Algebras for Agent Norm-Regulation

An abstract architecture for idealized multi-agent systems whose behaviour is regulated by normative systems is developed and discussed. Agent choices are determined partially by the preference ordering of possible states and partially by normative considerations: The agent chooses that act which leads to the best outcome of all permissible actions. If an action is non-permissible depends on if the result of performing that action leads to a state satisfying a condition which is forbidden, according to the norms regulating the multi-agent system. This idea is formalized by defining set-theoretic predicates characterizing multi-agent systems. The definition of the predicate uses decision theory, the Kanger-Lindahl theory of normative positions, and an algebraic representation of normative systems.Comment: 25 page

Private Information: Similarity as Compatibility

We investigate the continuity of equilibrium in differential information economies with a finite number of agents. In this setting, agents can make contingent contracts based on events that are commonly observed. With private information modelled as finite partitions of a compact and metrizable space of states of nature, we introduce a topology on information that takes into account the compatibility of information fields in assessing similarity between private information fields. This topology allows us to establish upper semicontinuity of the private core correspondence.Differential Information Economy, Asymmetric Information, Radner Equilibrium, Private Core, Topologies on Information.

An essay on msic-systems

A theory of many-sorted implicative conceptual systems (abbreviated msic-systems) is outlined. Examples of msic-systems include legal systems, normative systems, systems of rules and instructions, and systems expressing policies and various kinds of scientific theories. In computer science, msic-systems can be used in, for instance, legal information systems, decision support systems, and multi-agent systems. In this essay, msic-systems are approached from a logical and algebraic perspective aiming at clarifying their structure and developing effective methods for representing them. Of special interest are the most narrow links or joinings between different strata in a system, that is between subsystems of different sorts of concepts, and the intermediate concepts intervening between such strata. Special emphasis is put on normative systems, and the role that intermediate concepts play in such systems, with an eye on knowledge representation issues. In this essay, normative concepts are constructed out of descriptive concepts using operators based on the Kanger-Lindahl theory of normative positions. An abstract architecture for a norm-regulated multi-agent system is suggested, containing a scheme for how normative positions will restrict the set of actions that the agents are permitted to choose from

Analytic Controllability of Time-Dependent Quantum Control Systems

The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation in which the state moves in an infinite-dimensional Hilbert space, a drift term is present, and the operators driving the state evolution may be unbounded. However, considerations are restricted by the assumption that there exists an analytic domain, dense in the state space, on which solutions of the controlled Schrodinger equation may be expressed globally in exponential form. The issue of controllability then naturally focuses on the ability to steer the quantum state on a finite-dimensional submanifold of the unit sphere in Hilbert space -- and thus on analytic controllability. A relatively straightforward strategy allows the extension of Lie-algebraic conditions for strong analytic controllability derived earlier for the simpler, time-independent system in which the drift Hamiltonian and the interaction Hamiltonia have no intrinsic time dependence. Enlarging the state space by one dimension corresponding to the time variable, we construct an augmented control system that can be treated as time-independent. Methods developed by Kunita can then be implemented to establish controllability conditions for the one-dimension-reduced system defined by the original time-dependent Schrodinger control problem. The applicability of the resulting theorem is illustrated with selected examples.Comment: 13 page

Dynamic Łukasiewicz logic and its application to immune system

AbstractIt is introduced an immune dynamicn-valued Łukasiewicz logicID{\L }_nIDŁnon the base ofn-valued Łukasiewicz logic{\L }_nŁnand corresponding to it immune dynamic$$MV_n$$MVn-algebra ($$IDL_n$$IDLn-algebra),$$1< n < \omega$$1<n<ω, which are algebraic counterparts of the logic, that in turn represent two-sorted algebras$$(\mathcal {M}, \mathcal {R}, \Diamond )$$(M,R,◊)that combine the varieties of$$MV_n$$MVn-algebras$$\mathcal {M} = (M, \oplus , \odot , \sim , 0,1)$$M=(M,⊕,⊙,∼,0,1)and regular algebras$$\mathcal {R} = (R,\cup , ;, ^*)$$R=(R,∪,;,∗)into a single finitely axiomatized variety resemblingR-module with "scalar" multiplication$$\Diamond$$◊. Kripke semantics is developed for immune dynamic Łukasiewicz logicID{\L }_nIDŁnwith application in immune system