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Algebra, Logic, Locality, Concurrency [chapter]

Peter W. O'Hearn
2011 Lecture Notes in Computer Science  
Rules of program logic, related to Hoare and Separation logics, flow at once from the algebraic axioms.  ...  others -on models and logics for concurrent processes [10, 6, 5] . The approach we are taking abstracts from syntax or particular models.  ...  Perhaps surprisingly, the algebra is seen to contain a general account of locality, which strictly generalizes the modular reasoning of Concurrent Separation Logic [5] .  ... 
doi:10.1007/978-3-642-25379-9_2 fatcat:5t7wapdh6jhgzcskoplmzuc7me

On Locality and the Exchange Law for Concurrent Processes [chapter]

C. A. R. Hoare, Akbar Hussain, Bernhard Möller, Peter W. O'Hearn, Rasmus Lerchedahl Petersen, Georg Struth
2011 Lecture Notes in Computer Science  
This paper studies algebraic models for concurrency, in light of recent work on Concurrent Kleene Algebra and Separation Logic.  ...  It establishes a strong connection between the Concurrency and Frame Rules of Separation Logic and a variant of the exchange law of Category Theory.  ...  Conclusion In this paper we have described links between a standard model of Concurrent Separation Logic, the Resource model, and algebraic models inspired by the recent Concurrent Kleene Algebra.  ... 
doi:10.1007/978-3-642-23217-6_17 fatcat:jk7iielqfrcxzppozglnkpmcrq

Precision and the Conjunction Rule in Concurrent Separation Logic

Alexey Gotsman, Josh Berdine, Byron Cook
2011 Electronical Notes in Theoretical Computer Science  
Concurrent separation logic is a Hoare logic for modular reasoning about concurrent heap-manipulating programs synchronising via locks.  ...  However, to date it has been an open question whether concurrent separation logic without the conjunction rule is sound when the restriction on resource invariants is dropped: all the published proofs  ...  lifted from functions on the underlying algebra without logical variables, we can extend concurrent separation logic with the following two proof rules for manipulating logical variables: I {P } C {Q}  ... 
doi:10.1016/j.entcs.2011.09.021 fatcat:y26e7zhqnvasdac6yuhzra3lde

Local Action and Abstract Separation Logic

Cristiano Calcagno, Peter W. O'Hearn, Hongseok Yang
2007 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)  
We also show that our conditions on local actions allow a general soundness proof for a separation logic for concurrency, interpreted over arbitrary separation algebras.  ...  We formulate local actions for a class of models called separation algebras, abstracting from the RAM and other specific concrete models used in work on separation logic.  ...  In particular, our treatment of concurrency shows that soundness of a concurrent version of separation logic relies only on locality properties of the primitive actions (basic commands) in the programming  ... 
doi:10.1109/lics.2007.30 dblp:conf/lics/CalcagnoOY07 fatcat:emmrf2hk6vg3vlsly3hfsl72rq

Models, Languages and Logics for Concurrent Distributed Systems: CEDISYS Workshop (Aarhus, 1991, May 21--24)

Uffe Engberg, Mogens Nielsen, Glynn Winskel
1992 DAIMI Report Series  
<p>The EEC Esprit Basic Research Action No 3011, Models, Languages and Logics for Con current Distributed Systems, CEDISYS, held its second workshop at Aarhus University in May, l991, following the successful  ...  Introduction The EEC Esprit Basic Research Action No 3011, Models, Languages and Logics for Concurrent Distributed Systems, CEDISYS, held its second workshop at Aarhus University in May, 1991, following  ...  The Observation Algebra of Spatial Histories, Ugo Montanari Abstract Observations can be described in a uniform way by introducing certain algebras called observation algebras: they lift to an algebraic  ... 
doi:10.7146/dpb.v21i392.6627 fatcat:z7kwdje4ebdkrmvhynaomrvqu4

Page 1190 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
Summary: “As part of an effort to give a ‘truly concurrent’ seman- tics to process algebra, we propose a framework of refinements of the failures model for CSP with concurrency, conflict and causal- ity  ...  The expected outcomes of this research are at least twofold: new insights in the design of concurrent languages and formalisms and a strong starting point for relating linear logic semantics to concurrency  ... 

