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Infinitary Completeness in Ludics

2010
*
2010 25th Annual IEEE Symposium on Logic in Computer Science
*

*In*order to extend the

*completeness*theorem of the original

*ludics*to the

*infinitary*setting, we modify the notion of orthogonality by defining it via safety rather than termination of the interaction. ... Our work arises from studies on recursive types

*in*denotational and operational semantics, but is conceptually simpler, due to the purely logical setting of

*ludics*, the

*completeness*theorem, and use of ... PROOF SYSTEM AND FULL

*COMPLETENESS*

*In*this section we introduce an

*infinitary*(coinductive) proof system and show interactive

*completeness*. A. ...

##
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The Ackermann Award 2018

2018
*
Annual Conference for Computer Science Logic
*

The Ackermann Award is the EACSL Outstanding Dissertation Award for Logic

doi:10.4230/lipics.csl.2018.1
dblp:conf/csl/KozenS18
fatcat:enjy7e5ltvbarlumyxu5tzq2zy
*in*Computer Science. It is presented during the annual conference of the EACSL (CSL'xx). ... linear logic with fixed points*in**Ludics*, the thesis investigates*completeness*problems*in*more expressive logics and develops potential connections with ω-automata. ... By identifying new connections between*infinitary*proofs and automata theory (e.g., non-determinization of alternating parity automata), she has managed to obtain a new constructive*completeness*argument ...##
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An Infinitary Affine Lambda-Calculus Isomorphic to the Full Lambda-Calculus

2012
*
2012 27th Annual IEEE Symposium on Logic in Computer Science
*

of this space is shown to yield an

doi:10.1109/lics.2012.57
dblp:conf/lics/Mazza12
fatcat:ldqkg5sxyzb75lfgmanlhbwsl4
*infinitary*affine lambda-calculus, whose quotient under a suitable partial equivalence relation is exactly the full (non-affine) lambda-calculus. ... It is well known that the real numbers arise from the metric*completion*of the rational numbers, with the metric induced by the usual absolute value. ... For instance, Theorem 22 is false*in*KKSV's*infinitary*calculi, where*complete*developments do not always exist (the infinite family of redexes*in*the term I(I(I . . .)) mentioned above has no*complete*...##
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Infinitary Classical Logic: Recursive Equations and Interactive Semantics

2014
*
Electronic Proceedings in Theoretical Computer Science
*

*In*this paper, we present an interactive semantics for derivations

*in*an

*infinitary*extension of classical logic. ... We show that

*in*our setting every recursive formula equation has a unique solution. As for derivations, we use an

*infinitary*variant of Tait-calculus to derive sequents. ... The motivation for introducing our semantics comes from our interest

*in*extending the

*completeness*theorem of

*ludics*[5] to logics which are not necessarily polarized fragments of linear logic. ...

##
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On the Meaning of Focalization
[chapter]

2011
*
Lecture Notes in Computer Science
*

*In*this paper, we use Girard's

*Ludics*to analyze focalization, a fundamental property of linear logic. ...

*In*particular, our study of Focalization

*in*

*Ludics*was primarily motivated by the concluding remarks of the third author's paper on Computational

*Ludics*[17] where focalization on data designs was conjectured ...

*Ludics*

*in*three pages Syntax. ...

##
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On the meaning of logical completeness

2010
*
Logical Methods in Computer Science
*

Goedel's

doi:10.2168/lmcs-6(4:11)2010
fatcat:hoy3cxrdtnaylnew6zr562bghu
*completeness*theorem is concerned with provability, while Girard's theorem*in**ludics*(as well as full*completeness*theorems*in*game semantics) are concerned with proofs. ... Compared with proofs of full*completeness**in*game semantics, ours exhibits a striking similarity with proofs of Goedel's*completeness*,*in*that it explicitly constructs a countermodel essentially using ...*In*particular,*infinitary*designs are included*in*our syntax, just as*in*the original*ludics*[21] . ...##
###
On the Meaning of Logical Completeness
[chapter]

2009
*
Lecture Notes in Computer Science
*

Gödel's

doi:10.1007/978-3-642-02273-9_6
fatcat:6k4dx42s6rexhj5v5gsstxlslu
*completeness*theorem is concerned with provability, while Girard's theorem*in**ludics*(as well as full*completeness*theorems*in*game semantics) are concerned with proofs. ... Compared with proofs of full*completeness**in*game semantics, ours exhibits a striking similarity with proofs of Gödel's*completeness*,*in*that it explicitly constructs a countermodel essentially using König's ...*In*particular,*infinitary*designs are included*in*our syntax, just as*in*the original*ludics*[21] . ...##
###
Infinitary λ-Calculi from a Linear Perspective (Long Version)
[article]

