage explicite.L'assistant à la preuve pvs utilise abondamment le sous-typage par prédicat. On montre comment sa bibliothèque standard peut être exportée vers Dedukti. Par ailleurs, PVS ne préserve que des traces de preuves. Dans la pénultième section, on décrit une procédure pour générer des preuves complètes à partir des traces laissées par PVS.La dernière section détaille une architecture pour l'entrepôt et l'échange de preuves formelles, afin de promouvoir l'interopérabilité
Safe programming as well as most proof systems rely on typing. The more a type system is expressive, the more these types can be used to encode invariants which are therefore verified mechanically through type checking procedures. Dependent types extend simple types by allowing types to depend on values. For instance, it allows to define the types of lists of a certain length. Predicate subtyping is another extension of simple type theory in which types can be defined by predicates. A predicate subtype, usually noted {x: A | P(x)}, is inhabited by elements t of type A for which P(t) is true. This extension provides an extremely rich and intuitive type system, which is at the heart of the proof assistant PVS, at the cost of making type checking undecidable.This work is dedicated to the encoding of predicate subtyping in Dedukti: a logical framework with computation rules. We begin with the encoding of explicit predicate subtyping for which the terms in {x: A | P(x)} and terms of Aare syntactically different. We show that any derivable judgement of predicate subtyping can be encoded into a derivable judgement of the logical framework. Predicate subtyping, is often used implicitly: with no syntactic difference between terms of type A and terms of type {x: A | P(x) }. We enrich our logical framework with a term refiner which can add these syntactic markers. This refiner can be used to refine judgements typed with implicit predicate subtyping into explicited judgements.The proof assistant PVS uses extensively predicate subtyping. We show how its standard library can be exported to Dedukti. Because PVS only store proof traces rather than complete proof terms, we sketch in the penultimate section a procedure to generate complete proof terms from these proof traces.The last section provides the architecture of a repository dedicated to the exchange of formal proofs. The goal of such a repository is to categorise and store proofs encoded in Dedukti to promote interoperability
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Lawley, Michael John, and n/a. "Program Transformation for Proving Database Transaction Safety." Griffith University. School of Computing and Information Technology, 2000. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20070228.150125.

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In this thesis we propose the use of Dijkstra's concept of a predicate transformer [Dij75] for the determination of database transaction safety [SS89] and the generation of simple conditions to check that a transaction will not violate the integrity constraints in the case that it is not safe. The generation of this simple condition is something that can be done statically, thus providing a mechanism for generating safe transactions. Our approach treats a database as state, a database transaction as a program, and the database's integrity constraints as a postcondition in order to use a predicate transformer [Dij75] to generate a weakest precondition. We begin by introducing a set-oriented update language for relational databases for which a predicate transformer is then defined. Subsequently, we introduce a more powerful update language for deductive databases and define a new predicate transformer to deal with this language and the more powerful integrity constraints that can be expressed using recursive rules. Next we introduce a data model with object-oriented features including methods, inheritance and dynamic overriding. We then extend the predicate transformer to handle these new features. For each of the predicate transformers, we prove that they do indeed generate a weakest precondition for a transaction and the database integrity constraints. However, the weakest precondition generated by a predicate transformer still involves much redundant checking. For several general classes of integrity constraint, including referential integrity and functional dependencies, we prove that the weakest precondition can be substantially further simplified to avoid checking things we already know to be true under the assumption that the database currently satisfies its integrity con-straints. In addition, we propose the use of the predicate transformer in combination with meta-rules that capture the exact incremental change to the database of a particular transaction. This provides a more general approach to generating simple checks for enforcing transaction safety. We show that this approach is superior to known existing previous approaches to the problem of efficient integrity constraint checking and transaction safety for relational, deductive, and deductive object-oriented databases. Finally we demonstrate several further applications of the predicate transformer to the problems of schema constraints, dynamic integrity constraints, and determining the correctness of methods for view updates. We also show how to support transactions embedded in procedural languages such as C.
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Lawley, Michael John. "Program Transformation for Proving Database Transaction Safety." Thesis, Griffith University, 2000. http://hdl.handle.net/10072/365511.

