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Involutions on Relational Program Calculi

I.M. Rewitzky, J.W. Sanders
2008 Scientific Annals of Computer Science  
relational model to one kind in the transformer model) carries over to relations.  ...  The standard Galois connection between the relational and predicate-transformer models of sequential programming (defined in terms of weakest precondition) confers a certain similarity between them.  ...  No Relational Involution In this section we establish that there is no function on R(X ) satisfying the minimum requirements of an involution-as exhibited by * on transformers.  ... 
doaj:93f23355303e4c27a88a7498112c909c fatcat:sihde3i6zve6nesn33h7pjiwyu

A Generalised Approach for Encoding and Reasoning with Qualitative Theories in Answer Set Programming

GEORGE BARYANNIS, ILIAS TACHMAZIDIS, SOTIRIS BATSAKIS, GRIGORIS ANTONIOU, MARIO ALVIANO, EMMANUEL PAPADAKIS
2020 Theory and Practice of Logic Programming  
as well as the interpretability of logic programs.  ...  A family of ASP encodings is proposed which can handle any qualitative calculus with binary relations.  ...  However, the vast majority of known qualitative calculi are not as restrictive and support one or both of the involution or identity law properties.  ... 
doi:10.1017/s1471068420000198 fatcat:gqqpwggpnzbktkr7bgmzexex4a

A Generalised Approach for Encoding and Reasoning with Qualitative Theories in Answer Set Programming [article]

George Baryannis, Ilias Tachmazidis, Sotiris Batsakis, Grigoris Antoniou, Mario Alviano, Emmanuel Papadakis
2020 arXiv   pre-print
as well as the interpretability of logic programs.  ...  A family of ASP encodings is proposed which can handle any qualitative calculus with binary relations.  ...  However, the vast majority of known qualitative calculi are not as restrictive and support one or both of the involution or identity law properties.  ... 
arXiv:2008.01519v1 fatcat:7axany7zevgnnitrqvp3ihjem4

Page 2417 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
These calculi dif- fer by their treatment of substitution. In this paper, we extend the 4o-calculi with a conditional rewriting relation, called cy.  ...  This relation coincides, on A-terms, with the classical 7-reduction of A- calculus.  ... 

Classical BI

James Brotherston, Cristiano Calcagno
2008 Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '09  
• Models of BBI are relational commutative monoids R, •, e (we assume • a partial function), where: R: a set of resources •: a way of (partially) combining resources e: the distinguished empty resource  ...  • Separation logic is based on a BBI-model of heaps. • Multiplicative formulas talk about resources r ∈ R: r |= * ⇔ r = e r |= F1 * F2 ⇔ r = r1 • r2 and r1 |= F1 and r2 |= F2 r |= F1 - * F2 ⇔ ∀r . r •  ...  . • Define composition +, involution − and empty portfolio e: (p 1 + p 2 )(x) = p 1 (x) + p 2 (x) (−p)(x) = −p(x) e(x) = 0 • P, +, e, − is an Abelian group, thus also a CBI-model.  ... 
doi:10.1145/1480881.1480923 dblp:conf/popl/BrotherstonC09 fatcat:llkksrajf5c55pjwfyf3xvxzcm

Page 7578 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
Equipped with the period-two lattice automorphism which maps each binary relation to its con- verse, Quord(A) becomes a lattice with involution.  ...  A quasiorder of a (partial) algebra A is a reflexive, transitive binary relation on A, which is a subalgebra of A”. The quasiorders of A form an algebraic lattice, Quord( A).  ... 

Shallow Linear Action Graphs and their Embeddings

James J. Leifer, Robin Milner
2002 Formal Aspects of Computing  
Action calculi, which generalise process calculi such as Petri nets, π-calculus and ambient calculus, have been presented in terms of action graphs.  ...  We here offer linear action graphs as a primitive basis for action calculi.  ...  A simple example arises even in sequential programming; a program context which makes one program variable an alias for another may be modelled naturally by a graph context with a link edge.  ... 
doi:10.1007/s001650200015 fatcat:dqilsz2kqrhubntw7ksilldpha

Inversion, Iteration, and the Art of Dual Wielding [article]

Robin Kaarsgaard
2019 arXiv   pre-print
Finally, we relate the results to applications in the design and semantics of reversible programming languages.  ...  Notably, such a structure guarantees the existence of fixed point adjoints, which we show are intimately related to the conjugates arising from a canonical involutive monoidal structure in the enrichment  ...  Theseus is based on the Π-family of reversible combinator calculi [27] , which bases itself on dagger traced symmetric monoidal categories augmented with a certain class of algebraically ω-compact functors  ... 
arXiv:1904.01679v1 fatcat:4w5vovhxcfcbppgd7vknc3yos4