A Repository for Tarski-Kleene Algebras

Walter Guttmann, Georg Struth, Tjark Weber
2011 Workshop on Automated Theory Engineering  
It covers variants of Kleene algebras and relation algebras with many of their models. Most theorems have been obtained by automated theorem proving within Isabelle.  ...  We have implemented a repository of algebraic structures and theorems in the theorem proving environment Isabelle/HOL.  ...  Concurrent Kleene Algebra: The development is discussed in more detail in Section 4. Propositional Hoare Logic: A more basic setting (than modal Kleene algebra) suffices to encode this logic.  ... 
dblp:conf/ate/GuttmannSW11 fatcat:gsxscqdtvfhtfkmx2ikwr6yfci

Communicating evolving algebras [chapter]

Paola Glavan, Dean Rosenzweig
1993 Lecture Notes in Computer Science  
As a basic tool we introduce a'modal' logic of transition rules and runs, which is, in the context of evolving algebras, just a de nitional extension of ordinary rst order logic.  ...  A notion of independence of rules and runs enables us to introduce a notion of (and notation for) concurrent runs, on which a logical theory of ('true') concurrency may be based.  ...  Happily, the needed fragment of the logic of evolving algebras turns out to be (a de nitional extension of) ordinary rst order logic.  ... 
doi:10.1007/3-540-56992-8_13 fatcat:qqz6m72povdhphksfomebpkc44

Page 3876 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
Gylys (Vilnius) 98f:68171 68Q55 68Q10 68Q60 Corradini, Flavio (I-LAQL-PM; Coppito); De Nicola, Rocco (I-FRNZ-I; Florence) Locality based semantics for process algebras.  ...  (English summary) Algebraic and logic programming (Aachen, 1996), 150-164, Lecture Notes in Comput. Sci., 1139, Springer, Berlin, 1996.  ... 

Models of Computation: A Tribute to Ugo Montanari's Vision [chapter]

Roberto Bruni, Vladimiro Sassone
2008 Lecture Notes in Computer Science  
To mention just three (in alphabetic order): algebraic techniques, concurrency theory, and unification mechanisms.  ...  Algebraic techniques. By algebraic techniques we refer broadly to the use of universal algebras and initial model semantics; of universal coalgebras and final semantics; and of bialgebras.  ...  The CHARM [31] , Concurrency and Hiding in an Abstract Rewriting Machine, is an abstract machine that combines algebraic techniques typical of process calculi with the experience in constraint logic programming  ... 
doi:10.1007/978-3-540-68679-8_31 fatcat:2ten745a2fe37ahbgbc4wukcsi

Page 2766 of Mathematical Reviews Vol. , Issue 2002D [page]

2002 Mathematical Reviews  
Another kind of non-interleaving treatment of concurrency is put forth in Chapter 15, Castellani’s ‘Process algebras with localities’.  ...  Modal logics, which extend classical logic with operators for pos- sibility and necessity, play an important role in filling out the semantic picture of process algebra.  ... 

Between quantum logic and concurrency

Luca Bernardinello, Carlo Ferigato, Lucia Pomello
2014 Electronic Proceedings in Theoretical Computer Science  
Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of events.  ...  The resulting logic is non-classical; we show that maximal antichains in a causal net are associated to Boolean (hence "classical") substructures of the overall quantum logic.  ...  We have already noted that a regular quantum logic can be seen as a family of partially overlapping Boolean algebras. In our context, these component Boolean algebras are atomic.  ... 
doi:10.4204/eptcs.158.6 fatcat:eix5fcaktjavllugu2apruq2mi

A Program Construction and Verification Tool for Separation Logic [chapter]

Brijesh Dongol, Victor B. F. Gomes, Georg Struth
2015 Lecture Notes in Computer Science  
An algebraic approach to the design of program construction and verification tools is applied to separation logic.  ...  These are linked to the separation algebra by soundness proofs.  ...  The third author would like to thank Tony Hoare, Peter O'Hearn and Matthew Parkinson for discussions on concurrent Kleene algebra and separation logic.  ... 
doi:10.1007/978-3-319-19797-5_7 fatcat:o4cbszfqz5cxvfaj3v5sk4q2l4

Page 5680 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
99h:68009 bility theory, and the impact of order (490-500); Leonid Libkin, 68 COMPUTER SCIENCE 99h:68011 68-06 68Q10 68T20 On counting logics and local properties (501-512); Phokion G. 4COTIC ’98: Second  ...  Workshop on Concurrent Constraint Kolaitis and Martin Otto, On the boundedness problem for two- variable first-order logic (513-524); Jean-Marie Le Bars, Frag- ments of existential second-order logic  ... 

Orthomodular algebraic lattices related to combinatorial posets

Luca Bernardinello, Lucia Pomello, Stefania Rombolà
2014 Italian Conference on Theoretical Computer Science  
Orthomodular lattices are families of partially overlapping Boolean algebras and have been studied as the algebraic model of quantum logic [7] .  ...  In [1] we have considered as model of non sequential processes a class of locally finite posets and shown that the closed subsets, obtained via a closure operator defined on the basis of concurrency,  ...  Hence, if A ⊂ B then B contains at least an element x concurrent with A. The orthomodular law is weaker than the distributive law. Orthocomplemented distributive lattices are called Boolean algebras.  ... 
dblp:conf/ictcs/BernardinelloPR14 fatcat:3wuka6uf55fctpfdj6p2v2os54
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