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Recursion Schemes and Logical Reflection

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

In this paper, we prove that higher-order

doi:10.1109/lics.2010.40
dblp:conf/lics/BroadbentCOS10
fatcat:qpkit35y3fb6zc6xo5z4jjw2be
*recursion**schemes*are*reflective*w.r.t. both modal µ-calculus*and*monadic second order (MSO)*logic*. ... (Order-n*recursion**schemes*are equi-expressive with order-n CPDA for generating trees.) ... Let t be a Σ-labelled tree gererated by an order-n*recursion**scheme*S*and*let ϕ(x) be an MSOformula. (i) There is an algorithm that transforms (S, ϕ) to an order-n CPDA A such that L(A) = ||t|| ϕ . ...##
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Higher-order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties

2021
*
ACM Transactions on Computational Logic
*

This article studies the

doi:10.1145/3452917
fatcat:e7pseftknfcxzdwunjwrk6ofkm
*logical*properties of a very general class of infinite ranked trees, namely, those generated by higher-order*recursion**schemes*. ... We consider, for both monadic second-order*logic**and*modal -calculus, three main problems: model-checking,*logical**reflection*(a.k.a. global model-checking, that asks for a finite description of the set ... This*logic*is incomparable with MSO*logic*. He showed that model-checking is decidable*and*that both*reflection**and*selection hold for trees generated by*recursion**schemes*. ...##
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Higher-Order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties
[article]

2021
*
arXiv
*
pre-print

This paper studies the

arXiv:2010.06366v2
fatcat:htqiqtp3rfaxxattbycq4hlhsq
*logical*properties of a very general class of infinite ranked trees, namely those generated by higher-order*recursion**schemes*. ... We consider, for both monadic second-order*logic**and*modal mu-calculus, three main problems: model-checking,*logical**reflection*(aka global model-checking, that asks for a finite description of the set ... This*logic*is incomparable with MSO*logic*. He showed that model-checking is decidable*and*that both*reflection**and*selection hold for trees generated by*recursion**schemes*. ...##
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Page 7161 of Mathematical Reviews Vol. , Issue 95m
[page]

1995
*
Mathematical Reviews
*

So the

*logic*provides easy loop construction*and*allows one to obtain totally correct program*schemes*. In Nepeivoda calculi, Q actions are investigated inside a propositional*logic*framework. ... (I13-*reflecting*ordinals may be regarded as the*recursion*-theoretic analogue of weakly compact cardinals.) ...##
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Page 2857 of Mathematical Reviews Vol. , Issue 87f
[page]

1987
*
Mathematical Reviews
*

(S-UPPS) Definability

*and*forcing in E-*recursion*. Math. Scand. 57 (1985), no. 1, 5-28. Set*recursion*is obtained by adding an enumeration*scheme*to the*schemes*for the rudimentary functions. ... Dag Normann (Oslo) Slaman, Theodore A. (1-CHI) 87£:03133*Reflection**and*the priority method in E-*recursion*theory. ...##
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Relational semantics of linear logic and higher-order model-checking
[article]

2015
*
arXiv
*
pre-print

*recursion*

*schemes*. ... Our starting point is the observation that once embedded in the relational semantics of linear

*logic*, the Church encoding of any higher-order

*recursion*

*scheme*(HORS) comes together with a dual Church encoding ...

*recursion*

*scheme*G. ...

