Modeling dynamics of legal relations with dynamic logic

Abstract The fundamental relations in private law are claims and duties. These legal relations can be changed by agents with the appropriate legal powers. We use propositional dynamic logic and ideas about propositional control from the agency literature to formalize these changes in legal relations. Our models are sets of states with functions specifying atomic facts, agents' abilities to change atomic facts, legal relations between agents concerning changing atomic facts and agents' powers. We present a formal language that allows us to describe models and changes of models caused by two kinds of actions: actions that change atomic facts and actions that change legal relations. Next, we present a sound and complete calculus for this language. The paper demonstrates that the perspective on actions borrowed from computer science can be used to shed interesting light on the dynamics of legal relations

Action Emulation

The effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multi-agent models with update action models, now in widespread use. There is a natural extension of the definition of a bisimulation to action models. Surely enough, updating with bisimilar action models gives the same result (modulo bisimulation). But the converse turns out to be false: update models may have the same update effects without being bisimilar. We propose action emulation as a notion of equivalence more appropriate for action models, and generalizing standard bisimulation. It is proved that action emulation provides a full characterization of update effect. We first concentrate on the general case, and next focus on the important case of action models with propositional preconditions. Our notion of action emulation yields a simplification procedure for action models, and it gives designers of multi-agent systems a useful tool for comparing different ways of representing a particular communicative action

From soft harmonic phonons to fast relaxational dynamics in CH3_{3}NH3_{3}PbBr3_{3}

The lead-halide perovskites, including CH$_{3}$NH$_{3}$PbBr$_{3}$, are components in cost effective, highly efficient photovoltaics, where the interactions of the molecular cations with the inorganic framework are suggested to influence the electronic and ferroelectric properties. CH$_{3}$NH$_{3}$PbBr$_{3}$ undergoes a series of structural transitions associated with orientational order of the CH$_{3}$NH$_{3}$ (MA) molecular cation and tilting of the PbBr$_{3}$ host framework. We apply high-resolution neutron scattering to study the soft harmonic phonons associated with these transitions, and find a strong coupling between the PbBr$_{3}$ framework and the quasistatic CH$_{3}$NH$_{3}$ dynamics at low energy transfers. At higher energy transfers, we observe a PbBr$_{6}$ octahedra soft mode driving a transition at 150 K from bound molecular excitations at low temperatures to relatively fast relaxational excitations that extend up to $\sim$ 50-100 meV. We suggest that these temporally overdamped dynamics enables possible indirect band gap processes in these materials that are related to the enhanced photovoltaic properties.Comment: (main text - 5 pages, 4 figures; supplementary information - 3 pages, 3 figures

Action Emulation

The effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multi-agent models with update action models, now in widespread use. There is a natural extension of the definition of a bisimulation to action models. Surely enough, updating with bisimilar action models gives the same result (modulo bisimulation). But the converse turns out to be false: update models may have the same update effects without being bisimilar. We propose action emulation as a notion of equivalence more appropriate for action models, and generalizing standard bisimulation. It is proved that action emulation provides a full characterization of update effect. We first concentrate on the general case, and next focus on the important case of action models with propositional preconditions. Our notion of action emulation yields a simplification procedure for action models, and it gives designers of multi-agent systems a useful tool for comparing different ways of representing a particular communicative action

Epistemic Logic with Partial Dependency Operator

In this paper, we introduce $\textit{partial}$ dependency modality $\mathcal{D}$ into epistemic logic so as to reason about $\textit{partial}$ dependency relationship in Kripke models. The resulted dependence epistemic logic possesses decent expressivity and beautiful properties. Several interesting examples are provided, which highlight this logic's practical usage. The logic's bisimulation is then discussed, and we give a sound and strongly complete axiomatization for a sub-language of the logic

A Denotational Semantics for First-Order Logic

In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic. Additionally, by allowing an assignment of a non-ground term to a variable we introduce in this framework logical variables. The semantics combines a number of well-known ideas from the areas of semantics of imperative programming languages and logic programming. In the resulting computational view conjunction corresponds to sequential composition, disjunction to ``don't know'' nondeterminism, existential quantification to declaration of a local variable, and negation to the ``negation as finite failure'' rule. The soundness result shows correctness of the semantics with respect to the notion of truth. The proof resembles in some aspects the proof of the soundness of the SLDNF-resolution.Comment: 17 pages. Invited talk at the Computational Logic Conference (CL 2000). To appear in Springer-Verlag Lecture Notes in Computer Scienc