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In this thesis we propose the use of Dijkstra's concept of a predicate transformer [Dij75] for the determination of database transaction safety [SS89] and the generation of simple conditions to check that a transaction will not violate the integrity constraints in the case that it is not safe. The generation of this simple condition is something that can be done statically, thus providing a mechanism for generating safe transactions. Our approach treats a database as state, a database transaction as a program, and the database's integrity constraints as a postcondition in order to use a predicate transformer [Dij75] to generate a weakest precondition. We begin by introducing a set-oriented update language for relational databases for which a predicate transformer is then defined. Subsequently, we introduce a more powerful update language for deductive databases and define a new predicate transformer to deal with this language and the more powerful integrity constraints that can be expressed using recursive rules. Next we introduce a data model with object-oriented features including methods, inheritance and dynamic overriding. We then extend the predicate transformer to handle these new features. For each of the predicate transformers, we prove that they do indeed generate a weakest precondition for a transaction and the database integrity constraints. However, the weakest precondition generated by a predicate transformer still involves much redundant checking. For several general classes of integrity constraint, including referential integrity and functional dependencies, we prove that the weakest precondition can be substantially further simplified to avoid checking things we already know to be true under the assumption that the database currently satisfies its integrity con-straints. In addition, we propose the use of the predicate transformer in combination with meta-rules that capture the exact incremental change to the database of a particular transaction. This provides a more general approach to generating simple checks for enforcing transaction safety. We show that this approach is superior to known existing previous approaches to the problem of efficient integrity constraint checking and transaction safety for relational, deductive, and deductive object-oriented databases. Finally we demonstrate several further applications of the predicate transformer to the problems of schema constraints, dynamic integrity constraints, and determining the correctness of methods for view updates. We also show how to support transactions embedded in procedural languages such as C.
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Computing and Information Technology
Faculty of Information and Communication Technology
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Peach, Glen. "Visualização gráfica dos fundamentos da lógica matemática por meio de diagramas de conjuntos." Universidade Federal de São Carlos, 2017. https://repositorio.ufscar.br/handle/ufscar/9278.

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The purpose of this work is to propose a method that allow to bring the fundamentals of mathematical logic to high school through the use of set theory, however making the whole approach of the subject through diagrams, making it possible to avoid, for the demonstrations and understanding necessary to the development of the subject, the rigors of writing used in mathematical logic, which, in a first contact, tend to discourage the interest of beginning students.
O objetivo deste trabalho é propor um método que permita levar os fundamentos da lógica matemática para o ensino médio por meio da utilização da teoria dos conjuntos, porém fazendo todo a aproximação do assunto utilizando diagramas, tornando possível evitar assim, para as demonstrações e o entendimento necessários ao desenvolvimento do assunto, os rigores da escrita utilizada na lógica matemática, que, em um primeiro contato, podem desestimular o interesse dos alunos iniciantes
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Aleksandar, Kupusinac. "Analiza osobina dinamičkih postuslova u Horovim tripletima." Phd thesis, Univerzitet u Novom Sadu, Fakultet tehničkih nauka u Novom Sadu, 2010. http://dx.doi.org/10.2298/NS20101213KUPUSINAC.

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Doktorska disertacija prezentuje nov i opštiji način analiziranja semantike strukturiranih i objektno orijentisanih programa i to isključivo u okvirima predikatske logike prvog reda. Doktorska disertacija razmatra sledeće teme:1.) S-programski račun,2.) Definicija i osobine dinamičkih postuslova u S-računu,3.) Konceptualne definicije objekta, klase i invarijante,4.) Analiza invarijanata u klasi (SP-analiza i DP-analiza).
Doctoral thesis presents a new and more general method for analizing of structured and object-oriented program semantics, based on the first-order predicate logic. Doctoral thesis consideres next topics:1.) S-program calculus,2.) Definition and characteristics of dynamic postconditions in S-calculus,3.) Conceptual definitions of object, class and invariant,4.) Analyses of invariants in class (SP-analyses and DP-analyses).
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Sanctos, Cassia Sampaio. "Considerações sobre a demonstração original do teorema da completude de Kurt Gödel." Pontifícia Universidade Católica de São Paulo, 2015. https://tede2.pucsp.br/handle/handle/11683.

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The thesis constitutes a critical review of Gödel´s doctoral dissertation which presents a proof for the completeness of first order logic. The introduction addresses the concepts of formalism, axiomatic method and completeness, thus the proof can be contextualized. The language for the restricted functional calculus is defined, with the corresponding syntax and semantics, and the original Gödel´s demonstration is updated. The appendix contains a translation of the referred dissertation, which is unprecedented in Portuguese
O trabalho constitui um comentário crítico da dissertação de doutorado de Gödel que apresenta uma prova de completude da lógica de primeira ordem. A introdução trata dos conceitos de formalismo, método axiomático e completude, para que seja possível contextualizar a prova. A linguagem para o cálculo funcional restrito é definida, com sua sintaxe e semântica, e a demonstração original de Gödel é atualizada. O apêndice contém a tradução da referida dissertação, que é inédita em língua portuguesa
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Cialdea, Marta. "Une methode de deduction automatique en logique modale." Toulouse 3, 1986. http://www.theses.fr/1986TOU30179.

