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Predicate Logic with Definitions [article]

Victor Makarov
1999 arXiv   pre-print
Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics.  ...  A definition is a definition of variables, a definition of constants, or a composite definition (D-logic has also abbreviation definitions called abbreviations).  ...  In this paper, Predicate Logic with Definitions (PLD or D-logic) intended mostly for practical formalization of mathematics is introduced.  ... 
arXiv:cs/9906010v1 fatcat:ftu5au2wzrgclliw2ull47btba

THE HISTORICAL SYNTAX OF PHILOSOPHICAL LOGIC

Yaroslav Hnatiuk, Vasyl Stefanyk Precarpathian National University, Ukraine
2022 The European philosophical and historical discourse  
The main attention is paid to two scientific revolutions in elementary subject-predicate syntax, which led to the emergence of modified definitive-specific and standard propositional-functional syntaxes  ...  This syntax provides information interaction between Aristotle's elementary subject-predicate syntax, and Frege's standard propositional-functional syntax based on Hegel's modified definitive-specificative  ...  In the first definitive specification, subject and predicate terms are identified with the propositional function and become the term and predicatore as the logical subject and logical predicate.  ... 
doi:10.46340/ephd.2021.8.1.11 fatcat:axvznx7udjayxpv7nfxmc2ffia

Extending Classical Logic with Inductive Definitions [article]

Marc Denecker
2000 arXiv   pre-print
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships  ...  to other logics in the area of non-monotonic reasoning, logic programming and deductive databases, and to show its application for knowledge representation by giving a typology of definitional knowledge  ...  Acknowledgements This work has benefitted from discussions with the following people: Maurice Bruynooghe, Danny Deschreye, Michael Gelfond, Vladimir Lifschitz, Victor Marek, Ray Reiter, Eugenia Ternovskaia  ... 
arXiv:cs/0003019v1 fatcat:svyilctko5hprckbrzjvpcc7ee

On the Definitional Embeddability of the Combinatory Logic Theory into the First-Order Predicate Calculus

В. И. Шалак
2015 Logical Investigations  
In this article we prove a theorem on the definitional embeddability of the combinatory logic into the first-order predicate calculus without equality.  ...  Since all efficiently computable functions can be represented in the combinatory logic, it immediately follows that they can be represented in the first-order classical predicate logic.  ...  Defining new predicate symbols We can use definitions in order to extend the language L(Σ) of theories with new predicate symbols.  ... 
doi:10.21146/2074-1472-2015-21-2-9-14 fatcat:u64xyelytvfxlfbpu77y7lrwta

Adaptive Fuzzy Logics for Contextual Hedge Interpretation

Stephan van der Waart van Gulik
2009 Journal of Logic, Language and Information  
The logics are all sound and complete with respect to the standard [0, 1]-semantics.  ...  As the logics are adaptive logics, they have a dynamic proof theory, cf. (Batens 2004; Batens 2007) . This enables them to deal with non-monotonic interpretation dynamics.  ...  Nixon is a Quaker 'in some definitional sense' because a definitional criterium associated with the predicate Quaker, i.e. the predicate Born-into-Quaker-Family, can be applied to Nixon.  ... 
doi:10.1007/s10849-009-9084-y fatcat:fx6im3xoz5afbfe7pnwsimtzda

On First-order Theories Which Can Be Represented by Definitions

V. I. Shalack
2016 Logical Investigations  
As we know all theorems of logic are true in the models with any number of elements. At the same time, many mathematical theories impose restrictions on size of their models.  ...  for a mathematical theory to be reducible to logic.  ...  These examples motivate us to find the general criterion of definability of the specific predicates with the help of predicate logic. Definition 1.  ... 
doi:10.21146/2074-1472-2016-22-1-125-135 fatcat:mhi4a3ccdza45bznq5xu6cjgtq

In Praise of Impredicativity: A Contribution to the Formalisation of Meta-Programming [article]

François Bry
2019 arXiv   pre-print
Logic, a conservative extension of first-order logic, which provides a simple formalisation of meta-programming.  ...  aims at overcoming this unsatisfactory situation by discussing the relevance of impredicativity to meta-programming, by revisiting former formalisations of meta-programming and by defining Reflective Predicate  ...  Endowed with, and modified by, the strong typing of a type theory, Frege's logic became classical predicate logic.  ... 
arXiv:1807.06051v3 fatcat:7b3yzhf5u5awngbvqndvarfbhm

Learnability of constrained logic programs [chapter]

