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Justification by Infinite Loops

2010
*
Notre Dame Journal of Formal Logic
*

In the present paper we demonstrate that the same holds if the

doi:10.1215/00294527-2010-025
fatcat:p3st52x4j5cktlxajos567wrti
*justification*takes the form of a closed*loop*. ... This suggests that*infinitism*sits more comfortably with a coherentist view of*justification*than with an approach in which*justification*is portrayed as a linear process. ... In Section 4 we extend our study to*loops*of*infinite*size. We demonstrate that*justification**by*an*infinite*linear chain is usually indistinguishable from*justification**by*an*infinite**loop*. ...##
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Loops and Networks
[chapter]

2017
*
Fading Foundations
*

We show that generally, i.e. in what we have called the usual class,

doi:10.1007/978-3-319-58295-5_8
fatcat:667z6mokzrfxrjigebuivvmbdu
*infinite**loops*yield the same value for the target as do*infinite*chains; it is only in the exceptional class that the values differ ... The first treats*loops*rather than chains. ... However, from the fact that a finite*loop*differs from an*infinite*'*loop*', it does not follow that an*infinite**loop*is in fact an*infinite*chain. ...##
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Pluralism in Probabilistic Justification
[chapter]

2012
*
Probabilities, Laws, and Structures
*

Thus it makes sense to say that a target proposition, E 0 , can be epistemically justified not only

doi:10.1007/978-94-007-3030-4_6
fatcat:35yrhoubzrf4npszvy3hyiaudq
*by*an*infinite*one-dimensional chain or an*infinite*one-dimensional*loop*, but also*by*an*infinite*network ... A target proposition, E 0 , can be probabilistically justified*by*a chain or*by*a*loop*, and both the chain and the*loop*can be finite or*infinite*. 2 Moreover, in each of these four cases the conditional ... Appendix When the special equality (16) does not hold, the quadratic iteration (15) can be put into canonical form*by*means of the substitution With this transformation, (15) becomes 9 where The conditional ...##
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Loop checking and negation

1993
*
The Journal of Logic Programming
*

*By*replacing in T every

*justification*J

*by*its corresponding J', we obtain a tree T". ... However, the (loopchecked) interpreter need not be effective: in general, traversing

*infinite*

*justifications*is required. ... Partial support

*by*Esprit BRA-project 3020 Integration is gratefully acknowledged. ...

##
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Exploiting Game Theory for Analysing Justifications
[article]

2020
*
arXiv
*
pre-print

In this paper, we continue the study of

arXiv:2008.01609v1
fatcat:tgknop7zefhatb3wpcrhr3ev2q
*justification*theory*by*means of three major contributions. The first is studying the relation between*justification*theory and game theory. ... The third contribution is establishing a precise criterion of when a semantics induced*by**justification*theory yields consistent results. ... If M is a set of*loops*, M * denotes the set of (finite) paths obtained*by*a finite iteration of*loops*in M; M ω denotes the set of*infinite*paths obtained*by**infinite*iterations of*loops*in M. ...##
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Justifications and a Reconstruction of Parity Game Solving Algorithms
[article]

2021
*
arXiv
*
pre-print

*By*carefully ordering Justify steps, we reconstruct three algorithms well known from the literature. ... Parity games are

*infinite*two-player games played on directed graphs. Parity game solvers are used in the domain of formal verification. ... The function starts its main

*loop*

*by*attracting nodes for level p. ...

##
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Exploiting Game Theory for Analysing Justifications

2020
*
Theory and Practice of Logic Programming
*

The third contribution is establishing a precise criterion of when a semantics induced

doi:10.1017/s1471068420000186
fatcat:7ivdncdeozh3dklfb364v7k5lu
*by**justification*theory yields consistent results. ... why a property holds (or does not hold) in a model.In this paper, we continue the study of*justification*theory*by*means of three major contributions. ... If M is a set of*loops*, M * denotes the set of (finite) paths obtained*by*a finite iteration of*loops*in M; M ω denotes the set of*infinite*paths obtained*by**infinite*iterations of*loops*in M. ...##
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Extensions to Justification Theory
[article]

2019
*
arXiv
*
pre-print

Knowledge representation languages covered

arXiv:1905.06184v1
fatcat:s2zlxc5suzbkziaaq5ilbdjf7a
*by**justification*theory include logic programs, argumentation frameworks, inductive definitions, and nested inductive and coinductive definitions. ... In addition,*justifications*are also used for implementation purposes. ... We can also view a*justification*as a partial function from F to subsets of F*by*mapping a defined fact to the body of the rule in the*justification*if it exists. ...##
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A Compact Linear Translation for Bounded Model Checking

