Logic Journal of IGPL - current issue

A defeasible logic for modelling policy-based intentions and motivational attitudes

Governatori, G., Padmanabhan, V., Rotolo, A., Sattar, A. — 2009-05-24

In this paper we show how defeasible logic could formally account for the non-monotonic properties involved in motivational attitudes like intention and obligation. Usually, normal modal operators are used to represent such attitudes wherein classical logical consequence and the rule of necessitation comes into play, i.e., A/ A, that is from A derive A. This means that such formalisms are affected by the Logical Omniscience problem. We show that policy-based intentions exhibit non-monotonic behaviour which could be captured through a non-monotonic system like defeasible logic. To this end we outline a defeasible logic of intention that specifies how modalities can be introduced and manipulated in a non-monotonic setting without giving rise to the problem of logical omniscience. In a similar way we show how to add deontic modalities defeasibly and how to integrate them with other motivational attitudes like beliefs and goals. Finally we show that the basic aspect of the BOID architecture is captured by this extended framework.

On complete representations of algebras of logic

Khaled, M., Sayed-Ahmed, T. — 2009-05-24

We show that there exists an atomic polyadic equality algebra of dimension n that is elementary equivalent to a completely representable algebra, but its diagonal free reduct (obtained by deleting diagonals and substitutions) is not completely representable.

Algorithms for finding coalitions exploiting a new reciprocity condition

Boella, G., Sauro, L., van der Torre, L. — 2009-05-24

We introduce a reciprocity criterion for coalition formation among goal-directed agents, which we call the indecomposable do-ut-des property. It refines an older reciprocity property, called the do-ut-des or give-to-get property by considering the fact that agents prefer to form coalitions whose components cannot be formed independently. A formal description of this property is provided as well as an analysis of algorithms and their complexity. We provide an algorithm to decide whether a coalition has the desired property, and we show that the problem to verify whether a single coalition satisfies the property is tractable. Moreover, we provide an algorithm to search all the sub-coalitions of a given coalition satisfying the new property. Even if this problem is not computationally tractable, we show that in several cases, also the complexity of this problem may decrease considerably.

Logics for Qualitative Coalitional Games

Agotnes, T., Van Der Hoek, W., Wooldridge, M. — 2009-05-24

Qualitative Coalitional Games (QCGs) are a variant of coalitional games in which an agent's desires are represented as goals that are either satisfied or unsatisfied, and each choice available to a coalition is a set of goals, which would be jointly satisfied if the coalition made that choice. A coalition in a QCG will typically form in order to bring about a set of goals that will satisfy all members of the coalition. Our goal in this paper is to develop and study logics for reasoning about QCGs. We begin by introducing a logic for reasoning about "static" QCGs, where participants play a single game, and we then introduce and study Temporal QCGs (TQCGs), i.e., games in which a sequence of QCGs is played. In order to represent and reason about such games, we introduce a linear time temporal logic of QCGs, called L(TQCG). We give a complete axiomatisation of L(TQCG), use it to investigate the properties of TQCGs, identify its expressive power, establish its complexity, characterise classes of TQGCs with formulas from our logical language, and use it to formulate several (temporal) solution concepts for TQCGs.

Acknowledgements

2009-05-24