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Step-indexed kripke models over recursive worlds

2011
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Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '11
*

A recent line of work has identified a common solution to some of these challenges:

doi:10.1145/1926385.1926401
dblp:conf/popl/BirkedalRSSTY11
fatcat:lmkx6nkutjhtfbpw6xcwksp5ai
*Kripke**models**over**worlds*that are*recursively*defined in a category of metric spaces. ... Moreover, the method provides a high-level understanding of the essence of recent approaches based on*step**indexing*. ... at is the same as . 2 Observe that the natural*model*of types here is a*Kripke**model**over*a*recursively*-defined set of*worlds*. ...##
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Step-indexed kripke models over recursive worlds

2011
*
SIGPLAN notices
*

A recent line of work has identified a common solution to some of these challenges:

doi:10.1145/1925844.1926401
fatcat:2j33cl3unnbx5pxjrrwdqn5nci
*Kripke**models**over**worlds*that are*recursively*defined in a category of metric spaces. ... Moreover, the method provides a high-level understanding of the essence of recent approaches based on*step**indexing*. ... at is the same as . 2 Observe that the natural*model*of types here is a*Kripke**model**over*a*recursively*-defined set of*worlds*. ...##
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OUP accepted manuscript

2019
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Journal of Logic and Computation
*

This raises the question of whether every

doi:10.1093/logcom/exz028
fatcat:starp6pbvfhjvemvfmt36m7qya
*Kripke*complete,*recursively*enumerable predicate modal logic can be characterized by an elementary class of*Kripke*frames. ... formula, is*recursively*enumerable. ... ., w = w k , for some k > 1 (notice that the case w = w * is identical to k being the maximal*index*of a*world*in M), we define the sought*model*as follows. ...##
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Sequent Calculus in the Topos of Trees
[article]

2015
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arXiv
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pre-print

Birkedal et al

arXiv:1501.03293v2
fatcat:gjav5oyn3vbbnbo43xzx46o6yi
*modelled*this modality via the internal logic of the topos of trees. ... Nakano's "later" modality, inspired by Gödel-Löb provability logic, has been applied in type systems and program logics to capture guarded*recursion*. ... We regard the positive integers as*worlds*and functions x : 1 → Ω as truth values*over*these*worlds*, by considering x true at j iff x j = j. ...##
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Sequent Calculus in the Topos of Trees
[chapter]

2015
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Lecture Notes in Computer Science
*

As a logical connective, ⊲ was married to separation logic in [18] , then to higher-order separation logic in [2] , and to

doi:10.1007/978-3-662-46678-0_9
fatcat:hxn3oyxyf5dvzij4abuepbdrke
*step*-*indexed*logical relations for reasoning about programming languages with ... Nakano's "later" modality, inspired by Gödel-Löb provability logic, has been applied in type systems and program logics to capture guarded*recursion*. ... We regard the positive integers as*worlds*and functions x : 1 → Ω as truth values*over*these*worlds*, by considering x true at j iff x j = j. ...##
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Logic of subtyping

2006
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Theoretical Computer Science
*

We also consider logics S and S that incorporate into S mutually

doi:10.1016/j.tcs.2006.03.017
fatcat:whfco7nxdfctlch4npdqs66qrq
*recursive*types*over*arbitrary and well-founded universes correspondingly. ... We introduce new modal logical calculi that describe subtyping properties of Cartesian product and disjoint union type constructors as well as mutually*recursive*types defined using those type constructors ... Lemma 23 . 23 For any positive*recursion*, every -sound*Kripke**model*can be extended to a -sound grounded*Kripke**model*preserving relation on the existing*worlds*. ...##
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A very modal model of a modern, major, general type system

2007
*
SIGPLAN notices
*

We present a

doi:10.1145/1190215.1190235
fatcat:xipuoxv6crg3vaa2l6prx4ahai
*model*of*recursive*and impredicatively quantified types with mutable references. ... It is also simple, and reduces mainly to defining a*Kripke*semantics of the Gödel-Löb logic of provability. ... program safety,*models*induction*over*future*steps*,*models*type preservation, ! ...##
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Bisimulation-invariant PTIME and higher-dimensional μ-calculus

1999
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Theoretical Computer Science
*

Consider the class of all those properties of

doi:10.1016/s0304-3975(98)00314-4
fatcat:klwctsikb5fhpm45567db6vn6y
*worlds*in finite*Kripke*structures (or of states in finite transition systems), that are l recognizable in polynomial time, and l closed under bisimulation ... It is also shown that higher-dimensional p-calculus is undecidable for satisfiability in finite structures, and even Et-hard*over*general structures. ... For the standard semantics of ML, ML, and L,, one usually deals with*Kripke*structures ('%,a) in which one element is designated, one also speaks of*model*-*world*pairs: -a E A the distinguished*world*of ...##
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Undecidability and non-axiomatizability of modal many-valued logics
[article]