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Le but de ce travail consiste a etendre au calcul des predicats la methode de resolution pour la logique propositionnelle modale qui a ete definie par m. Luis farinas del cerro. Le systeme modal considere, appele q, est un sous-systeme de ceux plus connus, t, s4 et s5. Nous considerons toutefois que les resultats obtenus dans ce travail peuvent facilement etre etendus a ceux-ci. Nous definissons une propriete de herbrand modale pour le systeme q et en donnons la preuve. Cette propriete nous permet ensuite de definir un systeme de regles de resolution dans lequel l'unification des termes est soumise a certaines restrictions, et d'en prouver sa correction et sa completude
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Raddaoui, Béchir. "Le calcul des predicats : application aux bases de donnees." Toulouse 3, 1987. http://www.theses.fr/1987TOU30046.

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Rappel sur la logique mathematique et ses applications dans le domaine des languages predicatifs. Rappel sur les languages de base de donnees et de leurs principes fondamentaux. Si l'on trouve les memes principes elementaires par courbe en ce qui concerne les techniques d'optimisation, elles different d'un systeme a l'autre. Presentation de la syntaxe du language et du traitement general. Il est montre comment les algorithmes decrits peuvent etre repris dans le cadre du language pascal objet relationnel
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Books on the topic "Predicate calculus"

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Dijkstra, Edsger W., and Carel S. Scholten. Predicate Calculus and Program Semantics. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4612-3228-5.

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Dijkstra, Edsger Wybe. Predicate calculus and program semantics. New York: Springer-Verlag, 1990.

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Dijkstra, Edsger Wybe. Predicate calculus and program semantics. New York: Springer-Verlag, 1990.

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Dijkstra, Edsger Wybe. Predicate Calculus and Program Semantics. New York, NY: Springer New York, 1990.

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Simpson, Stephen G. Subsystems of second order arithmetic. Berlin: Springer, 1999.

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Simpson, Stephen G. Subsystems of second-order arithmetic. 2nd ed. Cambridge: Cambridge University Press, 2009.

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Simpson, Stephen G. Subsystems of second-order arithmetic. 2nd ed. Cambridge: Cambridge University Press, 2009.

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Simpson, Stephen G. Subsystems of Second Order Arithmetic. 2nd ed. Leiden: Cambridge University Press, 2009.

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Büning, H. Kleine. Aussagenlogik: Deduktion und Algorithmen. Stuttgart: B.G. Teubner, 1994.

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Naishtat, Francisco S. Lógica para computación. [Buenos Aires]: Editorial Universitaria de Buenos Aires, 1986.

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Book chapters on the topic "Predicate calculus"

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Booth, Dexter J. "Predicate calculus." In Foundation Discrete Mathematics for Computing, 151–70. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-7114-2_5.

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Baxter, Nancy, Ed Dubinsky, and Gary Levin. "Predicate Calculus." In Learning Discrete Mathematics with ISETL, 225–63. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3592-7_5.

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Fenton, William E., and Ed Dubinsky. "Predicate Calculus." In Introduction to Discrete Mathematics with ISETL, 73–96. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-4052-5_4.

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Gries, David, and Fred B. Schneider. "Predicate Calculus." In A Logical Approach to Discrete Math, 157–77. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4757-3837-7_10.

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Pace, Gordon J. "Predicate Calculus." In Mathematics of Discrete Structures for Computer Science, 57–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29840-0_3.

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Zeugmann, Thomas, Pascal Poupart, James Kennedy, Xin Jin, Jiawei Han, Lorenza Saitta, Michele Sebag, et al. "Predicate Calculus." In Encyclopedia of Machine Learning, 781. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-0-387-30164-8_654.

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Polkowski, Lech. "Predicate Calculus." In Rough Sets, 273–96. Heidelberg: Physica-Verlag HD, 2002. http://dx.doi.org/10.1007/978-3-7908-1776-8_9.

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Back, Ralph-Johan, and Joakim Wright. "Predicate Transformers." In Refinement Calculus, 187–202. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1674-2_11.

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Ben-Ari, Mordechai. "Predicate Calculus: Resolution." In Mathematical Logic for Computer Science, 139–72. London: Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-0335-6_7.

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Anglin, W. S., and J. Lambek. "Intuitionistic Predicate Calculus." In The Heritage of Thales, 281–83. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-0803-7_58.

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Conference papers on the topic "Predicate calculus"

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Dell'aquila, Carlo, Francesco Di Tria, Ezio Lefons, and Filippo Tangorra. "Dimensional fact model extension via predicate calculus." In 2009 24th International Symposium on Computer and Information Sciences (ISCIS). IEEE, 2009. http://dx.doi.org/10.1109/iscis.2009.5291846.

