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A Dynamic Deontic Logic over Synchronous Actions
, 2010
"... We present a dynamic deontic logic for specifying and reasoning about complex contracts. The concepts that our contract logic CL captures are drawn from legal contracts, as we consider that these are more general and expressive that what is usually found in computer science (like in software contrac ..."
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We present a dynamic deontic logic for specifying and reasoning about complex contracts. The concepts that our contract logic CL captures are drawn from legal contracts, as we consider that these are more general and expressive that what is usually found in computer science (like in software contracts, web services specifications, or communication protocols). CL is intended to be used in specifying complex contracts found in computer science. This influences many of the design decisions behind CL. We adopt an ought-to-do approach to deontic logic and apply the deontic modalities exclusively over actions. The actions that we consider are not just basic atomic actions, as in standard multi-modal logics, but have a complex structure that extends the regular structure of the dynamic logic actions. We add to CL the dynamic logic modality so to be able to reason about what happens after an action is performed. CL incorporates the notions of contrary-to-duty and contrary-to-prohibition by explicitly attaching to the deontic modalities a reparation which is meant to be enforced in the case of violations. We prove results of decidability and tree model property for the CL logic, as well as specific properties for the modalities.
Concurrent Kleene Algebra and its Foundations <
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit:
Unification and Matching in Separable Theories⋆
"... Abstract. We study unification and matching in equational theories based on semirings, which include Kleene algebra and extensions with different forms of concurrency, constraint semirings, and synchronous ac-tions algebra. Generally the unification problems are undecidable in this setting, but diff ..."
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Abstract. We study unification and matching in equational theories based on semirings, which include Kleene algebra and extensions with different forms of concurrency, constraint semirings, and synchronous ac-tions algebra. Generally the unification problems are undecidable in this setting, but different undecidability proofs are required. On the other hand, the matching problems are decidable and a general pattern can be drawn. This pattern is developed into a matching algorithm, relying on a new way of combining non-disjoint theories, which we call stratification, and on a relaxation of the finite variant property, which we call separa-bility. Consequently, we believe that our algorithm and the notions that we introduce have an importance i) beyond theories based on semirings; ii) for other problems related to unification and matching. 1
Derivative Based Methods for Deciding SKA and SKAT
, 2014
"... Synchronous Kleene algebra (SKA) is a decidable framework that combines Kleene algebra (KA) with a synchrony model of concurrency. Elements of SKA can be seen as processes taking place within a fixed discrete time frame and that, at each time step, may execute one or more basic actions or then come ..."
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Synchronous Kleene algebra (SKA) is a decidable framework that combines Kleene algebra (KA) with a synchrony model of concurrency. Elements of SKA can be seen as processes taking place within a fixed discrete time frame and that, at each time step, may execute one or more basic actions or then come to a halt. The extension synchronous Kleene algebra with tests (SKAT) combines SKA with a boolean algebra. Both algebras were introduced by C. Prisicariu, who proved the completeness of SKA axioms, and thus decidability, through a Kleene theorem based on the classical Thompson ε-NFA construction. Using the notion of partial derivatives, we present a new decision procedure for SKA terms equivalence. The results are extended for SKAT considering automata with transitions labeled by boolean expressions instead of atoms. This work extends previous one done for KA and KAT, where derivative based methods have been used in feasible algorithms for testing terms equivalence.