2022
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arXiv
*
pre-print

This family includes the global modal logics arising from

arXiv:2101.08767v2
fatcat:effdf4mpqfehlmrqcctjbutv2q
*Kripke*frames evaluated*over*the standard Lukasiewicz and Product algebras. ... In this work we study the decidability of a class of global modal logics arising from*Kripke*frames evaluated*over*certain residuated lattices, known in the literature as modal many-valued logics. ... The logics studied in this work are defined*over*valued*Kripke**models*:*Kripke*frames W, R enriched with a*world*-wise evaluation 1 of the formulas e : W × F m → A into some algebra A, and where , ✸ are ...##
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Logics of Kripke meta-models

2009
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Logic Journal of the IGPL
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In particular we show that refinement of logics preserves the effective finite

doi:10.1093/jigpal/jzp047
fatcat:q7zj246tb5blzfrsadzsaogmju
*model*property and decidability for a wide class of constituent logics. 2 Logics of*Kripke*meta-*models*of frames from K*indexed*... by clusters of F, where each F C is based on the cluster C ⊆ F (i.e., Thus, in a refinement, the*Kripke*structure of frames from the*indexed*family X is imposed on the clusters of the frame F, in addition ...*Kripke*frame of the*Kripke*signature R I , I ∩J =∅. The refinement of F by the*indexed*family of frames {F C DEFINITION 2.2. ...##
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On Kripke-style Semantics for the Provability Logic of Gödel's Proof Predicate with Quantifiers on Proofs

2005
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Journal of Logic and Computation
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*Kripke*-style semantics is suggested for the provability logic with quantifiers on proofs corresponding to the standard Gödel proof predicate. It is proved that the set of valid formulas is decidable. ... Suppose, for any σ ⊂ σ there is an algorithm to transform any sentence S

*over*σ (in the language LPqC ) into a propositional modal formula µ(S) such that for any

*world*w of any

*Kripke*

*model*one has w S ... Lemma 5.10 (Inductive

*step*for σ A ) Suppose that for all σ B such that σ B ⊂ σ A the set of true formulas

*over*σ B is decidable in every

*world*w. ...

##
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Model Checking Social Network Models

2017
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Electronic Proceedings in Theoretical Computer Science
*

*Kripke*

*models*are also sound w.r.t. ... SNMs; iii) We give a satisfaction-preserving encoding of SNMs into canonical

*Kripke*

*models*, and we also characterise which

*Kripke*

*models*may be translated into SNMs; iv) We show that, for SNMs, the

*model*... PPF has been specifically designed for privacy policies for real social networks, and that is why the language PPL and the underlying logic K BL are interpreted

*over*SNMs and not

*over*

*Kripke*

*models*(possible-

*worlds*...

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Model Checking BDI Logics over Finite-state Worlds

2019
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International Conference of the Italian Association for Artificial Intelligence
*

In this paper, we introduce the

dblp:conf/aiia/TorreP19
fatcat:agryolx2rvgbnnakv4nbgf6eny
*model*-checking problem of Ctl * bdi*over*finite-state*models*that are described by tuples of*Kripke*structures (one for each*world*) and where the BDI relations are captured ... We consider the logic Ctl * bdi that augments the branching-time logic Ctl * with the BDI modalities and adopt the possible-*world*semantics by Rao and Georgeff. ... For the*model*-checking problem we consider (1) a finite number of possible*worlds*each corresponding to the unrolling of a*Kripke*structure, and (2) each bdi relation defined by a finite automaton*over*...##
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Multimodal Separation Logic for Reasoning About Operational Semantics

2008
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Electronical Notes in Theoretical Computer Science
*

The final component of a traditional

doi:10.1016/j.entcs.2008.10.002
fatcat:vi5buoqlavcojmj3kp6toxq3vu
*Kripke**model*is a binary relation on*worlds*, R, called the accessibility relation. ...*Kripke*semantics in particular are a standard way to to*model*about these logics [19, 17] . ...##
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The impact of higher-order state and control effects on local relational reasoning

2010
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Proceedings of the 15th ACM SIGPLAN international conference on Functional programming - ICFP '10
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In this paper, we marry the aspirations of the semantic cube to the powerful proof method of

doi:10.1145/1863543.1863566
dblp:conf/icfp/DreyerNB10
fatcat:6tx5tvqr7fc4xcmsd4ojwhiksi
*step*-*indexed**Kripke*logical relations. ... Central to our story is the use of state transition systems to*model*the way in which properties of local state evolve*over*time. ...*Worlds*and Auxiliary Definitions HOS As described in Section 3, we employ a*step*-*indexed**Kripke*logical relation, which is a kind of possible-*worlds**model*. ...
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