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Separation Logic with Linearly Compositional Inductive Predicates and Set Data Constraints
[article]

2018
*
arXiv
*
pre-print

We integrate DBS into separation

arXiv:1811.00699v1
fatcat:wmu53znpejfhto72wctn6hb724
*logic*with linearly compositional*inductive*predicates, obtaining a*logic*thereof where*set*data constraints of linear data structures can be specified. ... We show that the satisfiability of this*logic*is decidable. ... Linearly compositional SLID with*set*data constraints In this section, we introduce separation*logic*with linearly compositional*inductive*predicates*and**set*data constraints, denoted by SLID S LC rP s ...##
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TRUTHS, INDUCTIVE DEFINITIONS, AND KRIPKE-PLATEK SYSTEMS OVER SET THEORY

2018
*
Journal of Symbolic Logic (JSL)
*

AbstractIn this article we study the systems KF

doi:10.1017/jsl.2017.77
fatcat:lx5fovnfmnh53nwaih7rpl42ca
*and*VF of truth over*set*theory as well as related systems*and*compare them with the corresponding systems over arithmetic. ... Let L ∈ = {∈} be the language of firstorder*set*theory with the membership relation ∈ as its only non-*logical*symbol. ZF stands for Zermelo-Fraenkel*set*theory over L ∈ . ... We write I(L) for the*set*of L-*inductive*operator forms. ...##
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The Type Theoretic Interpretation of Constructive Set Theory: Inductive Definitions
[chapter]

1986
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Studies in Logic and the Foundations of Mathematics
*

We present a generalisation of the type-theoretic interpretation of constructive

doi:10.1016/s0049-237x(09)70683-4
fatcat:skeuy4t4cbd3nf6kpenyv5vmd4
*set*theory into Martin-Löf type theory. ... Date: October 12th, 2005. 2000 Mathematics Subject Classification. 03F25 (Relative consistency*and*interpretations), 03F50 (Metamathematics of constructive systems). ... The structural axiom schemes of CZF are Extensionality (1)*and**Set**Induction*(2) . ...##
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Discovering relational knowledge from two disjoint sets of literatures using inductive Logic Programming

2009
*
2009 IEEE Symposium on Computational Intelligence and Data Mining
*

In this paper, we report an application of an

doi:10.1109/cidm.2009.4938661
dblp:conf/cidm/ThaicharoenAGC09
fatcat:ilepo6mtirdhbd2ciwms6maafq
*Inductive**Logic*Programming (ILP), specifically the WARMR algorithm, to the field of literature-based discovery. ... The discovery approach is based on Swanson's discovery models where indirect connections between two disjoint*sets*of literatures A*and*C could be found through a*set*of common terms B extracted from A ... It could be typically attained by the use of*Inductive**Logic*Programming (ILP). ILP is an*inductive*machine learning technique at the intersection of machine learning*and**logic*programming [9] . ...##
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A Framework for Set-Oriented Computation in Inductive Logic Programming and Its Application in Generalizing Inverse Entailment
[chapter]

2005
*
Lecture Notes in Computer Science
*

We propose a new approach to

doi:10.1007/11536314_5
fatcat:ypdqsuvlevaobbysz4e3s3zm2e
*Inductive**Logic*Programming that systematically exploits caching*and*offers a number of advantages over current systems. ... It avoids redundant computation, is more amenable to the use of*set*-oriented generation*and*evaluation of hypotheses,*and*allows relational DBMS technology to be more easily applied to ILP systems. ... Introduction The goal of*Inductive**Logic*Programming (ILP) [1] is to autonomously learn first-order*logic*programs that model relational data. ...##
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Set Theory INC# ∞# Based on Infinitary Intuitionistic Logic with Restricted Modus Ponens Rule (Part.II) Hyper Inductive Definitions

2021
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Journal of Advances in Mathematics and Computer Science
*

In this paper intuitionistic

doi:10.9734/jamcs/2021/v36i430359
fatcat:egi7kk2mcjcdvh7zz35kzqhxsi
*set*theory INC# ∞# in infinitary*set*theoretical language is considered. External*induction*principle in nonstandard intuitionistic arithmetic were derived. ... Infinitary*and*Hyperinfinitary*Logics*Classical infinitary*logic*By a vocabulary, we mean a*set*L of constant symbols,*and*relation*and*operation symbols with finitely many argument places. ... The syntax of bivalent hyperinfinitary first-order*logics*L # ∞ # consists of a (ordered)*set*of sorts*and*a*set*of function*and*relation symbols, these latter together with the corresponding type, which ...##
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Set Theory INC# ∞# Based on Innitary Intuitionistic Logic with Restricted Modus Ponens Rule. Hyper Inductive Denitions. Application in Transcendental Number Theory. Generalized Lindemann-Weierstrass Theorem

