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Mechanised Modal Model Theory [chapter]

Yiming Xu, Michael Norrish
2020 Lecture Notes in Computer Science  
In this paper, we discuss the mechanisation of some fundamental propositional modal model theory.  ...  The focus on models is novel: previous work in mechanisations of modal logic have centered on proof systems and applications in model-checking.  ...  Introduction The theory of modal logic has long been a fruitful area when it comes to mechanisation.  ... 
doi:10.1007/978-3-030-51074-9_30 fatcat:qguhb43w45gsxi4nlg7pd5w2la

Page 6592 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
The finite model property is inherited by these modalized intuitionistic logics as by the earlier combinations.  ...  Fibring involves a jump function for each modal- ity in the semantics which associates with each possible world an actual world of another model.  ... 

Page 4934 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
For nonclassical logic theorem proving, we show that LDS is flex- ible and generic, and can be mechanised directly.  ...  The transformation process not only preserves satisfiability but also en- sures that any model of the transformed formula is a model of the original one.  ... 

Mechanising a Modal Logic for Value-Passing Agents in HOL

Monica Nesi
1997 Electronical Notes in Theoretical Computer Science  
The resulting proof environment allows one to formally verify modal properties of communicating agents, which are de ned over an in nite value domain.  ...  Current w ork is to complete the HOL mechanisation of the modal theory for the value-passing calculus.  ...  Given a -calculus agent P and a modal formula , the Automata Generator module of Pmc builds the nite -automaton aut (if it exists) associated to P and then the Model Checker module checks the truth of  ... 
doi:10.1016/s1571-0661(05)80682-6 fatcat:exekvfulgbf2rcs5vb6j6xrory

Contents and abstracts of the electronic notes in Theoretical Computer Science Vol. 5

1998 Theoretical Computer Science  
Monica Nesi Mechanising a modal logic for value>passing agents in HOL http://wwu.elsevier.nl/locate/entcs/volume5.html An extension of Hennessy-Milner logic to value-passing CCS is embedded in the HOL  ...  of the alternation-free modal pcalculus.  ...  For this logic we present a proof system for model checking sequential processes defined in the value-passing CCS.  ... 
doi:10.1016/s0304-3975(97)00248-x fatcat:sdn5br4hkvhjnowkexgso4rute

Special issue on 'Logical frameworks and metalanguages'

GÉRARD HUET
2003 Journal of functional programming  
Professional logicians such as Gödel and later Tarski studied mathematical models, consistency and completeness, computability and complexity issues, set theory and foundations, etc.  ...  Some others tried to capture common sense, and modeled the revision of beliefs with so-called nonmonotonic logics.  ...  Girard developed new models such as Coherent Spaces. A fine-grained analysis of substitution yielded a new theory of explicit substitutions.  ... 
doi:10.1017/s0956796802004549 fatcat:zkmf6ncdjnhbvfhmshmsevmvt4

Mechanised Reasoning and Model Generation for Extended Modal Logics [chapter]

Renate A. Schmidt, Ullrich Hustadt
2003 Lecture Notes in Computer Science  
We review and discuss the development of decision procedures for decidable extended modal logics and look at methods for automatically generating models.  ...  We focus on a class of extended modal logics very similar in spirit to propositional dynamic logic and closely related to description logics.  ...  Mechanising correspondence theory.  ... 
doi:10.1007/978-3-540-24615-2_3 fatcat:jypyr3tokzhh7erjlyu5faipsi

Machine-checked semantic session typing

Jonas Kastberg Hinrichsen, Daniël Louwrink, Robbert Krebbers, Jesper Bengtson
2021 Proceedings of the 10th ACM SIGPLAN International Conference on Certified Programs and Proofs  
We overcome these shortcomings with a semantic approach to binary asynchronous affine session types, by developing a logical relations model in Coq using the Iris program logic.  ...  This modality carves out the step-indexed subset of the Iris logic. The rules of the plainly modality can be found in https://gitlab.mpi-sws.org/iris/iris/-/blob/master/theories/bi/plainly.v.  ...  The definition and proof rules of the coreP modality can be found at https://gitlab.mpi-sws. org/iris/iris/-/blob/master/theories/bi/lib/core.v.  ... 
doi:10.1145/3437992.3439914 fatcat:ci7przzqtvas3ejlazfpnzwsx4

