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Relational semantics of linear logic and higher-order model-checking [article]

Charles Grellois, Paul-André Melliès
2015 arXiv   pre-print
In this article, we develop a new and somewhat unexpected connection between higher-order model-checking and linear logic.  ...  ) in higher-order model-checking.  ...  Putting all together: relational semantics of linear logic and higher-model model-checking Once the connection between higher-order model-checking and indexed tensorial logic established in §4, there remains  ... 
arXiv:1501.04789v3 fatcat:4yd3ryhkpzgzfhpy52fctlmglq

Finitary semantics of linear logic and higher-order model-checking [article]

Charles Grellois, Paul-André Melliès
2015 arXiv   pre-print
In this paper, we explain how the connection between higher-order model-checking and linear logic recently exhibited by the authors leads to a new and conceptually enlightening proof of the selection problem  ...  Given a higher-order recursion scheme G, the finiteness of its interpretation in the model enables us to associate to any MSO formula phi a new higher-order recursion scheme G_phi resolving the selection  ...  This connection between higher-order model checking and linear logic leads to a coloring comonad on the relational semantics of linear logic, which we adapt here to the qualitative Scott semantics.  ... 
arXiv:1502.05147v2 fatcat:lseygm2skzcorilqj7s7o55n4m

An infinitary model of linear logic [article]

Charles Grellois, Paul-André Melliès
2015 arXiv   pre-print
We conclude the paper by sketching the connection between the resulting model of lambda-calculus with recursion and higher-order model-checking.  ...  In this paper, we construct an infinitary variant of the relational model of linear logic, where the exponential modality is interpreted as the set of finite or countable multisets.  ...  The present paper is part of a wider research project devoted to the relationship between linear logic, denotational semantics and higher-order model-checking.  ... 
arXiv:1411.4380v3 fatcat:lxj4n52rqbardkoji5747wv3c4

Indexed linear logic and higher-order model checking

Charles Grellois, Paul-André Melliès
2015 Electronic Proceedings in Theoretical Computer Science  
While this work is very preliminary and does not integrate key ingredients of higher-order model-checking like priorities, it reveals an interesting and promising connection between higher-order model-checking  ...  and linear logic.  ...  We hope that the bridge with linear logic will clarify the constructions of higher-order model checking and reveal the deep and beautiful semantic ideas underlying it.  ... 
doi:10.4204/eptcs.177.4 fatcat:76shpi2nn5ckphb4myagjd54b4

Automated techniques for higher-order program verification

Naoki KOBAYASHI, Luke ONG, David Van HORN
2013 Progress in Informatics  
Studies of game semantics have yielded compositional model checkers and automated program equivalence checkers for Algol-like programming languages, and studies of higher-order recursion schemes and pushdown  ...  The workshop also aimed for cross-fertilization of different techniques for higher-order program verification, such as game semantics, type theories, higher-order grammars and pushdown systems, control  ...  HORS model checking and logical relation Akihiko Tozawa (IBM Research, Tokyo) Let us recall the relation between type/semantic-based HORS model checking algorithm and Plotkin's logical relation, i.e.  ... 
doi:10.2201/niipi.2013.10.9 fatcat:xqfyvx6m25d4jcodwl373vlxlq

Page 803 of Mathematical Reviews Vol. , Issue 82b [page]

1982 Mathematical Reviews  
Kamp showed in his doctoral dissertation [“Tense logic and the theory of linear order”, Ph.D. Thesis, Univ.  ...  Let L be the language of the theory of linear order augmented by monadic predicates P,,---,P,,.  ... 

A Survey on Temporal Logics [article]

Savas Konur
2011 arXiv   pre-print
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability  ...  (or undecidability) results, expressiveness and proof systems.  ...  Although model checking is expensive in linear time logics (for example, it is exponential for LTL), model checking complexity of CTL is very efficient, which is linear in the size of model and formula  ... 
arXiv:1005.3199v3 fatcat:nogsv2iggvd5likbkrnmnzpsdu

PhD Abstracts

GRAHAM HUTTON
2015 Journal of functional programming  
The Journal of Functional Programming would like to change that!  ...  A dissertation is eligible if parts of it have or could have appeared in JFP, that is, if it is in the general area of functional programming. The abstracts are not reviewed.  ...  Driven by applications, fragments have been studied, algorithms developed and extensions proposed; the emerging theme is called higher-order model checking.  ... 
doi:10.1017/s0956796815000040 fatcat:g7yt23qxivevte45fkiqv6xwna

A survey on temporal logics for specifying and verifying real-time systems

Savas Konur
2013 Frontiers of Computer Science  
We give decidability, axiomatizability, expressiveness, model checking results for each logic analysed. We also provide a comparison of features of the temporal logics discussed.  ...  In this paper we analyse various temporal formalisms introduced for specification, including propositional/first-order linear temporal logics, branching temporal logics, interval temporal logics, real-time  ...  Some parts of this paper exists in [231] .  ... 
doi:10.1007/s11704-013-2195-2 fatcat:5lyaji5wnzbyfdmbxwzbxjosku

A Brief Survey of Quantum Programming Languages [chapter]

Peter Selinger
2004 Lecture Notes in Computer Science  
This article is a brief and subjective survey of quantum programming language research.  ...  A different approach to a semantics for higher-order quantum computation is given by Abramsky and Coecke [1] .  ...  Girard [8] recently defined a notion of quantum coherent spaces as a possible semantics for higher-order quantum computation.  ... 
doi:10.1007/978-3-540-24754-8_1 fatcat:27yiduvvkbeupkhxapnmm4ocem

Real-time and Probabilistic Temporal Logics: An Overview [article]

Savas Konur
2011 arXiv   pre-print
We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed.  ...  Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature.  ...  [11] proves that the model checking problem is polynomial. Real-Time Logic (RTL): RTL is a first-order temporal logic, introduced in [56] to reason about events and their relations.  ... 
arXiv:1005.3200v3 fatcat:xhrrcy26bzeehg7wqvjfikm26e

Page 1441 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
Our vehicle is a small higher-order imperative language, with operations for inter- active character I/O and based on ML syntax.  ...  to this property of programs.” 2000b:68144 68Q60 03B44 03B70 Bhat, Girish; Peled, Doron (1-BELL; Murray Hill, NJ) Adding partial orders to linear temporal logic.  ... 

Page 5210 of Mathematical Reviews Vol. , Issue 2002G [page]

2002 Mathematical Reviews  
(DK-ARHS-BR; Aarhus) Algebraic specifications, higher-order types and set-theoretic models. (English summary) Type and set theoretical foundations of computation. J.  ...  SCIENCE 5210 or using higher-order features.  ... 

Page 8274 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
We com- bine the ideas of loop checking and tabling to establish a linear tabulated resolution called TP-resolution.  ...  Two fundamental prop- erties of these constraints are that they have an execution model and algebraic semantics. The model theory is based on temporal order-sorted algebras with predicates.  ... 

Quantification in frame semantics with binders and nominals of hybrid logic

Laura Kallmeyer, Rainer Osswald, Sylvain Pogodalla
2017 Journal of Language Modelling  
We also show how the key ingredients of hybrid logic, nominals and binders, can be used to model semantic coercion, such as the one induced by the begin predicate.  ...  We use its hybrid logic extension in order to incorporate quantification and thereby allow for inference and reasoning.  ...  This logical formula is to be checked against the possible models, and the sentence is true w.r.t. a model in case this model satisfies the logical formula.  ... 
doi:10.15398/jlm.v5i2.147 fatcat:nxahfzs2mbetrirgpy5keii62e
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