Sašo Džeroski, Stephen Muggleton, Stuart Russell
1993 Lecture Notes in Computer Science  
The field of Inductive Logic Programming (ILP) is concerned with inducing logic programs from examples in the presence of background knowledge.  ...  More specifically, k-literal predicate definitions consisting of constrained, function-free, nonrecursive program clauses are polynomially PAC-learnable under arbitrary distributions.  ...  Acknowledgements The work reported in this paper is part of the ESPRIT BRA Project 6020 Inductive Logic Programming. Thanks to Luc De Raedt for his comments on the paper.  ... 
doi:10.1007/3-540-56602-3_148 fatcat:yjwrdw5hvjcbzo6fkspjq6dhcu

In Praise of Impredicativity: A Contribution to the Formalization of Meta-Programming

FRANÇOIS BRY
2019 Theory and Practice of Logic Programming  
Logic, a conservative extension of first-order logic, which provides a simple formalization of meta-programming.  ...  aims at overcoming this unsatisfactory situation by discussing the relevance of impredicativity to meta-programming, by revisiting former formalizations of meta-programming, and by defining Reflective Predicate  ...  Endowed with, and modified by, the strong typing of a type theory, Frege's logic became classical predicate logic.  ... 
doi:10.1017/s1471068419000024 fatcat:et7sxc5fjzaxzjelpgh3os4jxu

Differentiable Inductive Logic Programming in High-Dimensional Space [article]

Stanisław J. Purgał, David M. Cerna, Cezary Kaliszyk
2022 arXiv   pre-print
Synthesizing large logic programs through Inductive Logic Programming (ILP) typically requires intermediate definitions.  ...  However, cluttering the hypothesis space with intensional predicates often degrades performance.  ...  We assume familiarity with the basics of predicate logic and logic programming, see (Raedt 2008) .  ... 
arXiv:2208.06652v1 fatcat:llteibxvrjeolpn6zqrruu3yym

A Universal Relation Approach For Natural Query In Logic Database System

Harihodin Selamat
1992 Jurnal Teknologi  
The concept of predicate universal relation is introduced as an interface to bridge the natural query and the corresponding primitive logic query.  ...  Very litde effort has been put to the development of the user's query system to facilitate the naive users interacting with the database.  ...  Definition 3.9: Definition 3.10: A regular unary logic (RUL) programme P is a logic program satisfying the following syntactic rules.  ... 
doi:10.11113/jt.v20.1065 fatcat:xf552brvlzdhldxkyydwkiu34e

Page 14 of Ratio Vol. 1, Issue [page]

1957 Ratio  
That a predicate applies to one and only one thing can be expressed with purely logical means, namely thus: “There exists an x to which the predicate applies and  ...  (a predicate of predicates), namely such a predicate as applies to all those and only those predicates which are equinumerous with one to which it applies.  ... 

Mapping Objects to Persistent Predicates [article]

José E. Zalacain Llanes
2017 arXiv   pre-print
The proposed alternative consists in a correspondence of the Logic Programming predicates with an Object Oriented approach, where for each element of the Logic Programming one Object Oriented element makes  ...  predicates aspect.  ...  The predicates declared in a logic program with this approach; do not denote a behavior or activity visible externally.  ... 
arXiv:1705.00556v1 fatcat:3sym7kavqvg6hakkjlfqraxwqq

Separation logic and abstraction

Matthew Parkinson, Gavin Bierman
2005 Proceedings of the 32nd ACM SIGPLAN-SIGACT sysposium on Principles of programming languages - POPL '05  
We build on the formalism of separation logic and introduce the new notion of an abstract predicate and, more generally, abstract predicate families.  ...  As well as demonstrating the soundness of our proof system, we illustrate its utility with a series of examples.  ...  We define abstract predicate family definitions, Λ f , with the following syntax.  ... 
doi:10.1145/1040305.1040326 dblp:conf/popl/ParkinsonB05 fatcat:5upqke663naixktykflnibpbuq

Model Theories of Set Theories and Type Theory

Robert Murray Jones
2014 Open Journal of Philosophy  
In the first part, we review the historical background of a system of logic devised by Henry S. Leonard to allow for reasoning using existence as a predicate.  ...  In the third and final part, we develop proofs of some underlying results of his logic, using modern notation but retaining his axioms and rules of inference.  ...  He suggested it as a formal account of Quine's view that the singular existence predicate is universal. We are indebted to former students of Henry S.  ... 
doi:10.4236/ojpp.2014.41008 fatcat:rm5xn3wvcvbmhnsm4hhfiic3ty
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