2016
*
arXiv
*
pre-print

Interestingly, it enjoys confluence, contrarily to what happens

arXiv:1604.08248v1
fatcat:wykju4emo5azna5iywpvds536y
*in*ordinary*infinitary*λ-calculi. ... We introduce a linear*infinitary*λ-calculus, called ℓΛ_∞,*in*which two exponential modalities are available, the first one being the usual, finitary one, the other being the only construct interpreted ...*In*all the obtained calculi, however, many of the properties one expects are not true: the*Complete*Developments Theorem (i.e. the*infinitary*analogue of the Finite*Complete*Theorem [4] ) does not hold ...##
###
Infinitary Lambda Calculi from a Linear Perspective

2016
*
Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16
*

Interestingly, it enjoys confluence, contrarily to what happens

doi:10.1145/2933575.2934505
dblp:conf/lics/Lago16
fatcat:om7mpkcnkzf2zcypjjpyukthgm
*in*ordinary*infinitary*λ-calculi. ... We introduce a linear*infinitary*λ-calculus, called Λ∞,*in*which two exponential modalities are available, the first one being the usual, finitary one, the other being the only construct interpreted coinductively ...*In*all the obtained calculi, however, many of the properties one expects are not true: the*Complete*Developments Theorem (i.e. the*infinitary*analogue of the Finite*Complete*Theorem [4] ) does not hold ...##
###
Infinitary Proof Theory: the Multiplicative Additive Case

2016
*
Annual Conference for Computer Science Logic
*

*ludics*' designs and proofs

*in*linear logic with fixed points [5]. ... To the best of our knowledge, while reversibility has since long been a key-ingredient

*in*

*completeness*arguments based on

*infinitary*proof systems, focalization has simply never been studied

*in*such settings ... Because

*infinitary*systems are easier to work with than the finitary proof systems (or axiomatizations) based on Kozen-Park (co)induction schemes, they are often found

*in*

*completeness*arguments for such ...

##
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Non-linearity as the Metric Completion of Linearity
[chapter]

2013
*
Lecture Notes in Computer Science
*

., lambda-terms

doi:10.1007/978-3-642-38946-7_3
fatcat:nxjfhz2hmfe6dczq3rwkmn644y
*in*which abstractions bind variables appearing at most once. ... We summarize some recent results showing how the lambdacalculus may be obtained by considering the metric*completion*(with respect to a suitable notion of distance) of a space of affine lambda-terms, i.e ... Roughly speaking, we take objects which are very much related to the designs of Girard's*ludics*[13] , introduce a metric*completely*analogous to the one given here, and construct the model*in*the*completed*...##
###
From Focalization of Logic to the Logic of Focalization

2010
*
Electronical Notes in Theoretical Computer Science
*

The aim of the present paper is to give a more abstract account on focalization

doi:10.1016/j.entcs.2010.08.010
fatcat:knwkldyquzhzdeymgefo42q3ne
*in*the framework of*ludics*. ... Andreoli originally discovered focalization as a concrete proof search strategy*in*proof theory of linear logic, putting to the foreground the role of polarity*in*logic. ... Logical behaviours are described*in*Section 6 together with internal*completeness*. Finally, we*complete*our study*in*Section 7 providing a*ludics*account of focalization. ...##
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Computational ludics

2011
*
Theoretical Computer Science
*

The acceptance relation between machines and words, a basic concept

doi:10.1016/j.tcs.2010.12.026
fatcat:gtwfqbwzezeqpmcqlfpbmadmia
*in*computability theory, is well expressed*in**ludics*by the orthogonality relation between designs. ... We finally describe a way of defining data sets by means of logical connectives, where the internal*completeness*theorem plays an essential role. ... The designs of*ludics*extend the lambda terms*in*this well-behaved fragment*in*several ways. First, designs can be*infinitary*. ...##
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Jumbo λ-Calculus
[chapter]

2006
*
Lecture Notes in Computer Science
*

Firstly, we show that the jumbo lambda-calculus provides a "

doi:10.1007/11787006_38
fatcat:jkkpbktghjckvkiepmgzkweeca
*complete*" range of connectives,*in*the sense of including every possible connective that, within the beta-eta theory, possesses a reversible ... Secondly,*in*the presence of effects, we show that there is no decomposition of jumbo connectives into non-jumbo ones that is valid*in*both call-by-value and call-by-name. ... But how many connectives must we include to obtain a "*complete*" range? ...##
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Imperative Programs as Proofs via Game Semantics

2011
*
2011 IEEE 26th Annual Symposium on Logic in Computer Science
*

*In*this paper we describe a logical counterpart to this extension,

*in*which proofs denote such strategies. ... We establish a full

*completeness*theorem for our logic, showing that every bounded strategy is the denotation of a proof. ... The rest of this section sketches the proof of this full

*completeness*result, and describes an extension to reify unbounded strategies as

*infinitary*core proofs. A. ...

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