Many-Sorted Implicative Conceptual Systems

Abstract: A theory of many-sorted implicative conceptual systems (abbreviated msic-systems) is presented. 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 the thesis, msic-systems are studied 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. 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. Technical results inlude a characterization of an msic-system in terms of the most narrow joinings between different strata, characterization of the structure of the most narrow joinings between two strata, conditions for the extendability of intermediate concepts, and finally, a specification of the conditions such that the Boolean operations on intermediate concepts will result in intermediate concepts and characterization of most narrow joinings in terms of weakest grounds and strongest consequences.