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Ganesan, G., and B. N. V. Satish. "A Study on Rough-Fuzzy Predicate Calculus." In 2014 7th International Conference on u- and e- Service, Science and Technology (UNESST). IEEE, 2014. http://dx.doi.org/10.1109/unesst.2014.9.

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Zellweger, H. Paul. "A Decision Tree Interface Based on Predicate Calculus." In 2017 21st International Conference on Information Visualisation (IV). IEEE, 2017. http://dx.doi.org/10.1109/iv.2017.68.

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Consoli, Robert H. "Predicate calculus for an architecture of multiple neural networks." In SPIE Proceedings, edited by Steven K. Rogers, Eustace L. Dereniak, P. McGeehin, Donald B. Carlin, David B. Kay, and Robert E. Sampson. SPIE, 1990. http://dx.doi.org/10.1117/12.21193.

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Leal, Antonio. "A predicate calculus based language for data verification and validation." In 9th Computing in Aerospace Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1993. http://dx.doi.org/10.2514/6.1993-4462.

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Nikitchenko, Mykola, Oksana Shkilniak, and Stepan Shkilniak. "Sequent Calculus for a Program-oriented Predicate Logic over Complex-Named Data." In 2020 10th International Conference on Advanced Computer Information Technologies (ACIT). IEEE, 2020. http://dx.doi.org/10.1109/acit49673.2020.9208809.

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Kosovskaya, Tatiana, and Juan Zhou. "Algorithms for Checking Isomorphism of Two Elementary Conjunctiоns." In Computer Science and Information Technologies 2023. Institute for Informatics and Automation Problems, 2023. http://dx.doi.org/10.51408/csit2023_01.

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When solving AI problems related to the study of complex structured objects, a convenient tool for describing such objects is the predicate calculus language. The paper presents two algorithms for checking two elementary conjunctions of predicate formulas for isomorphism (matches up to the names of variables and the order of conjunctive terms). The first of the algorithms checks for isomorphism elementary conjunctions containing a single predicate symbol. In addition, if the formulas are isomorphic, then it finds a one-to-one correspondence between the arguments of these formulas. If all predicates are binary, the proposed algorithm is an algorithm for checking two directed graphs for isomorphism. The second algorithm checks for isomorphism elementary conjunctions containing several predicate symbols. Estimates of their time complexity are given for both algorithms.
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Kosovskaya, Tatiana M. "Partial deduction in predicate calculus as a tool for artificial intelligence problem complexity decreasing." In 2015 IEEE Seventh International Conference on Intelligent Computing and Information Systems (ICICIS). IEEE, 2015. http://dx.doi.org/10.1109/intelcis.2015.7397199.

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Finch, William W., and Allen C. Ward. "Quantified Relations: A Class of Predicate Logic Design Constraints Among Sets of Manufacturing, Operating, and Other Variations." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/dtm-1550.

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Abstract This paper addresses a class of engineering design problems in which multiple sources of variations affect a product’s design, manufacture, and performance. Examples of these sources include uncertainty in nominal dimensions, variations in manufacture, changing environmental or operating conditions, and operator adjustments. Quantified relations (QR’s) are defined as a class of predicate logic expressions representing constraints between sets of design variations. Within QR’s, each variable’s quantifier and the order of quantification express a physical system’s causal relationships. This paper also presents an algorithm which propagates intervals through QR’s involving continuous, monotonic equations. Causal relationships between variables in engineering systems are discussed, and a tabular representation for them is presented. This work aims to broaden the application of automated constraint satisfaction algorithms, shortening design cycles for this class of problem by reducing modeling, and possibly computing effort. It seems to subsume Ward’s prior work on the Label Interval Calculus, extending the approach to a wider range of engineering design problems.
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Console, Marco, Paolo Guagliardo, and Leonid Libkin. "Do We Need Many-valued Logics for Incomplete Information?" In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/851.

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One of the most common scenarios of handling incomplete information occurs in relational databases. They describe incomplete knowledge with three truth values, using Kleene's logic for propositional formulae and a rather peculiar extension to predicate calculus. This design by a committee from several decades ago is now part of the standard adopted by vendors of database management systems. But is it really the right way to handle incompleteness in propositional and predicate logics? Our goal is to answer this question. Using an epistemic approach, we first characterize possible levels of partial knowledge about propositions, which leads to six truth values. We impose rationality conditions on the semantics of the connectives of the propositional logic, and prove that Kleene's logic is the maximal sublogic to which the standard optimization rules apply, thereby justifying this design choice. For extensions to predicate logic, however, we show that the additional truth values are not necessary: every many-valued extension of first-order logic over databases with incomplete information represented by null values is no more powerful than the usual two-valued logic with the standard Boolean interpretation of the connectives. We use this observation to analyze the logic underlying SQL query evaluation, and conclude that the many-valued extension for handling incompleteness does not add any expressiveness to it.
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