On Arbitrary Selection Strategies for Basic Superposition

For first-order Horn clauses without equality, resolution is complete with an arbitrary selection of a single literal in each clause [dN 96]. Here we extend this result to the case of clauses with equality for superposition-based inference systems. Our result is a generalization of the result given in [BG 01]. We answer their question about the completeness of a superposition-based system for general clauses with an arbitrary selection strategy, provided there exists a refutation without applications of the factoring inference rule.

Regular Derivations in Basic Superposition-Based Calculi

We prove the completeness of the regular strategy of derivations for superposition-based calculi. The regular strategy was pioneered by Kanger in [Kan63], who proposed that all equality inferences take place before all other steps in the proof. We show that the strategy is complete with the elimination of tautologies. The implication of our result is the completeness of non-standard selection functions by which in non-relational clauses only equality literals (and all of them) are selected.

A Model of Normative Power

A power describes the ability of an agent to act in some way. While this notion of power is critical in the context of organisational dynamics, and has been studied by others in this light, it must be constrained so as to be useful in any practical application. In particular, we are concerned with how power may be used by agents to govern the imposition and management of norms, and how agents may dynamically assign norms to other agents within a multi-agent system. We approach the problem by defining a syntax and semantics for powers governing the creation, deletion, or modification of norms within a system, which we refer to as normative powers. We then extend this basic model to accommodate more general powers that can modify other powers within the system, and describe how agents playing certain roles are able to apply powers, changing the system’s norms, and also the powers themselves. We examine how the powers found within a system may change as the status of norms change, and show how standard norm modification operations — such as the derogation, annulment and modification of norms— may be represented within our system.