We introduce and study the notion of j-monotonicity of RRand RRW -automata (special types of restarting automata without working symbols). We show that the j-monotonicity can be considered as a degree of non-context-freeness of languages recognized by RRW -automata and RR-automata. 1-monotonic RRW -automata recognize a subset of the class of context-free languages. For j > 1, the j-monotonic RR...

This paper deals with non-monotonic Choquet integral, a generalization of the regular Choquet integral. The discrete non-monotonic Choquet integral is considered under the viewpoint of aggregation. In particular we give an axiomatic characterization of the class of non-monotonic Choquet integrals.We show how the Shapley index, in contrast with the monotonic case, can assume positive values if t...

The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of regular languages is the maximal syntactic complexity of languages in that subclass, taken as a function of the state complexity n of these languages. We study the syntactic complexity of three subclasses of star-free languages. We find tight upper bounds for l...

The main objective of the paper is to study the locus of all core selection and aggregate monotonic point solutions of a TU-game: the aggregate-monotonic core. Furthermore, we characterize the class of games for which the core and the aggregate-monotonic core coincide. Finally, we introduce a new family of rules for TU-games which satisfy core selection and aggregate monotonicity.

Formal rules governing signed edges on causal directed acyclic graphs are described in this paper and it is shown how these rules can be useful in reasoning about causality. Specifically, the notions of a monotonic effect, a weak monotonic effect and a signed edge are introduced. Results are developed relating these monotonic effects and signed edges to the sign of the causal effect of an inter...

In this paper, we study two-player games played on infinite but monotonic game structures. We concentrate on coverability games, a natural subclass of reachability games in the context of monotonic game structures. On the negative side, we show that surprisingly, and contrary to the one-player case, coverability is undecidable on two-player monotonic game structures. On the positive side, we id...

This paper presents two results about preference domain conditions that deepen our understanding of anonymous and monotonic Arrovian social welfare functions (ASWFs). We characterize the class of anonymous and monotonic ASWFs on domains without Condorcet triples. This extends and generalizes an earlier characterization (as Generalized Majority Rules) by Moulin (Axioms of Cooperative Decision Ma...

The concept of local monotonicity appears in the study of the set of root signals of the median filter and provides a measure of the smoothness of a signal. The median filter is a suboptimal smoother under this measure of smoothness, since a filter pass does necessarily yield a locally monotonic output; even if a locally monotonic output does result, there is no guarantee that it will possess o...

We start by defining an approach to non-monotonic prob­ abilistic reasoning in terms of non-monotonic categorical reasoning. We identify a type of non-monotonic proba­ bilistic reasoning, akin to default inheritance, that seems to be commonly found in practice. We formulate this in terms of the Maximization of Conditional Independence (MCI), and identify a variety of applications for this sort ...

We present mechanisms for the creation of strategies by mixing behaviour-dependent and -independent tactics in multiissue negotiation. The traditional linear weighted combination of tactics may generate non-monotonic utilities over time even in the case of a monotonic series of opponent’s offers. The proposed methods guarantee monotonic utilities, which can improve negotiation outcomes in many ...