##
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Page 3225 of Mathematical Reviews Vol. , Issue 86g
[page]

1986
*
Mathematical Reviews
*

., 1976; MR 57 #18202], he shows how to define (

*and*find the least solution of) a system of*recursion*equations over the reducible*schemes*. ... In this very clearly written paper the author introduces new trans- formation rules for*recursive*program*schemes*. ...##
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Page 4412 of Mathematical Reviews Vol. , Issue 2001G
[page]

2001
*
Mathematical Reviews
*

The proofs are based on a characterization of IZ;

*and*IM; by means of*reflection*principles,*and*make use of modal prov- ability*logic*, more precisely the Gédel-Léb*logic*GL. ... The author studies parameter-free induction*schemes*IZ;*and*IIl; over Kalmar elementary arithmetic. He solves a problem of R. ...##
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Page 4964 of Mathematical Reviews Vol. , Issue 86k
[page]

1986
*
Mathematical Reviews
*

E-

*recursion*, or alternatively set-*recursion*, is defined by adding an enumeration*scheme*to the*schemes*for the rudimentary functions. ... “From the technical point of view, one can take this work 4s the theory of many-sorted, concurrent*and*(more significantly) second- order*recursion**schemes*. ...##
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Page 1181 of Mathematical Reviews Vol. 44, Issue 6
[page]

1972
*
Mathematical Reviews
*

*Reflecting*on this difference, the author introduces a

*recursion*

*scheme*for defining proper-class-valued mappings or operations by

*recursion*on the ordinal numbers. If we define Y.. ...

*Logic*Colloquium ’69 (Proc. Summer School

*and*Colloq., Manchester, 1969), pp. 67-76. North-Holland, Amster- dam, 1971. ...

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The Stable Models of a Predicate Logic Program

1994
*
The Journal of Logic Programming
*

Statement of problems

doi:10.1016/s0743-1066(14)80008-3
fatcat:ukrtmiky6ngvnasnonojeox4ye
*and*results In this paper we investigate*and*solve the problem classifying the Turing complexity of stable models of finite*and**recursive*predicate*logic*programs. ... Here we show that, up to a*recursive*1-1 coding, the set of all stable models of finite Predicate*Logic*Programs*and*the Π 0 1 classes (equivalently, the set of all infinite branches of*recursive*trees ... Acknowledgements This research was partially supported by NSF grants IRI 9012902, DMS-8902797, DMS-8702473*and*ARO contract DAAG629-85-C-0018. ...##
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Indexed linear logic and higher-order model checking

2015
*
Electronic Proceedings in Theoretical Computer Science
*

*and*linear

*logic*. ...

*recursion*

*scheme*G in an appropriate intersection type system associated to the automaton A. ... ,

*and*thus higher-order

*recursion*

*schemes*. ...

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Inductive Synthesis of Logic Programs by Composition of Combinatory Program Schemes
[chapter]

1999
*
Lecture Notes in Computer Science
*

The combinators comprise fold combinators for

doi:10.1007/3-540-48958-4_8
fatcat:ndvfpzjkb5gkxgzeujadumtr34
*recursion*on lists. ... Based on a variable-free combinatory form of definite clause*logic*programs we outline a methodology*and*supporting program environment CombInduce for inducing well-moded*logic*programs from examples. ... In [8] we prove that*logic*program*recursion*with the fold*schemes*suffices for expressing all partial*and*general*recursive*functions. ...##
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A Framework of Variant Logic Construction for Cellular Automata
[chapter]

2011
*
Cellular Automata - Innovative Modelling for Science and Engineering
*

All block matrices have

doi:10.5772/15400
fatcat:pazox26tj5hzbehif6qlqbxv64
*reflection*symmetric distributions via horizontal*and*vertical*reflection*symmetry distributions. ... There are 16 blocks in a comprised matrix in which thin lines separate different*recursive*images as blocks*and*each block under a function*recursively*, thick lines separate four 2x2 blocks*and*each 2x2 ...##
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Page 6651 of Mathematical Reviews Vol. , Issue 90K
[page]

1990
*
Mathematical Reviews
*

Another model, a natural

*recursion*-theoretic model, is constructed, in which only*recursive*operations from integers to integers are represented, even though the*logic*can be classical. ... The semantics is continuation-based,*and*so*reflects*the order in which expressions are evaluated. It provides a means by which lazy functional languages can be better understood.” ...
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