Algebraic Properties of Qualitative Spatio-temporal Calculi [chapter]

Frank Dylla, Till Mossakowski, Thomas Schneider, Diedrich Wolter
2013 Lecture Notes in Computer Science  
Qualitative spatial and temporal reasoning is based on socalled qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms.  ...  We also analyze existing qualitative calculi and provide a classification involving different notions of relation algebra.  ...  Algebraic Properties of Existing Calculi In this section, we report on tests for algebraic properties we have performed on spatio-temporal calculi.  ... 
doi:10.1007/978-3-319-01790-7_28 fatcat:3jw2wvnm7jed3oesw2dbxfpom4

Dual-context calculi for modal logic

G. A. Kavvos
2017 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
A complementation function is an involution on variables.  ...  On the other hand, the results in this paper are also meant to provide a solid foundation for applications in programming languages.  ... 
doi:10.1109/lics.2017.8005089 dblp:conf/lics/Kavvos17 fatcat:ymf4zjbx5vgzdh56xdd32rpu7i

A structural approach to reversible computation

Samson Abramsky
2005 Theoretical Computer Science  
Most foundational work on reversible computing to date has focussed on simulations of low-level machine models. By contrast, we develop a more structural approach.  ...  We show how high-level functional programs can be mapped compositionally (i.e. in a syntax-directed fashion) into a simple kind of automata which are immediately seen to be reversible.  ...  Partial Involutions Note that f ∈ I ⇒ f op ∈ I, where f op is the relational converse of f . We say that f ∈ I is a partial involution if f op = f . We write P for the set of partial involutions.  ... 
doi:10.1016/j.tcs.2005.07.002 fatcat:u7yszl5r4ra6hlsgh7zfehfneu

Reversible effects as inverse arrows [article]

Chris Heunen, Robin Kaarsgaard, Martti Karvonen
2018 arXiv   pre-print
These semantics inform the design of functional reversible programs supporting side-effects.  ...  Whereas arrows are monoids in the category of profunctors, dagger arrows are involutive monoids in the category of profunctors, and inverse arrows satisfy certain additional properties.  ...  There are also various other models of reversible automata [25, 23] and combinator calculi [1, 18] . We are interested in models of reversibility suited to functional programming languages.  ... 
arXiv:1805.08605v1 fatcat:e2ykhowi7bgbfi7zwhlnyj43ni

All bicovariant differential calculuses on GLq(3,C) and SLq(3,C)

K Bresser
1995 Journal of Physics A: Mathematical and General  
Some calculi induce bicovariant differential calculi on SLq(3,C) and on real forms of GLq(3,C). For generic deformation parameter q there are six calculi on SLq(3,C), on SUq(3) there are only two.  ...  All bicovariant first order differential calculi on the quantum group GLq(3,C) are determined. There are two distinct one-parameter families of calculi.  ...  Dathe for a helpful remark on the structure of some Reduce programs.  ... 
doi:10.1088/0305-4470/28/9/015 fatcat:tlxhwcscmndnvmyrpghwtagzsi

The geometry of the quantum Euclidean space

Gaetano Fiore, John Madore
2000 Journal of Geometry and Physics  
For each of its two SO_q(3)-covariant differential calculi we find its metric, the corresponding frame and two torsion-free covariant derivatives that are metric compatible up to a conformal factor and  ...  Acknowledgements One of the authors (JM) would like to thank J. Wess for his hospitality and the Max-Planck-Institut für Physik in Müchen for financial support.  ...  The commutation relations among the ξ i and theξ i are the same relations (4.6) and (4.44) found in Section 4 for the analogous elements in the conjugate calculi, whereas the cross relations are ξ iξ j  ... 
doi:10.1016/s0393-0440(99)00054-6 fatcat:fw6tk7etp5ekznb54mcgemahlq

Clausal Proofs and Discontinuity

GLYN MORRILL
1995 Logic Journal of the IGPL  
We consider the task of theorem proving in Lambek calculi and their generalisation to'multimodal residuation calculi'.  ...  A suitable uni cation strategy is obtained for calculi of discontinuity by normalisation of the ground goal term followed by recursive descent and redex pattern matching on the head term.  ...  Acknowledgements I thank Michael Moortgat and Dick Oehrle for comments on this work.  ... 
doi:10.1093/jigpal/3.2-3.403 fatcat:dd2uscjnobhgjajrwi4otegciy
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