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Predicate Logic with Definitions
[article]

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. ...

##
###
THE HISTORICAL SYNTAX OF PHILOSOPHICAL LOGIC

2022
*
The European philosophical and historical discourse
*

The main attention is paid to two scientific revolutions in elementary subject-

doi:10.46340/ephd.2021.8.1.11
fatcat:axvznx7udjayxpv7nfxmc2ffia
*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*. ...##
###
Extending Classical Logic with Inductive Definitions
[article]

2000
*
arXiv
*
pre-print

The goal of this paper is to extend classical

arXiv:cs/0003019v1
fatcat:svyilctko5hprckbrzjvpcc7ee
*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 ...##
###
On the Definitional Embeddability of the Combinatory Logic Theory into the First-Order Predicate Calculus

2015
*
Logical Investigations
*

In this article we prove a theorem on the

doi:10.21146/2074-1472-2015-21-2-9-14
fatcat:u64xyelytvfxlfbpu77y7lrwta
*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. ...##
###
Adaptive Fuzzy Logics for Contextual Hedge Interpretation

2009
*
Journal of Logic, Language and Information
*

The

doi:10.1007/s10849-009-9084-y
fatcat:fx6im3xoz5afbfe7pnwsimtzda
*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. ...##
###
On First-order Theories Which Can Be Represented by Definitions

2016
*
Logical Investigations
*

As we know all theorems of

doi:10.21146/2074-1472-2016-22-1-125-135
fatcat:mhi4a3ccdza45bznq5xu6cjgtq
*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. ...##
###
In Praise of Impredicativity: A Contribution to the Formalisation of Meta-Programming
[article]

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*. ...

##
###
Learnability of constrained logic programs
[chapter]

1993
*
Lecture Notes in Computer Science
*

The field of Inductive

doi:10.1007/3-540-56602-3_148
fatcat:yjwrdw5hvjcbzo6fkspjq6dhcu
*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. ...##
###
In Praise of Impredicativity: A Contribution to the Formalization of Meta-Programming

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*. ...

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

2022
*
arXiv
*
pre-print

Synthesizing large

arXiv:2208.06652v1
fatcat:llteibxvrjeolpn6zqrruu3yym
*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) . ...##
###
A Universal Relation Approach For Natural Query In Logic Database System

1992
*
Jurnal Teknologi
*

The concept of

doi:10.11113/jt.v20.1065
fatcat:xf552brvlzdhldxkyydwkiu34e
*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. ...##
###
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]

2017
*
arXiv
*
pre-print

The proposed alternative consists in a correspondence of the

arXiv:1705.00556v1
fatcat:3sym7kavqvg6hakkjlfqraxwqq
*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. ...##
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Separation logic and abstraction

2005
*
Proceedings of the 32nd ACM SIGPLAN-SIGACT sysposium on Principles of programming languages - POPL '05
*

We build on the formalism of separation

doi:10.1145/1040305.1040326
dblp:conf/popl/ParkinsonB05
fatcat:5upqke663naixktykflnibpbuq
*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. ...##
###
Model Theories of Set Theories and Type Theory

2014
*
Open Journal of Philosophy
*

In the first part, we review the historical background of a system of

doi:10.4236/ojpp.2014.41008
fatcat:rm5xn3wvcvbmhnsm4hhfiic3ty
*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. ...
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