Page 4561 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews  
Schnoebelen, A model for recursive-parallel programs (12 pp. (electronic)); Monica Nesi, Mechanising a modal logic for value-passing agents in HOL (16 pp. (electronic)); D. B. Gurov, S.  ...  Kapron, A modal y-calculus and a proof system for value passing processes (15 pp. (electronic)).  ... 

π with leftovers: a mechanisation in Agda [article]

Uma Zalakain, Ornela Dardha
2021 arXiv   pre-print
Our formalisation is fully mechanised in about 1850 lines of Agda.  ...  We use leftover typing to define a type system for a resource-aware π-calculus, a process algebra used to model concurrent systems.  ...  We have fully mechanised all meta-theory and the details of a proof of subject reduction can be found in Appendix B.  ... 
arXiv:2005.05902v4 fatcat:bq5rz72qancbbowukn55tsg3vq

Quasi-Open Bisimilarity with Mismatch is Intuitionistic

Ross Horne, Ki Yung Ahn, Shang-wei Lin, Alwen Tiu
2018 Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '18  
Examples and soundness results are mechanised using the proof assistant Abella.  ...  quasi-open bisimilarity is canonical and robust -coinciding with open barbed bisimilarity (an objective notion of bisimilarity congruence) and characterised by an intuitionistic variant of an established modal  ...  Mechanisation of the modal logic Completeness (Theorem 3.3) is partly mechanised with a gap in establishing Proposition 3.5, which correspond to sateq_ ▶ L (and R ) and sateq_➩ L (and R ) in Fig. 4 .  ... 
doi:10.1145/3209108.3209125 dblp:conf/lics/HorneALT18 fatcat:q77ttsgahbgwzbccdjcyohnv7y

Modal Logics are Coalgebraic

C. Cirstea, A. Kurz, D. Pattinson, L. Schroder, Y. Venema
2009 Computer journal  
Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts.  ...  This paper substantiates the authors' firm belief that the systematic exploitation of this coalgebraic nature will not only have impact on the field of modal logic itself but also lead to significant progress  ...  mechanised reasoning tools.  ... 
doi:10.1093/comjnl/bxp004 fatcat:gpm47rtxanb5xaei7nq3z4pnea

Page 4234 of Mathematical Reviews Vol. , Issue 81J [page]

1981 Mathematical Reviews  
He suggests the following criteria: the logic should express important properties of programs, should have a good model theory and a good semantics and the proofs in the logic should be mechanisable.  ...  Properties of programs are expressed in DL by means of modal formulas <a)>P, where a is a program and P is a formula. For every a, <a) is treated here as a kind of modality.  ... 

Page 604 of Mathematical Reviews Vol. , Issue 94b [page]

1994 Mathematical Reviews  
94b:03006 On model theory for intuitionistic bounded arithmetic with ap- plications to independence results (27-47); P.  ...  Scott, Bounded linear logic: a modular approach to poly- nomial time computability (extended abstract) (195-209); Yuri Gurevich, On finite model theory (extended abstract) (211-219); H.  ... 

Exploring the benefits of a traveller clustering approach based on multimodality attitudes and behaviours

Juan David Rodriguez Cote, Marco Diana
2017 Transportation Research Procedia  
Future work will build on those results to inform a behavioural model that will better clarify the relationship between multimodality habits and attitudes and the maximum possible extent of modal diversion  ...  While psychographic segmentations have proven their utility for travel forecast and planning purposes, especially if jointly considered with an appropriate behavioural theory such as the Theory of Planned  ... 
doi:10.1016/j.trpro.2017.05.295 fatcat:jfndzpjrevgpthc3ylcfntf5ci
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