2021
*
Journal of Advances in Mathematics and Computer Science
*

In this paper intuitionistic

doi:10.9734/jamcs/2021/v36i830394
fatcat:tqshlqhh25hyfjbl5hlbizpplu
*set*theory INC#∞# in infinitary*set*theoretical language is considered. External*induction*principle in nonstandard intuitionistic arithmetic were derived. ... Main results are: (i) number ee is transcendental; (ii) the both numbers e + π*and*e − π are irrational. ... Infinitary*Logic*Classical infinitary*logic*By a vocabulary, we mean a*set*L of constant symbols,*and*relation*and*operation symbols with finitely many argument places. ...##
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Definitions and notations
[chapter]

*
Logic, Induction and Sets
*

The words "cycle"

doi:10.1017/cbo9780511810282.003
fatcat:byjecik5mvezjp3xbhwiqy5mi4
*and*"path" mean simple cycle*and*simple path in a graph. ... Definitions*and*notations All the graphs under consideration are supposed to be without isolated vertices, multiple edges*and*loops. ... of construction of*sets*A*and*B). ...##
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Statistical Relational Learning: An Inductive Logic Programming Perspective
[chapter]

2005
*
Lecture Notes in Computer Science
*

shall start from

doi:10.1007/11564126_3
fatcat:vtoipejcmjcg7ow6piwy4eiyjm
*inductive**logic*programming*and*study how*inductive**logic*programming formalisms,*settings**and*techniques can be extended to deal with probabilistic issues. ...*settings*of the field of*inductive**logic*programming [3] . ... This work is part of the EU IST FET project APRIL II (Application of Probabilistic*Inductive**Logic*Programming II). ...##
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Statistical Relational Learning: An Inductive Logic Programming Perspective
[chapter]

2005
*
Lecture Notes in Computer Science
*

shall start from

doi:10.1007/11564096_3
fatcat:lwxyiiawqfbopjvgy5evuj2yzi
*inductive**logic*programming*and*study how*inductive**logic*programming formalisms,*settings**and*techniques can be extended to deal with probabilistic issues. ...*settings*of the field of*inductive**logic*programming [3] . ... This work is part of the EU IST FET project APRIL II (Application of Probabilistic*Inductive**Logic*Programming II). ...##
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Inductive equivalence in clausal logic and nonmonotonic logic programming

2010
*
Machine Learning
*

Conditions of

doi:10.1007/s10994-010-5189-4
fatcat:vxaidrnzg5brle4rxdazclg4pu
*inductive*equivalence change depending on the*logic*of representation languages*and*the*logic*of*induction*or*inductive**logic*programming (ILP). ...*and**logic*programming. ... abductive*and**inductive**logic*programming. ...##
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Inductive Equivalence of Logic Programs
[chapter]

2005
*
Lecture Notes in Computer Science
*

P1

doi:10.1007/11536314_19
fatcat:ytly42423rd5hbxn2wzr4x5n74
*and*P2 are weakly equivalent if they have the same declarative meaning. ... P1*and*P2 are strongly equivalent if P1∪R*and*P2∪R have the same declarative meaning for any program R. † These equivalence relations compare capabilities of deductive reasoning between programs. ... Two theories B1*and*B2 are*inductively*equivalent under a*logic*L if it holds that B1 ∪ H |= L E iff B2 ∪ H |= L E for any*set*E of examples*and*for any hypothesis H such that B1∪H*and*B2∪H are consistent.Results ...##
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Equivalence of Logic Programs Under Updates
[chapter]

2004
*
Lecture Notes in Computer Science
*

P1

doi:10.1007/978-3-540-30227-8_17
fatcat:jnclh6ctkjbfbgpkbdflkzbzci
*and*P2 are weakly equivalent if they have the same declarative meaning. ... P1*and*P2 are strongly equivalent if P1∪R*and*P2∪R have the same declarative meaning for any program R. † These equivalence relations compare capabilities of deductive reasoning between programs. ... Two theories B1*and*B2 are*inductively*equivalent under a*logic*L if it holds that B1 ∪ H |= L E iff B2 ∪ H |= L E for any*set*E of examples*and*for any hypothesis H such that B1∪H*and*B2∪H are consistent.Results ...##
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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 ... An abstract*inductive*definition (ID) D in this*logic*defines a*set*Def ined(D) of symbols, called the*set*of defined symbols, by a*set*of rules of the form p ← B where p is a defined atom*and*B a*set*...##
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Induction and Confirmation Theory: An Approach based on a Paraconsistent Nonmonotonic Logic

2011
*
Princípios
*

We pick up one of the most wide-spread nonmonotonic formalisms – default

doaj:fce609c5faa948e3b3a56efa667ff8e3
fatcat:kpcogg5l2vhqdkcbe76a4dbfyq
*logic*–*and*analyze to what extent*and*under what adjustments it could work as a*logic*of*induction*in the philosophical sense. ... This paper is an effort to realize*and*explore the connections that exist between nonmonotonic*logic**and*confirmation theory. ... A pseudo-*inductive**logic*of plausibility P is a pair <M*, *> where M* = < ⊱ ,> is a pseudo-*inductive*modal*logic**and**( ⊱ ) is a*set*of modal operators. ...
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