Corpus ID: 38189382

Binary Multirelations

@article{Furusawa2015BinaryM,
  title={Binary Multirelations},
  author={H. Furusawa and G. Struth},
  journal={Arch. Formal Proofs},
  year={2015},
  volume={2015}
}
Binary multirelations associate elements of a set with its subsets; hence they are binary relations of type A × 2. Applications include alternating automata, models and logics for games, program semantics with dual demonic and angelic nondeterministic choices and concurrent dynamic logics. This proof document supports an arXiv article that formalises the basic algebra of multirelations and proposes axiom systems for them, ranging from weak bi-monoids to weak bi-quantales. 
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References

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TLDR
This work proposes axiom systems for multirelations in contexts ranging from bi-monoids to bi-quantales and under the operations of union, intersection, sequential, and parallel composition, as well as finite and infinite iteration. Expand
Concurrent Dynamic Algebra
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Algebraic variants of Peleg’s axioms are shown to be derivable in these algebras, and their soundness is proved relative to the multirelational model. Expand
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This paper investigates extensions of dynamic logic tailored towards handling concurrent programs, with or without communication, and finds that both respects are dominated by the extent to which the capabilities of synchronization and (unbounded) counting are enabled in the system. Expand
Taming multirelations. CoRR, abs/1501
  • Taming multirelations. CoRR, abs/1501
  • 2015
lemma c6 : R · 1 π ⊆ 1 π by (clarsimp simp: mr-simp) Next we verify Lemma 3
  • lemma c6 : R · 1 π ⊆ 1 π by (clarsimp simp: mr-simp) Next we verify Lemma 3