2007
*
Electronical Notes in Theoretical Computer Science
*

A restriction function | k maps (k, l)

doi:10.1016/j.entcs.2006.12.020
fatcat:ia3mz56yozhdhg73c5afjiwsmm
*loop*paths and*infinite**loop*-case denotations to their finite representations. ... We call such*infinite*paths (k, l)*loop*paths. Similarly, a finite*loop*-case denotatioṅ a = a 0 , . . . , a k−1 where a i ∈ B represents the*infinite*denotation a 0 . . . a l−1 (a l . . . a k−1 ) ω . ... for the*loop*case and l = − for the prefix case. ...##
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Fractal Patterns in Reasoning

2012
*
Notre Dame Journal of Formal Logic
*

All three papers emphasize that a proposition can be justified

doi:10.1215/00294527-1626500
fatcat:c3ebdkhsfncspnaxodanb4na4m
*by*an*infinite*regress, on condition that epistemic*justification*is interpreted probabilistically. ... The first two papers showed this for one-dimensional chains and for one-dimensional*loops*of propositions, each proposition being justified probabilistically*by*its precursor. ... The matter becomes even more interesting if we replace the*infinite*onedimensional structure (a chain or a*loop*)*by*an*infinite*, many-dimensional probabilistic network. ...##
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Loop Quantization of the Schwarzschild Black Hole

2013
*
Physical Review Letters
*

We can construct explicitly the exact solutions of the physical Hilbert space annihilated

doi:10.1103/physrevlett.110.211301
pmid:23745855
fatcat:rmsz6tiirffixease5z5ypnaay
*by*all constraints. ... This allows the completion of the Dirac quantization procedure using*loop*quantum gravity techniques. ... until stopped*by*any other external force. ...##
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QUANTUM GRAVITY IN CYCLIC (EKPYROTIC) AND MULTIPLE (ANTHROPIC) UNIVERSES WITH STRINGS AND/OR LOOPS

2008
*
The Eleventh Marcel Grossmann Meeting
*

The anthropic principle can be studied

doi:10.1142/9789812834300_0482
fatcat:fo76hwhgjzht7cuu3x4ehq6x3i
*by*means of string theory [5] [6] [7] [8] . ... It is postulated that either string theory and /or*loop*quantum gravity might be able to substantiate these hypotheses. Recently, the cyclic or ekpyrotic model has been reported [1-2]. ... The anthropic principle can be studied*by*means of string theory [5] [6] [7] [8] . ...##
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Finite Reasons Without Foundations

2014
*
Metaphilosophy
*

A view of reasons that holds that the 'reason for' relation is constrained

doi:10.1111/meta.12078
fatcat:yh4z6ngou5az5ncwont6aq6a3i
*by*PAA and PAC can avoid an*infinite*regress if the 'reason for' relation is contextual. ... Moreover, such a view of reasons can maintain that skepticism is false*by*the maintaining that there is more to epistemic*justification*than what can be expressed in any reasoning session. ... What is problematic about circularity is the idea that a simple*loop*captures all there is to epistemic*justification*. ...##
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Justification by an Infinity of Conditional Probabilities

2009
*
Notre Dame Journal of Formal Logic
*

In this paper we show that the assumption invalidates some venerable attacks on

doi:10.1215/00294527-2009-005
fatcat:v3ardbrpobco3awzxda74jtcli
*infinitism*: once we accept that epistemic*justification*is gradual, an infinitist stance makes perfect sense. ... It is only without the assumption that*infinitism*runs into difficulties. ... A variant of the latter argument has recently been put forward*by*Gillet, who holds that an*infinite*regress of deferred*justification*cannot yield an unconditional, determinate*justification*for the target ...##
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On Nested Justification Systems (full version)
[article]

2022
*
arXiv
*
pre-print

Nested

arXiv:2205.04541v1
fatcat:bztwtgxhcnhwxf3b2a2e6hcgle
*justification*systems, first introduced*by*Denecker et al. (2015), allow for the composition of*justification*systems. ... Furthermore, we show how nested*justification*systems allow representing fixpoint definitions (Hou and Denecker 2009). ... So to eliminate x from the*justification*, we can replace this*loop*with the fact f . On the left side, w can be replaced*by*a and b. ...
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